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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf,len=1811
+page_content='Prepared for submission to JHEP  Dynamic Radius Jet Clustering Algorithm  Biswarup Mukhopadhyayaa, Tousik Samuia, and Ritesh K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Singha  aDepartment of Physical Sciences, Indian Institute of Science Education and Research Kolkata,  Mohanpur, 741246, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  E-mail: biswarup@iiserkol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='in, tousiksamui@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='com,  ritesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='singh@iiserkol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='in  Abstract:  The study of standard QCD jets produced along with fat jets, which may  appear as a result of the decay of a heavy particle, has become an essential part of collider  studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Current jet clustering algorithms, which use a fixed radius parameter for the  formation of jets from the hadrons of an event, may be inadequate to capture the differing  radius features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In this work, we develop an alternative jet clustering algorithm that  allows the radius to vary dynamically based on local kinematics and distribution in the η-φ  plane inside each evolving jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We present the usefulness of this dynamic radius clustering  algorithm through two Standard Model processes, and thereafter illustrate it for a scenario  beyond the Standard Model at the 13 TeV LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='13074v1  [hep-ph]  30 Jan 2023  Contents  1  Introduction  1  2  Methodology  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1  Standard Sequential Recombination Algorithms  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  Our Proposal: Dynamic Radius Jet Clustering Algorithm  4  3  Application to Standard Model Processes  7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1  Illustration I: pp → tj process  8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  Illustration II: pp → V j Subprocess  15  4  Usefulness in BSM signals  19  5  Summary and Outlook  25  1  Introduction  The physics extraction capacity of any high-energy collider depends crucially on the han-  dling of coloured particles in various final states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These are produced as partons via ei-  ther short-distance interactions of quantum chromodynamics (QCD) or electroweak pro-  cesses [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The partons, however, hadronize through long-distance QCD effects which  are not calculable ab initio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' One rather uses semi-empirical methods to predict the prob-  ability that energetic partons will fragment into more low-energy partons and ultimately  form colour-neutral hadrons which are observable in the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Groups of closely spaced  hadrons with varied degrees of collimation form ‘jets’ whose identification, isolation, and  merger are predicted once more with the help of semi-empirical (and by no means uniquely  decided) algorithms called jet clustering algorithms [3–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The aim always remains to define  jets with such algorithms which most accurately elicit the short-distance physics underly-  ing the events that are studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' They thus constitute some of our most important tools in  the analysis of phenomena at colliders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In the context of the Large Hadron Collider (LHC), a widely used class of jet criteria is  based on so-called kt-type sequential recombination jet algorithms [7–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These algorithms  (briefly discussed in the next section) typically try to merge ‘neighbouring’ hadrons to  identify the group as a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The neighbourhood of a hadron is defined by a single radius  parameter R0 in the η-φ plane of the detector, which is used to quantify the radius (or size)  of a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is because the hadrons within R0 are merged to form a jet while the hadrons  outside R0 are not included in that jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The choices for the value of R0 in these algorithms  depend on the physics searches one is carrying out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' At the 13 TeV LHC, the typical choices  for R0 are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8 for a ‘narrow’ or a ‘fat’ jet, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' There are, in addition, jet  isolation criteria depending on whether one is trying to separate a jet from a hard lepton  or another hadronic jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, the sequential recombination algorithms generally do  not accommodate varying choices of radii on a jet-by-jet basis in a single event since they  – 1 –  have a single constant parameter that determines the radius of a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Separate classifiers  for a ‘narrow’ jet and a ‘fat’ jet in a single event in the current kt-type algorithms are thus  difficult to set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' An important improvement over the current fixed radius algorithms would  be to make them adapt the jet radii dynamically jet-by-jet in each event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We make an  attempt in this direction in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Our central idea of choosing the radius dynamically of a jet, especially for a boosted fat  jet, is based on the kinematics of the decay products of the initiating heavy particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' From  the theoretical side, the formation of boosted fat jet occurs due to the high collimation of  the on-shell decay products – and their showering and subsequent hadronization – of the  energetic and therefore boosted heavy particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is very different from the formation of  light quark- or gluon-initiated jets, whose collimation is primarily due to parton showering  and subsequent hadronization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the other hand, at the operational level, as per the  standard kt-type algorithms, the fat jets are formed in the same way as the regular ‘narrow’  jets, which are initiated by light quarks or gluons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, the kinematics of on-shell decay  products and their radiation pattern of a heavy particle is different from the showering of  energetic light quarks or gluons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, the internal structure of a fat jet is very different  from a narrow one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These internal structure has been used to tag different heavy and  light jets in the LHC context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For example, jet substructure (JSS) observable generalized  angularities λκ  β [14, 15] is used to distinguish between quark- and gluon-initiated jets [16–  26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The same variable was used in the classification among the narrow jet, fat W jet,  or boosted top jet [27–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Another important set of JSS observables, namely the energy  correlation functions (ECFs) [31, 32], was shown to be useful in classifying different types  of jets [29, 33–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The observable N-subjettiness (τN) [38, 39] has been used to find the  multi-pronged nature of light or heavy jets [40–65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These variables have also been used  extensively by the experimental collaborations at the 13 TeV LHC [66–68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These examples  try to exploit the energy distribution pattern inside a jet to distinguish a heavy object from  a QCD jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The common theme of these jet substructure variables is the utilization of the  ‘multi-pronged’ nature of the fat jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Due to this multi-pronged nature, one expects the  variance of inter-constituent distance ∆R of a fat jet to be significantly different compared  to the narrow QCD jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  This variance of a jet can be used to grow the radius of a  jet starting from an initial radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Earlier attempts to make the jet radius variable, albeit  with somewhat different motivations and formalisms, can be found in references [69, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' [69], the effective radius of a pseudojet during their evolution was taken to be inversely  proportional to the pT with a maximum cut-off on the radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Essentially, this algorithm  starts from a big effective radius and the size shrinks as a process of evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the  other hand, in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' [70], an expectation-maximization approach was taken for clustering  the hadrons into a pre-determined number of clusters (jets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Our approach, in this work, is  to modify the standard fixed radius kt-type algorithms to make the radius grow depending  on the local kinematics and distribution (in the η-φ plane) of the hadrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The rest of the article is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In section 2, we briefly outline the kt-type  sequential recombination algorithms followed by our improvement to the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We test  the efficacy of our algorithms on two SM processes and discuss them in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Section 4  deals with one application in the BSM scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We summarize and conclude in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 2 –  2  Methodology  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1  Standard Sequential Recombination Algorithms  At the operational level, a jet is constituted by a bunch of four-momenta obtained using  some clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Among various possible ways of grouping up the four-momenta  of an event, we need to choose those relevant to physics at the collider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' It is important  that the clustering algorithm should ensure infrared and collinear (IRC) safety, which, in  our context, can be defined in terms of the following conditions [7]:  Infrared (IR) safety: The output of the algorithm should not be affected by the intro-  duction of a four-momentum with p → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Collinear (C) safety: The output of the algorithm should not be affected by a collinear  splitting of any four-momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The algorithm that best takes care of the issue of IRC safety is known as kt-type sequential  recombination jet clustering algorithms [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We briefly outline these algorithms below1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  If an event consists of N final state particles, whose four-momenta are taken in a list as  an input of the kt-type algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The distance dij between the ith and jth four-momenta  and the distance diB between the ith and the beam are then defined as  dij = min  �  p2p  Ti, p2p  Tj  �  ∆R2  ij,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)  diB = p2p  TiR2  0,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2)  where R0 is the radius parameter of the algorithm, ∆Rij is the Euclidean distance between  the ith and jth four-momenta in the η-φ plane, and pTi is pT of ith four-momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  exponent p sets the weight factor to the Euclidean distance in the η-φ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The three  choices of p = 1, 0 and −1 correspond to the kt (KT) [8–10], Cambridge-Aachen (CA) [11,  12], and anti-kt (AK) [13] algorithms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The algorithm for combining nearby  four-momenta with respect to the above distance measures to form jets has the following  steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The distances dij for all the possible pairs and beam distances diB for all the  four-momenta are calculated first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The minimum among all the dij and diB’s is determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Step 3a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' If the minimum occurs at one of the i, j pairs, the corresponding ith and jth  four-momenta are merged to form a new four-momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The older ones, ith and  jth four-momenta are removed from the list and the newly merged one is added to  the list and goes back to Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Step 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the other hand, if the minimum distance is one of the diB, the ith four-  momenta is declared as a final jet, and it is removed from the list and goes back to  Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  1Here, we only discuss the inclusive algorithms in the LHC context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For other jet clustering algorithms,  please see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 3 –  Step 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The process is stopped once the list gets empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  This class of algorithms is seedless because the clustering of four-momenta to form a  jet does not start from a particular seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Rather, the algorithms try to merge the closest  pair first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' A group of hadrons is then declared as a jet when an appropriate size is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The essential difference among the three different algorithms, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' AK, CA, and KT is  that they give different weights to the Euclidean distance in the η-φ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This typically  sets some sort of seed to the clustering algorithms in the sense that it gives a preference  to a hadron around which four-momenta merge to give rise to a final jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the case of  the KT algorithm, it is the softer (in terms of pT ) constituent which merges first and then  the harder ones get attached to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As a result, the shape of the final jet may not be  circular in the η-φ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the other hand, in the AK algorithm, the hardest particle in  a neighbourhood becomes some sort of seed for the jet and the softer ones merge at a later  stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Hence the final jet looks circular in the η-φ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the CA algorithm, the merging  is purely angular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Among the three algorithms, the AK algorithm is the most popular one  owing to its circular shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Importantly, in the kt-type algorithms, there is a fixed radius  parameter R0, whose value dictates the typical size of all the jets in a particular event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We note that these algorithms are unable to capture the essential features of the events  where narrow and fat jets may simultaneously arise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In our proposed algorithm, we have  modified these algorithms to bring out the features of varying sizes of the jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  Our Proposal: Dynamic Radius Jet Clustering Algorithm  The usual kt-type algorithms take a fixed radius as an input parameter, and hence the  algorithms return all the jets to be of the same size (or narrower) in a single event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This  lack of dynamicity in choosing a radius can be overcome by setting the radius parameter  dynamically during the construction of each jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In any kt-type algorithm, the starting point is a list of N four-momenta of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We will refer to these as fundamental particles or, sometimes, fundamental four-momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The algorithm follows Steps 1 to 3b, as defined in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1, iteratively until the list  gets empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' At every iteration, the number of contents of the list gets reduced by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The reduction happens in two ways: (1) via the merger of two four-momenta, (2) via the  declaration of four-momentum as a final jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Thus at an intermediate iteration, the list  contains two different types of objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These two types of objects are (1) fundamental  four-momenta, and (2) composite four-momenta, generated through the merger of two or  more fundamental four-momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These composite objects evolve through iterations to  give rise to the final jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For our convenience, let us label these composite evolving objects  as pseudojets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We borrowed the name pseudojet from the PseudoJet class in the FastJet3  package [71], where all the types of four-momenta are called pseudojet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, we will  call them by different names: fundamental, pseudojet (composite or evolving), and jet (or  final jet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Our proposal is to change the constant nature of the radius parameter R0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2)  to a dynamic quantity depending on the distribution, in the η-φ plane, of the fundamental  objects inside each evolving pseudojet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, the modified distance measure for the  – 4 –  dynamic radius algorithm takes the form  dij = min  �  p2p  Ti, p2p  Tj  �  ∆R2  ij,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3)  diB = p2p  Ti R2  di,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4)  where Rdi is the dynamical radius parameter, defined as  Rdi = R0 + σi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5)  The constant R0 is an input parameter similar to the standard kt-type algorithm and it  is the starting point of the dynamical growth of the radius of an evolving jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For the ith  pseudojet, σi is calculated as  σ2  i =  �  a<b  pTa pTb ∆R2  ab  �  a<b  pTa pTb  −  �  �  �  �  �  a<b  pTa pTb ∆Rab  �  a<b  pTa pTb  �  �  �  �  2  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6)  where the summation indices a and b run over the fundamental constituents of the pseudo-  jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The modifier σi of the radius parameter in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6) is basically ‘pT -weighted’ standard  deviation of the distances between pairs of fundamental constituents of an evolving pseu-  dojet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In our proposal, this standard deviation σi is used to capture the size feature of an  evolving jet dynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For a single fundamental four-momentum, σi is taken to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The motivation for choosing the modifier of the radius parameter to be pT -weighted  standard deviation is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As more than one fundamental objects merge to become  a new pseudojet, it no longer represents a single point in the η-φ plane;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' it is a composite  object whose constituents are distributed in that plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The standard deviation σi for a  pseudojet i, defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6), provides a measure of its fuzziness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We want to incorporate  this fuzziness in the radius parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the measure of its fuzziness, we also want the  harder components to be more dominant than the softer ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Essentially, if the pseudojet  is dominated by a single pT -hard fundamental constituent or many extremely collimated  but similar pT objects, we do not want its radius to get increased further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is because,  in these scenarios, the final jet is expected to be a narrow jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  On the other hand, if  the pseudojet has more than one pT -hard fundamental constituents slightly separated, we  expect it to be a fat jet and therefore need an increment to its radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Both of these two  aspects are taken care of by the pT -weighted standard deviation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Thus, in our proposal, we first take a starting radius R0 to be our input parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The algorithm then calculates Rdi for each pseudojet, which at an intermediate state accu-  mulates some constituents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' At every iteration, the value of the dynamic radius parameter  is calculated as the sum of the starting radius R0 and the radius modifier σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In a nutshell,  the proposed algorithm starts from an initial radius R0 and grows its radius dynamically  using the information from the distribution of its constituents in the η − φ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In the proposed algorithm, the exponent p to the pT in the expressions of distance  measures dij and diB in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4) can take three possible values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We will call the  – 5 –  corresponding algorithms as dynamic radius AK (DR-AK), dynamic radius CA (DR-CA),  and dynamic radius KT (DR-KT) jet clustering algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The IRC safety of the algorithm through the definitions provided in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1 can  be approximately ensured in the radius modifier σ as well as in the final output of the  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' With the introduction of an additional four-momentum, say pq, the additive  contributions to the numerators and to the denominators of the two terms in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6) can  be generically written as pTq  �  a  �  pTa∆Rα  aq  �  (for the denominators, α = 0, and for the two  numerators α = 1 and 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Clearly, all the additive contributions go to zero as pTq → 0,  thereby ensuring the IR safety of the quantity σi for ith pseudojet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For the consideration of  IR safety of the algorithm, let us assume an extra particle of momentum pq is introduced  in an existing event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This extra particle actively participates in the clustering process only  by one of the three actions: (a) by getting merged to another fundamental particle, (b) by  getting recombined to a composite pseudojet, or (c) by getting declared as a singleton jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The action (a) does not change the value of σ or the four-momentum of the pseudojet after  the merger of the four-momentum with pq → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The same is true for the merger of pq via  action (b) since the merger of two fundamental four-momenta keeps the value of σ at zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  After the merger of this p → 0 four-momentum, both the radius modifier σ and the total  momentum remain unaffected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' After this merger, the rest of the clustering process does  not get affected, and hence the final output of the clustering algorithm remains unaffected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Furthermore, action (c) does not give rise to an extra jet whenever p → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  For the collinear safety, one can see that the radius modifier σ remains almost unaltered  when a four-momentum is split collinearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Let a four-momentum pq gets split into pr and  ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Any general term pTapTq∆Rα  aq then becomes pTa(pTr∆Rα  ar +pTs∆Rα  as).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the collinear  splitting limit, pTq = pTr + pTs, ∆Rar = ∆Ras = ∆Raq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Moreover, there will not be  any additional contribution due to the pr and ps combination except for the denominators  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6) since ∆Rrs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This ensures an approximate collinear safety of σi for any  ith pseudojet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the other hand, for the collinear safety of the algorithm, if any four-  momentum collinearly splits into two four-momenta, then the distance dij → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Hence,  these two collinearly split four-momenta get merged together at a very early stage;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' a feature  that is inherently present in the kt-type algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Other IRC safety features (due to pT -  dependent prefactors in the dij and diB definitions) of the standard kt-type algorithms will  be inherited by the dynamic radius algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We have implemented the method of dynamic radius jet clustering algorithm as a  FastJet3 plug-in [71, 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This package has many built-in data-types and functionalities  to optimize the implementation and computation of jet clustering algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In particu-  lar, we have used NNBase and NNH classes to help us keep track of the distance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  As required by these two classes, our dij measure is also symmetric in i and j indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  ClusterSequence class has then been used to merge two four-momenta and keep track of  the clustering sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The PseudoJet class has been used to store the four-momenta  information of all the initial, intermediate, and final jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The user info property of  PseudoJet data-type has been used to store the information related to the radius modifier  σi of the ith pseudojet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This way of implementation has at most N2 computational com-  – 6 –  plexity for an event of size N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The worst possible complexity arises when all the particles  in an event are merged to form a single jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Since this worst possibility does not generally  occur, we expect the computational expense to be less in a practical scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We note that  the standard kt-type algorithms also have N2 complexity via the basic implementation of  the FastJet algorithm [71, 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  One important point to note is that the equations for distance measures, defined in  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2), can be recast to in the radius parameter in the expression of dij rather than  in the expression of diB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' That is to say that the modified set of equations can be taken to  be  ˜  dij = min  �  p2p  Ti, p2p  Tj  � �∆Rij  R0  �2  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7)  ˜  diB = p2p  Ti  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8)  The standard sequential recombination algorithm yields identical results in both formalisms  since the radius is a constant parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, if this latter formalism is chosen to  incorporate dynamicity, the form of the dynamic radius parameter Rd will be different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The dynamic radius Rd, in this type of modification, will be dependent on both pseudojets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  One option would be to add the standard deviations σi and σj of the ith and jth pseudojets,  respectively, to the constant parameter R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This way of defining Rd ensures the symmetry  in i and j indices and, therefore, the implementation of the method via NNBase and NNH  as a FastJet3 plug-in can easily be performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In any case, the output of the algorithm  is modified according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8) will be different from that of the one considered in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We now are ready to apply our formalism to some simple SM processes and check how  it performs compared to the standard sequential recombination algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We discuss  this in the next section in connection with SM processes and consider its application to  BSM in the section after that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  3  Application to Standard Model Processes  We take the following two SM processes to illustrate the performance of our newly developed  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' pp → tj  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' pp → V j, (V = W or Z)  For both cases, we have generated parton-level events using MadGraph5 (MG5) [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We will  refer to these events as MG5 parton-level events and the final state partons in these events  as MG5 partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' A lower cut of 500 GeV on the pT of the jets has been imposed during the  generation of the MG5 parton-level events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This helps us in generating events with boosted  top or vector bosons at the parton-level, which then form fat jets after subsequent decays  and hadronization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  For the purpose of the following studies, only the hadronic decays  of top and W/Z are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We have then passed the MG5 parton-level events to  – 7 –  Pythia8 [74, 75] for showering and hadronization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The Monash 2013 Tune [76], the default  tune of Pythia8, has been used to take care of the simulations of underlying events and  multi-parton interactions in the proton-proton collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The output of Pythia8 has then  been transferred to FastJet3 for the formation of jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1  Illustration I: pp → tj process  The top quark, when highly boosted, results in a fat jet while the j yields a narrow jet after  the effects of showering and hadronization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In order to compare various jet properties be-  tween the dynamic radius and fixed radius algorithm, we run these two types of algorithms  on the same set of hadrons from each event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We first demonstrate how the dynamic radius  algorithms help in capturing the fat and narrow objects in a single event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This has been  demonstrated by depicting the hadrons and jets of an example event in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 1, where we  plotted, in the η-φ plane, the position of the hadrons in the event along with the high-pT  jets constructed out of these hadrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The sizes of the dots are kept proportional to √pT of  the hadrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The jets are represented by the unfilled black circles and the solid dots inside  the black circles comprise of the constituent hadrons of the jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The three panels on the  left show the jets for (a) AK, (c) CA, and (e) KT jet algorithms with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In all the  left panels, the algorithms return three high-pT jets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' one near (2,2) position and the other  two are near (0,5) position in the η-φ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' With the MG5 parton-level information, we  identified that the jet in (2,2) position is initiated by j while the two jets near the (0,5)  position is initiated by the decay products of the hard top quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Because of fixed radii  of the standard kt-type jet clustering algorithms, they could not capture all the hadrons  initiated by the decay products of the top quark inside a single jet;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' rather they have been  split into two different jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' A quick fix to this problem would be to increase the size of the  radius parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This prescription, however, ends up increasing the jet size unnecessarily,  for example at the (2,2) position where such increment is not required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This unnecessary  increase in the radius of a jet increases jet mass, especially in the high pile-up scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  One interesting option in such cases would be to choose the radius according to the need  of a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is precisely where the dynamic radius jet clustering algorithm is useful in  this type of scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This can be seen in the three panels on the right in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' There the  hadrons and the high-pT jets are drawn for dynamic radius jet clustering algorithms with  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The interesting point to note in all three right panels is that there are two jets  instead of three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The radius of the jet near the (0,5) position has been appropriately grown  to capture the full decay products of the top quark and their radiations while the radius  of the jet near the (2,2) position did not grow much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This desirable characteristic of a jet  algorithm would be beneficial for the studies of collider events, where narrow as well as fat  jets are expected to occur simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In all the panels, the radius of each black circle  is kept to be equal to the final radius Rd, as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5), of each individual jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  For the fixed radius jet algorithms, the final radius is essentially the fixed radius parameter  R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 1 gives an approximate idea of how the dynamic radius helps us in finding a fat jet  starting from a small radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Next, we show how often this dynamic radius jet algorithm  helps us in finding the fat jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In order to demonstrate that, we have employed the following  – 8 –  −4  −2  0  2  4  0  1  2  3  4  5  6  φ  pp → tj  AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (a)  Hadrons  −4  −2  0  2  4  0  1  2  3  4  5  6  φ  pp → tj  DR-AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (b)  Hadrons  −4  −2  0  2  4  0  1  2  3  4  5  6  φ  pp → tj  CA, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (c)  Hadrons  −4  −2  0  2  4  0  1  2  3  4  5  6  φ  pp → tj  DR-CA, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (d)  Hadrons  −4  −2  0  2  4  η  0  1  2  3  4  5  6  φ  pp → tj  KT, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (e)  Hadrons  −4  −2  0  2  4  η  0  1  2  3  4  5  6  φ  pp → tj  DR-KT, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (f)  Hadrons  Figure 1: Positions of final state hadrons and jets in the η-φ plane in an example event  for pp → tj process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The red dots represent the final state hadrons and their sizes are kept  proportional to √pT of the corresponding hadron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The unfilled circles represent the final  radius Rd of a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The teal coloured dots represent the constituents of the hard ‘narrow’  jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The green and blue (wherever applicable) dots represent the constituents of the fat  top jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The left panel, from top to bottom, is for (a) AK, (c) CA, and (e) KT algorithms  with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The right panel, from top to bottom, represents jets clustered using (b)  DR-AK, (d) DR-CA, and (f) DR-KT algorithms, respectively, with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 9 –  procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We first form the jets from the hadrons and choose only the high-pT (> 5 GeV)  jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We then tag the energetic jets, event by event, as reconstructed ‘top’ or reconstructed  ‘jet’ with the help of MG5 parton-level information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The events are classified into two  categories, as described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Category A1 consists of events satisfying the following conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  A jet should have mass in the range (150, 200) GeV and have ∆R(toptruth, jet) <  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This jet is identified as a reconstructed top jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We label these reconstructed  objects as ‘top (A1)’ in the subsequent discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  After the tagging of the top jet, another jet should have pT > 300 GeV and  should be within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 distance from the original jet as generated by MG5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These  jets are labelled as ‘jet (A1)’ in further discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Category A2 are the events which satisfy the following conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Two separate jets within 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='0 distance of the original top quark and having  an invariant mass between 150 and 200 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These two jets are tagged as  constituent jets of the reconstructed top jet, which is a combination of these  two constituents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These combinations are labelled as ‘top (A2)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Another jet having pT > 300 GeV and within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 radius from the original jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  This is labelled as ‘jet (A2)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In general, any inclusive kt-type clustering algorithm yields as output many soft jets  along with the hard ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The origin of these soft jets is primarily the soft radiation due  to underlying events and wide angle parton shower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These jets are expected in both the  category A1 and A2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Any jet having pT > 5 GeV and labelled neither as top nor as  jet is labelled as soft jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The two categories have been chosen to demonstrate the usefulness of the dynamic  radius jet algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Category A1 captures the whole top jet by the jet clustering algorithm  while the events in category A2 need post-processing after the jet clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, a  desirable criterion of a better-performing jet clustering algorithm would be to have more  events in category A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In order to illustrate that, for a given category, we define acceptance  efficiency  A = number of events accepted in a particular category  total number of events  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)  After the classification of the events into the above two categories, the distribution  of distances between the MG5 parton-level objects and reconstructed ones are plotted  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In both the panels of the figure, the blue and brown histograms are for top  jets, and the green and red ones are for energetic jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The corresponding categories of  the histograms are mentioned alongside the legends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The distributions are shown for jets  clustered using the AK algorithm with (a) R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5, and (b) R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Since this distance  between the MG5 parton-level and reconstructed ones are features of parton showering  and hadronization, the normalized distributions are kind of identical for different radius  – 10 –  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  ∆R(parton, reconstructed)  0  2  4  6  8  10  12  14  frequency (normalized)  (a)  AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top (A1)  top (A2)  jet (A1)  jet (A2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  ∆R(parton, reconstructed)  0  2  4  6  8  10  12  14  frequency (normalized)  (b)  AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  top (A1)  top (A2)  jet (A1)  jet (A2)  Figure 2: Normalized distribution of ∆R between the MG5 parton-level object and cor-  responding reconstructed jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The jets were clustered using the AK algorithm with radius  parameters (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 and (b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These ∆R distributions are very similar even with different choices of standard or  dynamic radius sequential recombination algorithms and, therefore, are not shown to avoid  repetition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This distribution also justified the choice of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 radius to find reconstructed  objects from the MG5 partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  500  1000  1500  2000  2500  jet energy [GeV]  10−4  10−3  frequency (normalized)  (a)  AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A1  top  jet  500  1000  1500  2000  2500  jet energy [GeV]  10−4  10−3  frequency (normalized)  (b)  AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A2  top  jet  Figure 3: Normalized distribution of jet energy for categories (a) A1 and (b) A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  blue and green histograms are respectively for the reconstructed top and the high-pT jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 3 the jet energy distributions for the objects of our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The left  and right panels show the distributions for categories A1 and A2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue  and green histograms are for the top and the high-pT jet produced in association with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 11 –  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (a)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A1  DR-AK A = 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='79%  AK A = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='71%  DR-AK top  DR-AK jet  DR-AK soft  AK top  AK jet  AK soft  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (b)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A2  DR-AK A = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='21%  AK A = 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='23%  DR-AK top  DR-AK jet  DR-AK soft  AK top  AK jet  AK soft  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (c)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A1  DR-CA A = 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='52%  CA A = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='67%  DR-CA top  DR-CA jet  DR-CA soft  CA top  CA jet  CA soft  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (d)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A2  DR-CA A = 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='48%  CA A = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='43%  DR-CA top  DR-CA jet  DR-CA soft  CA top  CA jet  CA soft  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (e)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A1  DR-KT A = 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='87%  KT A = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='71%  DR-KT top  DR-KT jet  DR-KT soft  KT top  KT jet  KT soft  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (f)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category A2  DR-KT A = 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='70%  KT A = 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15%  DR-KT top  DR-KT jet  DR-KT soft  KT top  KT jet  KT soft  Figure 4: Normalized distribution of jet mass for the process pp → tj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The left panel  shows the distribution for category A1 events while the right panel is the distribution for  category A2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue, green, and red histograms are for reconstructed top, hard  jet, and soft jets (defined in the text), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The histograms, from top to bottom,  are for AK, CA, and KT algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The filled histograms correspond to fixed radius  algorithms and the unfilled ones correspond to their dynamic radius (DR) counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 12 –  One of the primary obligations of choosing the appropriate size for jets according to  requirements is to avoid the rise of jet mass even with soft but widely separated constituents  inside a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We, therefore, choose to show the distribution of masses of reconstructed top  jets, reconstructed energetic jets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The jet energy ranges corresponding to the  mass distributions shown can be approximately 500-2000 GeV, as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The left  panel of the figure represents the distribution for category A1 events while the right panel  represents the distribution for category A2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue, green, and red histograms  are for reconstructed top, hard jet, and soft jets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The histograms, from top to  bottom, are for anti-kt, C/A, and kt algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The filled histograms are for standard jet  clustering algorithms and the unfilled ones are their dynamic radius counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the  legends, the prefix ‘DR’ to AK, CA, or KT stands for dynamic radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In all the panels, the  starting radius parameter has been taken to be R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For standard kt-type algorithms,  the starting radius is the fixed constant radius parameter, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=', Rd = R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The values for  A for different algorithms and different categories are quoted inside each panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In all the panels, it is seen that the acceptance efficiencies for A1 category events in the  cases with dynamic radius algorithms are higher than their fixed radius counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  An interesting feature to notice is that the mass distribution for the energetic jet re-  mains almost the same for both the standard and dynamic radius jet clustering algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The similarity between these two are more prominent for AK and CA algorithms and less  so for the KT algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is expected as the KT algorithm starts to merge softer  momenta first and then capture the harder ones almost at the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As a result, this al-  gorithm lets the size of the dynamic radius grow in the beginning and hence allows the  softer hadron, even if they are a little wider, to merge with the evolving jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The top jet  mass distribution is also a little off with respect to their fixed radius analogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These are  not very problematic since jet grooming [77–83], trimming [84], or pruning [85, 86] methods  help in cleaning soft and wide-angle radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' A similar strategy of grooming is useful in  the removal of soft jets as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The change in mass distribution for top jet but not for the energetic jet can easily  be understood from the behaviour of the final radius Rd = (R0 + σ) [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5)] a jet has  acquired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We, therefore, show the distribution of the final radii of the three different types  of jets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The three plots in the top panel are for category A1 events while those in  the bottom panel are for category A2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For category A2 events, ‘top c1’ and ‘top c2’  labels represent the two constituent jets of reconstructed top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The distributions are shown  for DR-AK, DR-CA, and DR-KT algorithms in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 5(a,d), 5(b,e), and 5(c,f), respectively,  with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 in each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  From all the histograms in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 5, some clear features emerge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For the case of category  A1 top jets, the final radius Rd grows to more than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6 with a peak at Rd ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='75, (ap-  proximately 50% increase with respect to the starting radius).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the other hand, for the  energetic jets, Rd does not grow by much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This indicates that the radius grows dynamically  according to the distribution of constituents inside the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The growth of the soft jets is  higher compared to the hard jets candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In general, this is will not be a problem in the  heavy object finding since they can easily be eliminated by choosing an appropriate pT or  mass cuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The story for the category A2 events is similar for jets and soft jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The only  – 13 –  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  20  frequency (normalized)  (a)  Category A1  DR-AK  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  20  frequency (normalized)  (c)  Category A1  DR-KT  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  20  frequency (normalized)  (b)  Category A1  DR-CA  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  20  frequency (normalized)  (d)  Category A2  DR-AK  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top c1  top c2  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  20  frequency (normalized)  (f)  Category A2  DR-KT  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top c1  top c2  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  20  frequency (normalized)  (e)  Category A2  DR-CA  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  top c1  top c2  jet  soft  Figure 5: Normalized distribution of the final radius Rd of three different types of jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The three plots in the top panel are for category A1 events while those in the bottom panel  are for category A2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The conventions for the colours and labels ‘top’, ‘jet’, and ‘soft’  are the same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For category A2, ‘topc1’ and ‘topc2’ labels represent the two  constituent jets of reconstructed top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The distributions are shown for DR-AK, DR-CA,  and DR-KT algorithms in the panels (a,d), (b,e), and (e,f), respectively, with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  difference is that the whole top could not be reconstructed as a single jet in these events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The normalized distributions of the final radii of these two constituent jets of reconstructed  tops are plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These constituents tend to grow more than the energetic jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The values of acceptance efficiencies A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] for different category events vary  with the choice of the value for the starting radius R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' If the starting radius is small, the  algorithms fail to capture the fat jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' On the other hand, the large starting radius R0 will  capture the unwanted contamination coming from underlying events or radiations from  other nearby showers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As a result, the jets will be unnecessarily fat and massive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' There  is a suitable range for R0 within which the algorithms work better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We, therefore, show  the variation of acceptance efficiencies A as a function of starting radius R0 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 6 for  both categories A1 (blue) and A2 (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The variations are shown for (DR-) AK, CA, and  KT algorithms in panels (a), (b), and (c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As expected, for small R0 values,  the efficiencies for category A1 (blue lines) are negligible in both dynamic radius and fixed  – 14 –  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  10  20  30  40  50  60  A [%]  (a)  A1, DR-AK  A2, DR-AK  A1, AK  A2, AK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  10  20  30  40  50  60  A [%]  (c)  A1, DR-KT  A2, DR-KT  A1, KT  A2, KT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  10  20  30  40  50  60  A [%]  (b)  A1, DR-CA  A2, DR-CA  A1, CA  A2, CA  Figure 6: The variation of acceptance efficiency A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] as a function of starting  radius R0 for pp → tj SM process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue and red lines represent the variations of A for  categories A1 and A2 events, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The dashed lines are for (a) AK, (b) CA, and  (c) KT algorithm and the solid lines are for their dynamic radius versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  radius analyses since the constituents of the entire top jet could not be captured with these  small values of R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Rather, the category A2 (red lines) which form the top with the help  of two jets yields more A .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This picture changes once we tend towards higher values for  R0 ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 as more and more top jets are being reconstructed in the A1 category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As a result,  the values of A for the A2 category get reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In all the panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 6, it is interesting  to note that the dynamic radius algorithms (solid) yield higher values for A than their  fixed radius counterparts (dashed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is indicative of the usefulness of the dynamic  radius algorithm over the fixed radius ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The dip in the blue solid lines after near  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7 is not essentially the failure of the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Rather, it is because of the capture  of unwanted contaminations along with the radiation coming from the top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, the  jet mass goes beyond 200 GeV, at which point we stop labelling them as a reconstructed  top jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Furthermore, a rough comparison among the curves in the three panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 6  indicates that DR-AK is better suited than DR-CA and DR-KT algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  Illustration II: pp → V j Subprocess  A similar study has been performed in SM pp → V j, (V = W or Z) processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In order  to ensure the formation of fat jets, a lower cut of 500 GeV on the pT of the jet has been  imposed at the time of generation of parton-level events via MG5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  These events were  then passed on to Pythia8 with Monash 2013 Tune [76] tune for parton showering and  hadronization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The final state hadrons of these events were then sent to FastJet3 for jet  clustering with starting radius R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  As before, we label the energetic jets coming from a jet clustering algorithm, as recon-  structed ‘V’ or reconstructed ‘jet’ with the help of MG5 parton-level information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The rest  – 15 –  0  50  100  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (a)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  Category B1  DR-AK A = 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='18%  AK A = 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='96%  DR-AK V  DR-AK jet  DR-AK soft  AK V  AK jet  AK soft  0  50  100  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (b)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  Category B2  DR-AK A = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='81%  AK A = 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='23%  DR-AK V  DR-AK jet  DR-AK soft  AK V  AK jet  AK soft  0  50  100  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (c)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  Category B1  DR-CA A = 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='46%  CA A = 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='30%  DR-CA V  DR-CA jet  DR-CA soft  CA V  CA jet  CA soft  0  50  100  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (d)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  Category B2  DR-CA A = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10%  CA A = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='25%  DR-CA V  DR-CA jet  DR-CA soft  CA V  CA jet  CA soft  0  50  100  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (e)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  Category B1  DR-KT A = 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='41%  KT A = 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='58%  DR-KT V  DR-KT jet  DR-KT soft  KT V  KT jet  KT soft  0  50  100  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (f)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  Category B2  DR-KT A = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='99%  KT A = 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='02%  DR-KT V  DR-KT jet  DR-KT soft  KT V  KT jet  KT soft  Figure 7: Normalized distributions of jet mass for the process pp → V j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The left panel  shows jet mass distributions of category B1 events and the right panel is the distribution for  category B2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue, green, and red histograms are for reconstructed V, energetic  jet and soft jets (defined in the text), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The histograms, from top to bottom,  are for AK, CA, and KT algorithms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The filled histograms correspond to  fixed radius algorithms and the unfilled ones correspond to their dynamic radius (DR)  analogues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 16 –  of the jets having pT > 5 GeV are tagged as ‘soft jets’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As in the previous illustration, we  classify the events into two separate categories based on the following criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' An event was labelled as a category B1 event if it satisfies the following two conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  A jet should have mass in the range (65, 105) GeV and ∆R(VMG5, jet) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  This jet was identified as a reconstructed V jet and we label them as ‘V (B1)’  in further discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  After the tagging of the V jet, another jet should have pT > 300 GeV and  ∆R(jMG5, jet) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These jets are labelled as ‘jet (B1)’ in further discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' An event, after failing to satisfy the criteria for the category B1, could be classified  as a category B2 event subject to satisfying the below conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Two separate jets within 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='0 distance from the original vector boson (W or Z)  and should have an invariant mass between 65 and 105 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These two jets are  tagged as constituent jets of the reconstructed ‘V’ jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The final reconstructed  ‘V’ jet should be within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 distance from the original boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This combination  is labelled as ‘V (B2)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Another jet having pT > 300 GeV and within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 radii of the original jet and  this is labelled as ‘jet (B2)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We show the jet mass distribution in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 7 for SM pp → V j process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' All the distribu-  tions in the left panel of the figure represent the category B1 events and the distributions  in the right panel are for category B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue, green, and red histograms are for recon-  structed ‘V’, jet and soft jets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The histograms, from top to bottom, are for  AK, CA, and KT algorithms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The filled histograms are for standard jet clus-  tering algorithms and the unfilled ones are their dynamic radius analogues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Quite clearly,  the two peaks in the blue histograms, in all the distributions, correspond to the mass peaks  of W and Z bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The jet mass distribution of the energetic jets using dynamic radius  algorithms remains similar to their fixed radius counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The increment in the per-  centage of the acceptance efficiencies A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] of category B1 events is representative  of the appropriateness of using the dynamic radius algorithms over the standard ones in  these types of scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We next show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 8 the normalized distributions of the final radius for three different  types of jets, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' ‘V’ jets, energetic jets, and soft jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As in the pp → tj process, the fat  V jets acquires a larger radius than the energetic jets after the dynamical expansion of the  jet size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Here, again, the soft jets acquire a higher radius compared to the energetic jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  These soft jetsare not of much concern since they are rather soft and hence they can be  removed easily from the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 9, we show the variation of A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] as a function of starting radius R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In  all the panels of the figure, the blue and red lines correspond to the variations for categories  B1 and B2 events, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The dashed lines are for fixed radius algorithms and the  solid lines are for dynamic radius jet algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The variations are shown for (a) AK, (b)  – 17 –  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  Rd  0  5  10  15  20  frequency (normalized)  (a)  Category B1  DR-AK  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  V  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  Rd  0  5  10  15  20  frequency (normalized)  (c)  Category B1  DR-KT  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  V  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  Rd  0  5  10  15  20  frequency (normalized)  (b)  Category B1  DR-CA  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  V  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  Rd  0  5  10  15  20  frequency (normalized)  (d)  Category B2  DR-AK  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  V c1  V c2  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  Rd  0  5  10  15  20  frequency (normalized)  (f)  Category B2  DR-KT  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  V c1  V c2  jet  soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  Rd  0  5  10  15  20  frequency (normalized)  (e)  Category B2  DR-CA  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  V c1  V c2  jet  soft  Figure 8: Normalized distribution of final radius Rd for the three different types of jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The top panel represents the distributions of Rd in the category B1 events and the whole  bottom panel is for category B2 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The conventions for the colours and labels V, jet,  and soft are the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For category B2 events, ‘V c1’ and ‘V c2’ labels represent  the two constituent jets of the reconstructed vector bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The distributions are shown for  DR-AK, DR-CA, and DR-KT algorithms in the panels (a,d), (b,e), and (c,f), respectively,  with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  CA, and (c) KT algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' A quick observation of the curves tells us that the behaviour  of these curves is similar to that of the curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 6 except the monotonic decreasing  nature of the category B2 curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The reason is as follows: in the case of V jets, the jets  are ‘two-pronged’ in nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, the small radius jets can capture one of the two  prongs of V jets, and thereby these two jets are able to reconstruct V jets in B2 category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  However, as the starting radius R0 is increasing, more and more events are migrating to  category B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The declining nature of the curves for large radii after 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 is because of the  fact that the jets capture more hadrons than are required for their optimal size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As a  result, the mass of the V jets tends to go beyond the mass window set to label them as V  jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Again, more variables than just the jet mass can help one to improve the tagger and  hence the acceptance efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We conclude this section with the note that the dynamic radius jet algorithms are  – 18 –  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  10  20  30  40  50  60  70  80  Acceptance [%]  (a)  B1, DR-AK  B2, DR-AK  B1, AK  B2, AK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  10  20  30  40  50  60  70  80  Acceptance [%]  (c)  B1, DR-KT  B2, DR-KT  B1, KT  B2, KT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  10  20  30  40  50  60  70  80  Acceptance [%]  (b)  B1, DR-CA  B2, DR-CA  B1, CA  B2, CA  Figure 9: The variation of A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] as a function of the starting radius R0 for pp → V j  SM process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue and red lines represent the values of A for categories B1 and B2  events, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The dashed lines are for (a) AK, (b) CA, and (c) KT algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  solid lines are for their dynamic radius versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  useful in finding fat as well as narrow jet in a single event in the colliders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We have  successfully illustrated this in two SM processes, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' pp → tj and pp → V j, at the 13 TeV  LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' A comparison among the three dynamic radius analogues of the standard kt-type  algorithm reveals that the DR-AK algorithm performs better compared to the DR-CA or  the DR-KT algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  4  Usefulness in BSM signals  We now illustrate the usefulness of the dynamic radius jet algorithm in the context of  a scenario beyond the standard model (BSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This is a scenario where an additional  vectorlike singlet quark b′ of charge −1/3 exists along with (d, s, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Such quarks occur, for  example, in E(6) grand unified theories, as also in some seesaw models of quark masses [87–  92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The b′ can mix with the three SM down-type quarks when electroweak symmetry  breaking takes place2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This causes the mass eigenstate dominated by b′ to decay into a top  quark and a W boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In addition, the mixing between a T3 = −1/2 quark and one with  T3 = 0 induces flavour-changing Z- and Higgs-couplings in the b-b′ sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Thus the b′,  produced via strong interactions at the LHC, has the decays b′ → tW, b′ → bZ, b′ → bh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The detailed theoretical framework and the resulting phenomenology have been discussed  widely in the literature [59, 93–101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The currently available data from the LHC restrict mb′ to be no less than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 TeV  [102–105].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' When such a massive quark decays thereafter, its decay products are consider-  2In the following discussion, we shall (a) denote this mass eigenstate itself by b′, (b) assume that  ordinary-exotic quark mixing takes place involving only the third family sequential quark, namely, b, and  (c) parametrize the b-b′ mixing by the angle θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 19 –  ably lighter compared to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore the b′ decay products are considerably boosted, so  as to produce fat jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Furthermore, the difference in mass between two product particles  leads to jets of varying degrees of fatness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Since our purpose here is to show the efficacy of the dynamic radius jet algorithm, we  illustrate our main points in the context of pp → b′¯b′ followed by each b′ decaying into a  top quark and a W boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The t’s and the W’s thus give rise to energetic jets of different  radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We demonstrate below how our newly developed algorithm can capture the identity  of the ensuing final state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' While the present work is aimed at capturing the essence of our  proposed jet algorithm, a more detailed discussion, including combinations of all the three  aforementioned decay channels of the b′, is going to be presented in a separate work [106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  mb′  sin θL  sin θR  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='3 TeV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='12  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='02 × 10−3  Table 1: Values of some important parameters of the vectorlike singlet b′ model considered  for the illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The model has been implemented in a Mathematica-based package SARAH [107–109].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The Universal FeynRules Output (UFO) [110] generated by SARAH is then used in MG5  for the generation of parton-level events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The parameter card for MG5 has been generated  using spectrum generator SPheno [111, 112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The values for the important parameters of  the model are tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The angles θL and θR in the table represent the mixing  angle between SM b quark and exotic b′ quark of chirality left and right, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' After  the generation of the MG5 parton-level events, the rest of the analysis pipeline is the same  as the previous illustrations of SM processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In this illustration, we choose DR-AK, based on the discussion in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We show the resultant jets having pT > 30 GeV formed out of the hadrons generated by  Pythia8 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The left panel shows the positions of the generated hadrons and jets  constructed using the AK algorithm with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The right panel shows the same for  the DR-AK algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In both panels, the red dots represent the position of final state  hadrons in the η-φ plane and the size of each dot is proportional to the √pT of the hadron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The unfilled circles represent the final radius (Rd) of a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The teal dots represent the  constituents of boosted fat ‘W’ jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The green, blue, and purple (wherever applicable) dots  represent the constituents of the fat ‘top’ jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The yellow dots containing texts represent  the position of the MG5 parton-level pT -hard quarks after the decay of top or W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  mothers of the q or b are mentioned in the subscripts of q or b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  An interesting point to observe in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 10(b) is that the DR-AK yields only 4 jets,  which are representative of 2 fat W and 2 fat t jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 10, the fixed radius  algorithm could form the fat W jets but fails to capture the entirety of the two fat t jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  One, of course, can use a bigger radius in the AK algorithm to capture the whole of the  top jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, this will make the W jet unnecessarily fat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This demonstrates the utility  of the dynamic radius jet algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 20 –  −4  −2  0  2  4  η  0  1  2  3  4  5  6  φ  pp → b′¯b′ → tW −¯tW +  AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (a)  Hadrons  −4  −2  0  2  4  η  0  1  2  3  4  5  6  φ  pp → b′¯b′ → tW −¯tW +  DR-AK, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  (b)  Hadrons  Figure 10: The distribution of final state hadrons and jets in η-φ plane for an example  event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The colours and sizes of the dots and circles follow the same convention as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The teal coloured dots represent the constituents of hard fat ‘W’ jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The green and blue  (wherever applicable) dots represent the constituents of the fat ‘top’ jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The yellow dots  containing texts represent the position of the hard quarks after the decay of top or W  which are mentioned as the subscripts of q or b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The plots are shown for (a) AK and (b)  DR-AK algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  To study the goodness of DR-AK quantitatively, we define the following criteria for  tagging of top and W jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  A jet having mass in the range (150, 200) GeV and having ∆R(toptruth, jet) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 is  identified as a reconstructed top jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  A jet will be called W jet if it has a mass in the range (65, 105) GeV and is within  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 distance from the original MG5 parton-level W boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Similar to the illustrations with SM processes, we classify the events into different  categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Due to the complex nature of the final states, we have classified the events into  more than two categories in the present scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The realization is based on the following  understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Out of the two W’s coming directly from b′ in an event, the number of reconstructed  W as fat jet from the algorithm could be 0, 1, or 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We call these reconstructed fat  W jets as primary W jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Similarly, out of the two t quarks, the number of reconstructed t as fat jets can be 0,  1, or 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In some particular cases, the whole top may not be reconstructed, but the W boson  coming from the top quarks may be reconstructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These are referred to as secondary  W jets in the subsequent discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 21 –  Based on the above observations, we classify the events into different categories, whose  generic name is given as Cij, where i and j are two integers encoding the number of  reconstructed top and reconstructed W’s, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For the present scenario, the allowed  value for i does not exceed two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For a given i, the values for j should not exceed 4 − i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  That is, to say, i ≤ 2 and j ≤ 4−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' An exhaustive list of all possible categories is tabulated  in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For example, the event shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 10 would be categorized as C22 for the  DR-AK algorithm while the same event would be classified as C03 for the AK algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  One may again subdivide some of the categories into subcategories based on how many W  jets are coming directly from b′ (primary W) and how many of them are coming from the  decay of the top quark (secondary W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, the generic name for the subcategories  can be given as Cijk with i, j, and k being the numbers of reconstructed top, primary W,  and secondary W jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The possible ranges for i, j, and k are 0 ≤ i, j ≤ 2 and 0 ≤ k ≤ 2−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Category  Subcategory  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' of top jet  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' of primary  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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+page_content='Table 2: The definitions of the list of categories and subcategories as according to how  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='many fat jets can be reconstructed from the jet algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 22 –  0  50  100  150  200  jet mass [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='20  frequency (normalized)  (a)  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  Category C22  DR-AK A = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='47%  AK A = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='62%  DR-AK top  DR-AK W  DR-AK soft  AK top  AK W  AK soft  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='9  Rd  0  5  10  15  frequency (normalized)  (b)  Category C22  DR-AK  top  W  soft  Figure 11: (a) The normalized distribution of jet mass of the category C22 events for the  pp → b′¯b′ → tW −¯tW + process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue, green, and red histograms are reconstructed top,  W, and soft jets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The unfilled histograms are for the jets clustered using the  DR-AK algorithm while the filled ones are for the jets using the AK clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  (b) The normalized distribution of the final radii of top, W, and soft jets with blue, green,  and red colours, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For both panels, R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 was used and any additional jets  having pT >5 GeV were considered as a soft jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  We plot the normalized distribution of jet mass of the category C22 events in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 11(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Jets were clustered using R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the plot, the blue, green, and red histograms are  reconstructed top, W, and soft jets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The unfilled histograms are for the jets  clustered using the DR-AK algorithm, and the filled ones are for the jets using the AK  clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Any untagged jet with pT > 5 GeV was considered to be a soft jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 11(b) shows the normalized distribution for the finally acquired radii of different jets  for category C22 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The desirable feature of the reconstructed W jets being narrower  than the reconstructed top jets is clearly apparent in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Here, again, the soft jets  are growing to larger radius are expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, as discussed in the previous section,  they can be removed from an analysis by pT or jet mass cuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The values of A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] for the two different algorithms, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' DR-AK and AK are  also quoted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 11(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These values (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='62% for AK and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='47% for DR-AK), clearly,  indicate that the dynamic radius jet algorithm is working better while probing the correct  mass windows for the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The shift of the mass distribution towards larger values is  indicative of capturing little extra than required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' As discussed previously, this can be recti-  fied by the techniques of grooming [77–81], trimming [84], or pruning [85, 86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Furthermore,  going beyond just the jet mass to tag the topor W jets would further help in extracting  signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The variation of A as a function of initial radius R0 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 12 for six categories,  namely C22, C21, C20, C13, C12, and C11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' These categories have at least one top jet  identified within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5 distance from the MG5 parton-level top quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The solid blue lines  – 23 –  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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+page_content='8  R0  0  5  10  15  20  Acceptance [%]  C22  DR-AK  AK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='8  R0  0  5  10  15  20  Acceptance [%]  C11  DR-AK  AK  Figure 12: The variation of A [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)] as a function of initial radius R0 for six categories,  namely C22, C21, C20, C13, C12, and C11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The solid blue lines are for the DR-AK  algorithm, and the dashed lines are for the AK algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The jets are clustered with  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  represent the efficiencies for the DR-AK algorithm, and the dashed lines are representative  of the AK algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For the case of dynamic radius, the quintessential feature is the  initial increment in the acceptance efficiencies A up to R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5, and, beyond this value,  the efficiencies decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The reason for this is an unnecessary accumulation of hadrons  and making the jets bigger than their optimal size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' However, for the AK algorithm, the  efficiencies keep on increasing until R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='7, which is kind of the optimal radius for this  scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  The most important point to note is that up to R0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5, the efficiencies for  the DR-AK algorithm are higher than those for the AK algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This feature, again,  establishes the utility of using dynamic radius algorithms over fixed radius ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In the end, we look at the bar plot of the acceptance efficiencies A for all the categories  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The blue and green bars are for DR-AK and AK algorithms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  initial radius R0 is taken to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The numbers under the curly braces below the x-axis  represent the values of A for the categories which capture 2 tops, 1 top, 0 top, and none of  the top or W jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The important observation in this regard is that the categories containing  2 top and 1 top jets have better efficiencies for the dynamic radius algorithm than the fixed  radius one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' This means that the events, where the AK algorithm could not capture the  whole of the top constituents, the DR-AK algorithm could capture the full tops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Thus the  credence of our proposed algorithm is established in a BSM context as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  – 24 –  C22 C21 C20 C13 C12 C11 C10 C04 C03 C02 C01 C00  Categories  0  5  10  15  20  25  30  Acceptance [%]  R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5  DR-AK:  AK:  �  ��  �  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='86%  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='38%  �  ��  �  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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+page_content='02%  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='75%  ����  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='79%  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='56%  DR-AK  AK  Figure 13: Bar plot of A for different categories for jet algorithms with R0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  blue, and green bars are for DR-AK and AK algorithm respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' From left to right,  The numbers under the braces represent the values of A for the categories which capture  2 top, 1 top, 0 top, and none of the top or W jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  5  Summary and Outlook  We go beyond the most popular jet clustering algorithms, where the formation of jets  is performed using a fixed radius parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  These algorithms return fixed-sized jets  corresponding to the input radius parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In this work, an attempt is made to make  the radius of each jet variable depending on the kinematics and hadronic activity in the  neighbourhood of an evolving jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The proposed method is based on the standard kt-type  sequential recombination jet clustering algorithms with the incorporation of the dynamic  nature of the radius parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Starting from a reasonable radius parameter, during the process of formation of a jet,  the radius of each evolving jet is allowed to grow based on fuzziness inside it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' For this  work, the measure of the fuzziness of each evolving jet is chosen to be the ‘pT -weighted’  standard deviation of the inter-particle distances (in the η-φ plane) of the particles inside  the evolving jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  After describing the proposed method, we have presented two different SM processes,  viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' pp → tj and pp → Wj +Zj, to demonstrate some applicabilities of the dynamic radius  jet clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In these two processes, differently-sized jets are expected in a sin-  gle event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In the two SM process examples, we observe that the jets are being formed with  radii varying in size on a jet-by-jet basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In terms of the acceptance efficiency [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='1)],  we show that the performance of the dynamic radius algorithm is better compared to their  – 25 –  fixed radius counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We take up a scenario beyond the Standard Model for further  illustration, where a vectorlike SU(2)L singlet charge −1/3 quark b′ is added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' We study  jet clustering in pp → b′¯b′ followed by each b′ decaying into tW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Once more, our proposed  method turns out to be effective in the reconstruction of the final state particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  In the examples given above, the dynamicity has been incorporated in the radius  parameter of the standard kt-type sequential recombination algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The central idea  is the usage of fuzziness of an evolving jet to appropriately increase its radius starting  from a starting radius R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Although examples with only one measure of fuzziness have  been shown in this work, one may consider other appropriate measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' depending upon  the underlying physics process or the final goal of the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' Therefore, the idea of the  dynamic radius jet algorithm should not be restricted only to this particular measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' The  applicability of these possibilities will be presented in a separate work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content=' In a nutshell, the  idea of dynamic radius jet clustering algorithm on a jet-by-jet basis is useful in collider  studies and will be beneficial in searches driven by processes in SM as well as BSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
+page_content='  Acknowledgments  The authors thank Jayita Lahiri for useful discussions during the initial phase of the work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dFPT4oBgHgl3EQfYjT_/content/2301.13074v1.pdf'}
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