Daily Papers

In this work we estimate the first unknown QCD correction to the decay of the Higgs boson into gluons, Hto gg, in the heavy-top limit using Padé approximants built to the perturbative series and to its Borel transform. In the process, we also obtain estimates for the first unknown coefficients of the QCD β function, of the QCD decoupling relation, and of the gluonium correlator. We also provide an updated prediction for the first unknown coefficient of Γ(Hto bb). We determine the polynomial dependence of the perturbative coefficients on the number of quark flavors, n_f. We point out that the large-n_f result for Hto gg can be obtained from results for the gluonium correlator already available in the literature. The coefficient of the highest power of n_f is then imposed as a constraint and is also used as a new test to discard unreliable approximants. The method is validated through the postdiction of the last known coefficient of the series. Our model-independent estimate for the yet unknown coefficient of order α_s^7 of Γ(Hto gg) is -312pm 15 (in the mathrm{MS} scheme with μ=m_H, where m_H is the Higgs mass). With our estimate the residual renormalization-scale dependence of Γ(Hto gg) is reduced by a factor of almost 1.5.

We perform a lattice QCD calculation of the hadronic light-by-light contribution to (g-2)_μ at the SU(3) flavor-symmetric point m_π=m_Ksimeq 420,MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain a_μ^{rm hlbl} = (65.4pm 4.9 pm 6.6)times 10^{-11}, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

The measure of indirect CP violation in the neutral kaon system, ε_K, is an important precision test of the Standard Model. A first-principles Standard Model prediction of ε_K requires evaluating the long-distance contribution in which the ΔS = 2 process proceeds via two ΔS = 1 operators. The non-perturbative nature of QCD in the relevant energy regimes requires a lattice QCD simulation. In this paper we present the two-loop, O(α_s) RI/SMOM - text{MS} matching factors required to renormalize a lattice QCD calculation of the long-distance contribution to ε_K.

Very recently, the two-photon decay width of the η_b meson was computed with lattice QCD methods. This decay has not yet been measured. The knowledge of this width allows for the calculation of the η_b production cross section through photon-photon interactions in ultra-peripheral PbPb collisions. In this work we present this calculation, which is the first application of the lattice result. Since UPCs are gaining an increasing attention of the heavy ion community, we take the opportunity to perform a comprehensive study of the different ways of defining ultra-peripheral collisions and of the different ways to treat the equivalent photon flux.

We present a detailed investigation on the structure of neutron stars, incorporating the presence of hyperons within a relativistic model under the mean-field approximation. Employing coupling constants derived from QCD sum rules, we explore the particle fraction in beta equilibrium and establish the mass-radius relationship for neutron stars with hyperonic matter. Additionally, we compute the stellar Love number (K_{2}) and the tidal deformability parameter (varLambda), providing valuable insights into the dynamical properties of these celestial objects. Through comparison with theoretical predictions and observational data, our results exhibit good agreement, affirming the validity of our approach. These findings contribute significantly to refining the understanding of neutron star physics, particularly in environments containing hyperons, and offer essential constraints on the equation of state governing such extreme astrophysical conditions.

A dynamical model based on a phenomenological charm quark-nucleon(c-N) potential v_{cN} and the Pomeron-exchange mechanism is constructed to investigate the J/Psi photo-production on the nucleon from threshold to invariant mass W=300 GeV. The J/Psi-N potential,V_{J/Psi N}(r),is constructed by folding v_{cN} into the wavefunction Phi_{J/Psi}(cc) of J/Psi within a Constituent Quark Model(CQM) of Ref.[43]. A photo-production amplitude is also generated by v_{cN} by a cc-loop integration over the gammarightarrow cc vertex function and Phi_{J/Psi}(cc). No commonly used Vector Meson Dominance assumption is used to define this photo-production amplitude which is needed to describe the data near the threshold. The potential v_{cN}(r) is parameterized in a form such that the predicted V_{J/Psi N}(r) at large distances has the same Yukawa potential form extracted from a Lattice QCD(LQCD) calculation of Ref.[18]. The parameters of v_{cN} are determined by fitting the total cross section data of JLab by performing calculations that include J/Psi-N final state interactions(FSI). The resulting differential cross sections are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near threshold region, allowing for sensitive testing of the predicted J/Psi-N scattering amplitudes. By imposing the constraints of J/Psi-N potential extracted from the LQCD calculation, we have obtained three J/Psi-N potentials which fit the JLab data equally well. The resulting J/Psi-N scattering lengths are in the range of a=(-0.05 fm sim -0.25 fm). With the determined v_{cN}(r) and the wavefunctions generated from the same CQM, the constructed model is used to predict the cross sections of photo-production of eta_c(1S) and Psi(2S) mesons for future experimental tests.

Non-Abelian gauge theories above four dimensions may admit an interacting ultraviolet fixed point through the competition between canonical scaling and gauge-field antiscreening. Using the four-loop mathrm{MS} beta function continued to D=4+2ε, we determine the largest dimension D_{pt}=4+2ε_{pt} below which successive loop corrections to the fixed point remain hierarchically ordered under a specified ratio criterion, and map D_{pt} over color and flavor numbers for fermions in the fundamental representation of SU(N). At D=5, we construct rational anomalous dimensions with a fixed, pole-regularized denominator inspired by the functional renormalization group (fRG). Matching to the mathrm{MS} series through one, two, and three loops produces progressively smaller shifts in the critical flavor number and coupling at the ultraviolet--infrared merger (the point where the infrared and ultraviolet fixed points coincide), yielding N_f^{cr}simeq 2.09 , N at large N in the three-loop construction. This low-order stabilization, together with qualitative evidence from fRG flows including higher gauge operators, suggests a potential merger scenario that bounds the candidate asymptotically safe region in flavor number. The resulting color--flavor map provides guidance for five-dimensional model building by displaying both the baseline perturbative-control boundary and the candidate three-loop merger boundary. Four-loop matching, however, retains an interacting ultraviolet fixed point beyond the three-loop merger boundary, with no merger found for integer 2le Nle15 and 0le N_f/Nle11/2. The sensitivity of the fixed-point structure to higher-order terms leaves both scenarios open, highlighting fixed-point annihilation as a potential constraint on five-dimensional asymptotic safety.

We propose a novel method to locate the QCD critical point by constructing an expansion along contours of constant entropy density. Applying two independent analysis of lattice QCD data at zero baryon chemical potential, we find a critical point at T_c = 114 pm 7 MeV and μ_{B_c} = 602 pm 62 MeV for an expansion truncated at order μ_B^2. This approach is consistent with recent lattice QCD results up to μ_B/T leq 3. A more precise determination of the required expansion coefficients from lattice simulations will be essential for reliably establishing the location of the QCD critical endpoint.

We present a new lattice QCD calculation of the leading order hadronic vacuum polarization (LO-HVP) contribution to the muon anomalous magnetic moment a_μ. We reduce uncertainties compared to our earlier computation arXiv:2002.12347 by a factor of 1.6. We perform simulations on finer lattices allowing for an even more accurate continuum extrapolation. We also include a small, long-distance contribution obtained using input from experiments in a low-energy regime where they all agree. Combined with other standard model contributions our result, a_μ^{LO-HVP}=715.1(2.5)(2.3)[3.4] times 10^{-10}, leads to a prediction that differs from the recent measurement of a_μ by only 0.5 standard deviations. This provides a remarkable validation of the standard model to 11 digits.

The perturbative QCD corrections to the hadronic decay width of the W boson are currently known up to next-to-next-to-next-to-next-to-leading order (N^4LO), whereas the exact N^5LO correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the N^5LO contributions by adopting Bayesian analysis (BA). Before performing the estimation, the Principle of Maximum Conformality (PMC) is employed to improve the precision of the initial scale-dependent perturbative series. Through recursive application of the renormalization group equation, non-conformal terms are absorbed into the strong running coupling, yielding a scheme-independent, scale-invariant perturbative series with improved convergence. The PMC procedure determines an effective coupling α_s(Q_*), with the PMC scale fixed as Q_* = 100.102~GeV at next-to-next-to-leading logarithmic accuracy. Based on the improved and more precise series, the 95.5% BA credible interval yields an uncertainty of Δδ_QCD|_{PMC, BA}^{N^5LO} = pm 1.0times 10^{-5}. The resulting hadronic branching ratio is B(Wto hadrons)|_PMC = (65.84pm 1.54)%, which is consistent with experimental data within reasonable errors.

The total charm-quark production cross section per unit of rapidity dσ({rm cc})/dy, and the fragmentation fractions of charm quarks to different charm-hadron species f(crm h_{c}), are measured for the first time in p-Pb collisions at s_mathrm{NN} = 5.02 TeV at midrapidity (-0.96<y<0.04 in the centre-of-mass frame) using data collected by ALICE at the CERN LHC. The results are obtained based on all the available measurements of prompt production of ground-state charm-hadron species: D^{0}, D^{+}, D_s^{+}, and J/ψ mesons, and Λ_c^{+} and Ξ_{rm c}^{0} baryons. The resulting cross section is dσ({rm cc})/dy =219.6 pm 6.3;(stat.) {;}_{-11.8}^{+10.5};(syst.) {;}_{-2.9}^{+8.3};(extr.)pm 5.4;(BR)pm 4.6;(lumi.) pm 19.5;(rapidity shape)+15.0;(Ω_{rm c}^{0}) mb, which is consistent with a binary scaling of pQCD calculations from pp collisions. The measured fragmentation fractions are compatible with those measured in pp collisions at s = 5.02 and 13 TeV, showing an increase in the relative production rates of charm baryons with respect to charm mesons in pp and p-Pb collisions compared with e^{+e^{-}} and e^{-p} collisions. The p_T-integrated nuclear modification factor of charm quarks, R_pPb({rm cc})= 0.91 pm 0.04;{rm (stat.)}{}^{+0.08}_{-0.09};{rm (syst.)}{}^{+0.05}_{-0.03};{rm (extr.)}{}pm 0.03;{rm (lumi.)}, is found to be consistent with unity and with theoretical predictions including nuclear modifications of the parton distribution functions.

Jet taggers built on the Lund declustering tree encode QCD radiation structure in the inputs and process it with graph networks. We ask whether the tree itself can also constrain the computation, and what becomes accessible when it does. For this, we construct a novel quantum-inspired Tree Tensor Network (TTN), where a single tensor core is shared among the internal nodes of the Cambridge/Aachen declustering tree, employing Lund coordinates, and with no particle-identification or detector-level information. The construction is based on a strong prior on the radiation history rather than on the constituents, complementary to compact equivariant taggers. Because the same learned map acts identically at every node, the trained model can be evaluated on truncated trees and its latent space compared across recursions, and used to localise where on the Lund jet plane the Pythia and Herwig jet representations diverge, showing the regions of generator-dependent concentration. The χ=8 model has 4014 trainable parameters against approximately 391,000 for LundNet. We evaluate boosted top tagging and quark/gluon discrimination at particle level on Pythia and Herwig samples, in both native (PythiatoPythia) and transfer (PythiatoHerwig) configurations. Despite differing in capacity by two orders of magnitude, the TTN reaches native performance close to LundNet in quark/gluon discrimination, slightly underperforming in top tagging, with a similar Pythia-to-Herwig transfer behavior in both tasks. Finally, we show the behavior of the network as a function of the bond dimension, and as a function of the perturbative scale.

Precision beta decay experiments serve as powerful probes of physics beyond the Standard Model, enabling stringent tests of fundamental symmetries of nature. In particular, these experiments primarily focus on precise determinations of the Cabibbo-Kobayashi-Maskawa matrix element Vud and the search for exotic weak currents, both of which depend critically on theoretical calculations of radiative, recoil-order, and isospin-breaking corrections with quantified uncertainties. In recent years, ab initio nuclear many-body methods--grounded in realistic nucleon-nucleon interactions and systematically improvable approximations--have advanced considerably in their ability to compute these higher-order corrections for various nuclei. This review provides a comprehensive overview of state-of-the-art ab initio calculations of beta-decay corrections, encompassing both radiative corrections and recoil-order terms, and examines their significance for precision tests of the Standard Model. We discuss the theoretical formalisms employed, including the integration of effective field theory frameworks with many-body approaches. Particular attention is given to recent results for superallowed Fermi decays (e.g., 10C -> 10B and 14O -> 14C) and allowed Gamow-Teller transitions (e.g., 6He -> 6Li, 8Li -> 8Be, 8B -> 8Be), where ab initio calculations have achieved unprecedented precision. We also highlight emerging calculations for unique forbidden decays, which offer complementary sensitivity to BSM physics. Finally, we outline future directions aimed at extending the reach of ab initio calculations to heavier nuclei and additional decay modes, thereby strengthening the synergy between theory and experiment in the ongoing search for new physics.

We construct an exact analytic solution of the revised small-x helicity evolution equations, where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-N_c&N_f limit and are double-logarithmic, resumming powers of alpha_sln^2(1/x). Here N_c and N_f are the numbers of quark colors and flavors, while alpha_s is the strong coupling constant and x is the Bjorken-x variable. Using our solution, we obtain analytic expressions for the flavor singlet quark and gluon helicity parton distribution functions (PDFs) and for the g_1 structure function as double-inverse Laplace transforms. We also extract analytic expressions for the four DGLAP polarized anomalous dimensions Delta gamma_{qq}, Delta gamma_{qG}, Delta gamma_{Gq}, and Delta gamma_{GG}: these expressions resum powers of alpha_s/omega^2 to all orders at large-N_c&N_f (with omega the Mellin moment variable). We extract the leading small-x growth of the helicity distributions, align \Delta\Sigma(x,Q^2) \sim \Delta G(x,Q^2)\sim g_1(x,Q^2) \sim \left(1{x}\right)^{\alpha_h}, align where the intercept alpha_h satisfies an algebraic equation. We determine alpha_h numerically for various values of N_c and N_f. We further obtain the explicit asymptotic expressions for the helicity distributions, which yield numerical values for the ratio of the gluon helicity PDF to the flavor singlet quark helicity PDF in the small-x asymptotic limit (for different N_f/N_c). We find that all our predictions for polarized DGLAP anomalous dimensions are fully consistent with the existing finite-order calculations. Similar to the large-N_c case, our intercept alpha_h exhibits a very slight disagreement with the predictions made within the infrared evolution equations framework.

The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack of a reliable bandwidth selector; practitioners currently rely on iterative optimization methods that are computationally expensive and prone to instability. We derive the ``Beta Reference Rule,'' a fast, closed-form bandwidth selector based on the unweighted Asymptotic Mean Integrated Squared Error (AMISE) of a beta reference distribution. To address boundary integrability issues, we introduce a principled heuristic for U-shaped and J-shaped distributions. By employing a method-of-moments approximation, we reduce the bandwidth selection complexity from iterative optimization to O(1). Extensive Monte Carlo simulations demonstrate that our rule matches the accuracy of numerical optimization while delivering a speedup of over 35,000 times. Real-world validation on socioeconomic data shows that it avoids the ``vanishing boundary'' and ``shoulder'' artifacts common to Gaussian-based methods. We provide a comprehensive, open-source Python package to facilitate the immediate adoption of the Beta kernel as a drop-in replacement for standard density estimation tools.

We present a lattice determination of the Bjorken sum rule via a Feynman-Hellmann calculation of the polarised forward Compton amplitude. We evaluate the lowest moment of the nucleon's polarised structure function, g_1, which we calculate over the range 0.5lesssim Q^2 lesssim 8 GeV^2, covering both non-perturbative and perturbative regions. We compare our calculated moments with the Bjorken sum rule, and discuss implications for the calculation of higher-twist effects, as well as evaluations of α_s(Q^2) from hadronic quantities to complement phenomenological and other lattice methods.

Constituent quarks in a nucleon are the essential elements in the standard ``quark model" associated with the electric charge, spin, mass, and baryon number of a nucleon. Quantum Chromodynamics (QCD) describes nucleon as a composite object containing current quarks (valence quarks and sea (anti-)quarks) and gluons. These subatomic elements and their interactions are known to contribute in complex ways to the overall nucleon spin and mass. In the early development of QCD theory in the 1970s, an alternative hypothesis postulated that the baryon number might manifest itself through a non-perturbative configuration of gluon fields forming a Y-shaped topology known as the gluon junction. In this work, we propose to test such hypothesis by measuring (i) the Regge intercept of the net-baryon distributions for e+(p)Au collisions, (ii) baryon and charge transport in the isobaric ratio between e+Ru and e+Zr collisions, and (iii) target flavor dependence of proton and antiproton yields at large rapidity, transported from the hydrogen and deuterium targets in e+p(d) collisions. Our study indicates that these measurements at the EIC can help determine what carries the baryon number.

We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with judicious selection of events.

We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and symbolic/numerical elimination. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram. We illustrate with a number of examples that this algebraic formalism allows to compute many components of the Landau singular locus. We adapt the GKZ framework by carefully specializing Euler integrals to Feynman integrals. For instance, ultraviolet and infrared singularities are detected as irreducible components of an incidence variety, which project dominantly to the kinematic space. We compute principal Landau determinants for the infinite families of one-loop and banana diagrams with different mass configurations, and for a range of cutting-edge Standard Model processes. Our algorithms build on the Julia package Landau.jl and are implemented in the new open-source package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

Beauty-hadron production in proton-nucleus collisions is a particularly powerful probe of cold nuclear matter (CNM) effects: thanks to the large beauty-quark mass, the production is initiated in early hard scatterings and is calculable in perturbative QCD, while the modifications observed in nuclear collisions directly constrain the nuclear parton distribution functions (nPDFs) in a kinematic region complementary to that accessed by charm. Precisely quantifying these effects is a prerequisite for isolating possible signatures of quark-gluon plasma formation in heavy-ion collisions. In this work, the production of open beauty hadrons in p-Pb collisions at s_{mathrm{NN}} = 5.02 and 8.16~TeV is studied via a data-driven Bayesian unfolding of ALICE and LHCb measurements of non-prompt D^{0} and J/ψ mesons. The unfolded p_{T}- and y-differential cross sections are mutually consistent across decay channels and compatible with directly reconstructed beauty-hadron measurements. The nuclear modification factor R_{pPb} is reported as a function of transverse momentum and rapidity, providing the first unfolding-based result spanning -4.0 < y < 4.0 of beauty-hadron R_{pPb} covering the full rapidity range, with a precision comparable to or better than that of existing data. The results are compared with calculations based on nPDFs and can provide valuable constraints for future global nPDF fits. The total inclusive B hadron production cross section in p-Pb collisions is also reported. A weaker CNM suppression is observed for beauty hadrons than for charm hadrons, consistent with the expected mass hierarchy of cold-nuclear-matter effects.

We present the quark weak-mixing component of a Froggatt--Nielsen program, with one flavon and three messengers, in which a single hierarchy parameter B (with εequiv 1/B) and a rational-exponent ``B-lattice'' organize fermion Yukawa textures. Building on companion mass-fit work, we translate the lattice into sharp predictions for quark mixing. The four-magnitude parameterization serves as a practical interface between the flavon Yukawa textures and quark weak mixing observables, yielding coefficient-free ratio tests of the lattice structure.

The decays of pseudoscalar mesons to real and virtual photons as well as neutrino-antineutrino pairs are considered in the framework of the dispersive method based on Anomaly Sum Rules. The contribution of singlet channel involving the new non-perturbative gluon form factor of virtual photon B(q^2) is systematically taken into account. The detailed analysis of its dependence on photon virtuality q^2 relying on the available data for meson transition fomfactors is performed. It is shown that B has quite a nontrivial structure at q^2 sim 1 GeV^2 which may be a signal of the existence of pseudoscalar glueball with a mass about 1.5-2 GeV. The calculation of the decay to νbar ν pairs leads to the compatibility with the result of Arnellos, Marciano and Parsa of 1982, when pion decay is considered neglecting the mixing effects. The account for these effects results, however, in the enhancement of pion branching ratio by a factor of 3, while that for eta decay is larger by several orders of magnitude. It is stressed, that dependence on the pair invariant mass is entirely defined by QCD and coincides with that of the meson transition form factor. The role of obtained results for the physics at HHaS detector at HIAF is discussed.

To account for the soft transverse dynamics overlooked by the k_T factorization formalism of exclusive QCD processes, we propose introducing the intrinsic transversal momentum distribution functions (iTMDs), in conjunction with the light-cone distribution amplitudes (LCDAs), to define the probability amplitude for finding a hadron state where partons move fast along the longitudinal axis while undergoing gentle oscillations in the transverse plane. We implement this framework in the calculation of the electromagnetic form factors of the pion and the proton. Our iTMDs-improved perturbative QCD predictions show good agreement with available experimental data and lattice QCD results. More importantly, we find that higher-twist, especially subleading-twist contributions, are indispensable for explaining the scaling behavior of both pion and proton form factors at intermediate momentum transfers. Furthermore, the inclusion of iTMD effects significantly improves the perturbative QCD predictions for the pion form factor in the few GeV^2.

We extend our measurement of the equation of state of isospin asymmetric QCD to small baryon and strangeness chemical potentials, using the leading order Taylor expansion coefficients computed directly at non-zero isospin chemical potentials. Extrapolating the fully connected contributions to vanishing pion sources is particularly challenging, which we overcome by using information from isospin chemical potential derivatives evaluated numerically. Using the Taylor coefficients, we present, amongst others, first results for the equation of state along the electric charge chemical potential axis, which is potentially of relevance for the evolution of the early Universe at large lepton flavour asymmetries.

We derive the tree-level interaction vertices of the linear sigma model with quarks in the presence of global rotation. Starting from the scalar and fermionic field solutions in a rotating background, we construct the corresponding spectral representations and use them to evaluate the mesonic self-interactions and Yukawa couplings of the model. We show that rotation modifies the usual momentum-space structure of the interaction vertices: conservation of longitudinal momentum is accompanied by angular-momentum selection rules, while the transverse dynamics is encoded in rotation-induced radial form factors involving products of Bessel functions. The resulting expressions provide a set of interaction rules adapted to the symmetries and finite geometry of the rotating system. Although derived within the linear sigma model with quarks, the structures obtained for scalar self-interactions and scalar-fermion couplings can be extended to a broader class of quantum field theories under global rotation. These results provide the building blocks for perturbative calculations and contribute toward a microscopic quantum-field-theoretical description of interacting matter in rotating environments.

We present compact analytic results for tree-level amplitudes containing a t t pair accompanied by up to four massless partons, t tgg, t tggg, t tgggg, t tqq, t tqqg, t tqqgg and ttqqq^prime q^prime. The results, obtained using BCFW on-shell recursion, are based both on previous published results and on the new calculations performed in this paper. These amplitudes are sufficient to calculate the production of a tt pair and zero, one, or two light parton jets, with the option to include the tree-level decays t to b νe^+ and t to b e^- barν efficiently. Our results are part of the NNLO corrections to t t production including the decay correlations for on-shell top quarks.

We study charm production in charged-current deep-inelastic scattering (DIS) using the xFitter framework. Recent results from the LHC have focused renewed attention on the determination of the strange-quark parton distribution function (PDF) and the DIS charm process provides important complementary constraints on this quantity. We examine the current PDF uncertainty, and use LHeC pseudodata to estimate the potential improvement from this proposed facility. As xFitter implements both fixed-flavor- and variable-flavor-number schemes, we can compare the impact of these different theoretical choices; this highlights some interesting aspects of multi-scale calculations. We find that the high-statistics LHeC data covering a wide kinematic range could substantially reduce the strange PDF uncertainty.

We present a holographic model of QCD to study the strong coupling constant α_s from the low-energy region to the high-energy regime. The approach uses a double-dilaton background, which breaks conformal and chiral symmetries, while large-N_c corrections are incorporated to connect the holographic description with perturbative QCD. The model leads to an infrared fixed point and provides a smooth transition to the pQCD running. The resulting background also produces linear Regge trajectories for scalar, vector, and tensor states in reasonable agreement with experimental data.

We consider beta-Dyson Brownian motion, with β>= 1, started from a deterministic configuration with uniformly bounded support. Let μ_t be the semicircular free-convolution flow issued from the initial empirical measure, and set S_t = supp(μ_t). For every fixed T, ε> 0, with probability at least 1 - C exp(-(log n)^2), every particle remains within an epsilon-neighborhood of S_t for all 0 <= t <= T. The result holds from time zero, requires no regularity assumption at the initial spectral edges, and applies to multi-cut supports with macroscopic interior gaps. A key ingredient is a deterministic local resolvent exclusion principle: an o((n η)^(-1)) comparison of Stieltjes transforms on a complex disc above a real point separated from the reference support excludes eigenvalues from the corresponding real interval. This gives a model-independent mechanism for converting local resolvent estimates into spectral confinement.

A persistent and fascinating problem at the high energy colliders are jets. Often trying to observe physics underlying the hard interactions at colliders requires experimental cuts in phase space, defining several jet or beam regions. QCD being a gauge theory that readily decays into infra-red modes, correlations between jet regions is almost inevitable, spoiling the predictivity of fixed order QCD calculations. One is faced with the task of calculating the evolution of a reduced density matrix, where successively less energetic (jet) regions are integrated out, to gain control of the calculation. I relate the decay rates governing the flow into the IR to an effective field theory expansion in soft jets, allowing a systematic and resummed calculation of these rates, while further relating them to physically observable features of the QCD cascade. To demonstrate the utility of the soft jet expansion, I present a factorization theorem for a soft subjet collinearly splitting in and out of a parent fat jet. Using the resummation properties of this factorization theorem, I elucidate the structure of the subleading non-global logs (encoding the jet correlations) in the hemisphere jet mass distribution, as well as give a collinear improvement of the leading order resummation equation, the BMS equation. I compare to other approaches to subleading resummation of NGLs, and find the collinear improvement of the leading order equation removes the need for kinematic-dependent corrections in the IR averaging procedure of the reduced density matrix, so that no further large logs can be generated in the IR. Finally I end with speculation about connections with collinear improvements of the NLO B-JIMWLK hierarchy for small-x resummation.

The last decade has seen a marked shift in how the internal structure of hadrons is understood. Modern experimental facilities, new theoretical techniques for the continuum bound-state problem and progress with lattice-regularised QCD have provided strong indications that soft quark+quark (diquark) correlations play a crucial role in hadron physics. For example, theory indicates that the appearance of such correlations is a necessary consequence of dynamical chiral symmetry breaking, viz. a corollary of emergent hadronic mass that is responsible for almost all visible mass in the universe; experiment has uncovered signals for such correlations in the flavour-separation of the proton's electromagnetic form factors; and phenomenology suggests that diquark correlations might be critical to the formation of exotic tetra- and penta-quark hadrons. A broad spectrum of such information is evaluated herein, with a view to consolidating the facts and therefrom moving toward a coherent, unified picture of hadron structure and the role that diquark correlations might play.

The conventional grid-based approach used for storing and evaluating ordinary parton distribution functions (PDFs), as implemented for example in LHAPDF, becomes much more demanding for double parton distributions (DPDs). While a collinear PDF depends on one longitudinal momentum fraction and one factorization scale, an unequal-scale DPD depends on two momentum fractions and two independent factorization scales for every parton-flavor combination. Direct tabulation of this four-dimensional dependence therefore requires considerably more disk space and runtime memory. In this work, we develop a hybrid neural-network method for compact storage and fast evaluation of y-independent unequal-scale DPDs. The network compresses the reference grid by reproducing most of its values, while the original values are stored only at points where the neural prediction does not reach the required accuracy. In this way, the neural model captures the bulk of the grid, with a sparse table covering the remaining difficult points. For the GS09-based dense grid studied here, only 0.694% of the active flavor values need to be stored in the sparse table. Compared with the compressed dense grid, the hybrid method reduces the disk footprint by a factor of 10.6, peak memory use by a factor of 31.6, and initialization time by about a factor of 10.6. At the same time, its evaluation throughput reaches about 85% of the dense-grid rate. The method is implemented natively in C++ within PDFxTMDLib and requires neither Python nor PyTorch at runtime. The hybrid scheme therefore offers much lower memory and startup costs, with only a modest reduction in evaluation speed.

Familial amyloid-β (Aβ) variants alter aggregation kinetics, but their interaction with structural brain connectivity remains incompletely understood. We developed a mutation-aware mechanistic model coupling a coarse-grained monomer--oligomer--fibril aggregation--fragmentation system to graph diffusion on the 540-node Budapest Reference Connectome component. Experimental Aβ_{42} nucleation scores scaled primary nucleation rates for seven variants relative to wild type. Robustness was examined using mutation-score uncertainty, alternative kinetic mappings, global sensitivity analysis, seed and edge-weight perturbations, degree-preserving randomized connectomes, spatial propagation analysis, synthetic ABC-SMC parameter recovery, posterior prediction, and Chemical Langevin simulations. E22G showed the earliest threshold crossing and greatest cumulative oligomer burden, whereas A2V was delayed under the selected mapping. Mutation rankings persisted across tested network perturbations, although regional burden patterns depended on topology. Connectome distance from seed regions was associated with later oligomer arrival (Spearman ρapprox0.92). Under inferred parameter uncertainty, the mean timing-rank correlation was 0.990 and cumulative-burden ordering was preserved in every posterior draw, while exact peak-amplitude ordering was less stable. Stochastic ensemble medians retained the deterministic ordering despite overlap among trajectories. Within this proof-of-concept framework, mutation-dependent kinetics primarily influence aggregation timing and cumulative burden, while connectivity shapes spatial propagation. Nominal background rates, model-time units, and synthetic parameter recovery limit interpretation to mechanistic comparisons rather than clinically calibrated prediction.

A comparative analysis of the special shapes (patterns, profiles) of the eclipses applied for the phenomenological modeling of the light curves of eclipsing binary stars is conducted. Families of functions are considered, generalizing local approximations (Andronov, 2010, 2012) and the functions theoretically unlimited in a width, based on a Gaussian (Mikulasek, 2015). For an analysis, the light curve of the star V0882 Car = 2MASS J11080308 - 6145589 of the classic Algol - subtype (\beta Persei) is used. By analyzing dozens of modified functions with additional parameters, it was chosen the 14 best ones according to the criterion of the least sum of squares of deviations. The best are the functions with an additional parameter, describing profiles, which are limited in phase.

In quantum mechanics the modulus square of the wave function is the probability of an event --- positivity is self-evident. Quantum field theory corresponds to quantum mechanics one-to-one: the wave function corresponds to the matrix element, so the probability of a process should be the modulus square of the matrix element, positive by construction. In the founding era of perturbative quantum field theory, however, Feynman, Schwinger and Tomonaga treated inclusive processes in quantum electrodynamics, where the truncation of the squared amplitude was forced by infrared cancellations and rendered harmless by the small coupling αsimeq1/137. Carried over to exclusive processes in quantum chromodynamics, where the coupling is large, this practice produced negative decay and production rates already at NLO, persisting at NNLO. We point out that for exclusive processes, whose initial and final states are colorless for QCD and electrically neutral for QED, the infrared divergences cancel amplitude by amplitude and the KLN constraint is absent, so the complete modulus square of the truncated amplitude is the proper, manifestly positive definition of the probability. We formulate amplitude-level NRQCD factorization as the systematic prescription that restores positivity, show that every amplitude-level truncated observable admits the effective representation Γ^{amp}=Γ_{LO}bigl|1+α_sπ(c_1+ic_2)+α_s^2{π^2}(c_3+ic_4)bigr|^2, and demonstrate, with the complete NNLO QCD corrections to J/ψto3γ, Υto3γ, e^+e^-to J/ψ+J/ψ and the eight exclusive charmonium production channels at B factories, that the prescription yields positive and better-converging predictions.

The production of a top-quark pair, the heaviest known elementary particle, in association with a light jet is a key process for studying the properties of the Standard Model of Particle Physics. Due to its significance as a signal process with considerable sensitivity to the top-quark mass and as a background process for new physics searches, it is crucial to predict differential cross sections with high precision. In this article, we present, for the first time, predictions for various kinematical observables at next-to-next-to-leading order in Quantum Chromodynamics. The perturbative behavior is analyzed, and uncertainties arising from missing higher-order contributions are substantially reduced. The necessary two-loop amplitudes have been evaluated in the leading-color approximation, and we provide estimates for the impact of the missing contributions.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

We study the pole mass for a heavy quark probe in the Gross--Neveu model, at the first non-trivial order in the 1/N expansion. We show that this mass suffers from a perturbative renormalon ambiguity structurally similar to the one in QCD. The exact large N solution leads however to an explicit expression for the pole mass which can be decoded as a trans-series, and we find that non-perturbative corrections cure the renormalon ambiguity. We also calculate the self-energy of the heavy quark beyond perturbation theory by using the OPE method with condensates, and show that the results are in agreement with the large N solution. The non-perturbative corrections to the pole mass turn out to be determined to a large extent by the condensate corrections to the self-energy. However, there is a class of corrections that has to be reorganized due to on-shell effects and cannot be obtained from the conventional condensate expansion. We discuss possible implications of this toy model for QCD.

Recent experimental results in B physics from Belle, BaBar and LHCb suggest new physics (NP) in the weak bto c charged-current and the bto s neutral-current processes. Here we focus on the charged-current case and specifically on the decay modes Bto D^{*+}ell^- barν with ell = e, μ, and τ. The world averages of the ratios R_D and R_D^{*} currently differ from the Standard Model (SM) by 3.4σ while ΔA_{FB} = A_{FB}(Bto D^{*} μν) - A_{FB} (Bto D^{*} e ν) is found to be 4.1σ away from the SM prediction in an analysis of 2019 Belle data. These intriguing results suggest an urgent need for improved simulation and analysis techniques in Bto D^{*+}ell^- barν decays. Here we describe a Monte Carlo Event-generator tool based on EVTGEN developed to allow simulation of the NP signatures in Bto D^*ell^- ν, which arise due to the interference between the SM and NP amplitudes. As a demonstration of the proposed approach, we exhibit some examples of NP couplings that are consistent with current data and could explain the ΔA_{FB} anomaly in Bto D^*ell^- ν while remaining consistent with other constraints. We show that the Δ-type observables such as ΔA_{FB} and ΔS_5 eliminate most QCD uncertainties from form factors and allow for clean measurements of NP. We introduce correlated observables that improve the sensitivity to NP. We discuss prospects for improved observables sensitive to NP couplings with the expected 50 ab^{-1} of Belle II data, which seems to be ideally suited for this class of measurements.

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental properties. We establish various analytic properties of these integrals with respect to both the exponent parameters and the main variables. Their key feature is invariance under simultaneous translation of the exponent parameters, which generates relations between integrals over possibly different coverings. This mechanism recovers notable identities for multiple zeta values and variants -- including Zagier's 2-3-2 formula, Murakami's t-value analogue, Charlton's t-value analogue, Zhao's 2-1 formula, and Ohno's relation -- and also yields new relations, such as a proof of a Galois descent phenomenon for multiple omega values.

The production of W^{pm}H, ZH, W^+W^-, and W^pm Z pairs probes non-Standard-Model interactions of quarks, gauge bosons, and the Higgs boson. New effects can be parameterized in terms of an effective field theory (EFT) where the Lagrangian is expanded in terms of higher-dimension operators suppressed by increasing powers of a high scale Λ. We examine the importance of including next-to-leading-order QCD corrections in global fits to the coefficients of the EFT. The numerical implications on the fits due to different approaches to enforcing the validity of the EFT are quantified. We pay particular attention to the dependence of the fits on the expansion in 1/Λ^2 since the differences between results calculated at {O}(1/Λ^2) and {O}(1/Λ^4) may give insight into the possible significance of dimension-8 effects.

We investigate spectral features of bottomonium at high temperature, in particular the thermal mass shift and width of ground state S-wave and P-wave state. We employ and compare a range of methods for determining these features from lattice NRQCD correlators, including direct correlator analyses (multi-exponential fits and moments of spectral functions), linear methods (Backus-Gilbert, Tikhonov and HLT methods), and Bayesian methods for spectral function reconstruction (MEM and BR). We comment on the reliability and limitations of the various methods.

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when the order v is large, and GPU-specific implementations are limited. We address the precision limitations of current numerical implementations while dramatically improving the runtime. We propose two novel algorithms for computing the logarithm of modified Bessel functions of the first and second kinds by computing intermediate values on a logarithmic scale. Our algorithms are robust and never have issues with underflows or overflows while having relative errors on the order of machine precision, even for inputs where existing libraries fail. In C++/CUDA, our algorithms have median and maximum speedups of 45x and 6150x for GPU and 17x and 3403x for CPU, respectively, over the ranges of inputs and third-party libraries tested. Compared to SciPy, the algorithms have median and maximum speedups of 77x and 300x for GPU and 35x and 98x for CPU, respectively, over the tested inputs. The ability to robustly compute a solution and the low relative errors allow us to fit von Mises-Fisher, vMF, distributions to high-dimensional neural network features. This is, e.g., relevant for uncertainty quantification in metric learning. We obtain image feature data by processing CIFAR10 training images with the convolutional layers of a pre-trained ResNet50. We successfully fit vMF distributions to 2048-, 8192-, and 32768-dimensional image feature data using our algorithms. Our approach provides fast and accurate results while existing implementations in SciPy and mpmath fail to fit successfully. Our approach is readily implementable on GPUs, and we provide a fast open-source implementation alongside this paper.

We present the new parton distribution functions (PDFs) from the CTEQ-TEA collaboration, obtained using a wide variety of high-precision Large Hadron Collider (LHC) data, in addition to the combined HERA I+II deep-inelastic scattering data set, along with the data sets present in the CT14 global QCD analysis. New LHC measurements in single-inclusive jet production with the full rapidity coverage, as well as production of Drell-Yan pairs, top-quark pairs, and high-p_T Z bosons, are included to achieve the greatest sensitivity to the PDFs. The parton distributions are determined at NLO and NNLO, with each of these PDFs accompanied by error sets determined using the Hessian method. Fast PDF survey techniques, based on the Hessian representation and the Lagrange Multiplier method, are used to quantify the preference of each data set to quantities such as α_s(m_Z), and the gluon and strange quark distributions. We designate the main resulting PDF set as CT18. The ATLAS 7 TeV precision W/Z data are not included in CT18, due to their tension with other data sets in the global fit. Alternate PDF sets are generated including the ATLAS precision 7 TeV W/Z data (CT18A), a new scale choice for low-x DIS data (CT18X), or all of the above with a slightly higher choice for the charm mass (CT18Z). Theoretical calculations of standard candle cross sections at the LHC (such as the gg fusion Higgs boson cross section) are presented.

According to the generally accepted phase diagram of QCD, at low temperature and high baryon number density the chiral phase transition of QCD is of first order and the co-existence of the Nambu-Goldstone phase and the Wigner phase should appear. This is in conflict with the usual claim that the quark gap equation has no Wigner solution in the case of nonzero current quark mass. In this paper we analyze the reason why the Wigner solution does not exist in the usual treatment and try to propose a new approach to discuss this question. As a first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study the Wigner solution at finite current quark mass. We then generalize this approach to the case of finite chemical potential and discuss partial restoration of chiral symmetry at finite chemical potential and compare our results with those in the normal NJL model.

Estimating the symbolic or analytical form of probability density functions (PDFs) from observed samples is a fundamental challenge in statistical and computational modelling. This process is critical for deriving interpretable and generalizable relationships characterizing the underlying phenomenon. Traditionally, this estimation depends strongly on domain expertise and prior field-specific knowledge, with experts selecting appropriate functional forms or parametric families based on empirical evidence and theoretical understanding. The coefficients of these forms are then typically determined through parameter estimation. In this paper, we develop a framework for estimating symbolic expressions of unnormalized distributions from observed samples using domain-specific prior knowledge, such as the range of interactions and a predefined set of primitive functions. We integrate deep generative models with symbolic regression (SR), incorporating inductive biases, such as factorizing large distributions, to keep the problem tractable. The deep generative models we examine include likelihood-based models, viz., flow models, and score-based models. Experiments show the effectiveness of the proposed framework for estimating density functions for multivariate toy distributions as well as lattices from computational physics, namely, XY model and ϕ^4 theory. When applied to the renormalization problem in ϕ^4 theory, the proposed framework estimates compact symbolic approximations of the hamiltonian function at different scales directly from samples, yielding expressions that may be challenging to derive using traditional perturbative or analytic approaches in nonperturbative settings.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

The interaction between Λ baryons and kaons/antikaons is a crucial ingredient for the strangeness S=0 and S=-2 sector of the meson-baryon interaction at low energies. In particular, the Λ{overline{K}} might help in understanding the origin of states such as the Ξ(1620), whose nature and properties are still under debate. Experimental data on Λ-{K} and Λ-{overline{K}} systems are scarce, leading to large uncertainties and tension between the available theoretical predictions constrained by such data. In this Letter we present the measurements of Λ-K^+oplus overlineΛ-K^- and Λ-K^-oplus overlineΛ-K^+ correlations obtained in the high-multiplicity triggered data sample in pp collisions at s=13 TeV recorded by ALICE at the LHC. The correlation function for both pairs is modeled using the Lednicky-Lyuboshits analytical formula and the corresponding scattering parameters are extracted. The Λ-K^-oplus overlineΛ-K^+ correlations show the presence of several structures at relative momenta k^* above 200 MeV/c, compatible with the Ω baryon, the Ξ(1690), and Ξ(1820) resonances decaying into Λ-K^- pairs. The low k^* region in the Λ-K^-oplus overlineΛ-K^+ also exhibits the presence of the Ξ(1620) state, expected to strongly couple to the measured pair. The presented data allow to access the ΛK^+ and ΛK^- strong interaction with an unprecedented precision and deliver the first experimental observation of the Ξ(1620) decaying into ΛK^-.

We investigate BZT shocks and the QCD phase transition in the dense core of a cold quark star in beta equilibrium subject to the multicomponent van der Waals (MvdW) equation of state (EoS) as a model of internal structure. When this system is expressed in terms of multiple components, it can be used to explore the impact of a phase transition from a hadronic state to a quark plasma state with a complex clustering structure. The clustering can take the form of colored diquarks or triquarks and bound colorless meson, baryon, or hyperon states at the phase transition boundary. The resulting multicomponent EoS system is nonconvex, which can give rise to Bethe-Zel'dovich-Thompson (BZT) phase changing shock waves. Using the BZT shock wave condition we find constraints on the quark density and examine how this changes the tidal deformability of the compact core. These results are then combined with the TOV equations to find the resulting mass and radius relationship. These state are compared to recent astrophysical high-mass neutron star systems, which may provide evidence for a core that has undergone a quark gluon phase transition such as PSR 0943+10 or GW 190814.

We present a technique for computing Drell-Yan lepton pair production at particle-level that achieves N^3LO and approximate N^4LL' accuracy at small to moderate transverse momentum, tree-level precision for Z+4, 5, and 6 jets, and approximate NLO EW precision at high transverse momentum. A crucial non-perturbative input, the Collins-Soper kernel, is obtained from continuum-limit lattice QCD results. High-precision theory results are recast into strictly positive event weights using an information-theoretic approach based on the maximum entropy principle.

Molecular docking is critical to structure-based virtual screening, yet the throughput of such workflows is limited by the expensive optimization of scoring functions involved in most docking algorithms. We explore how machine learning can accelerate this process by learning a scoring function with a functional form that allows for more rapid optimization. Specifically, we define the scoring function to be the cross-correlation of multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks, enabling rapid optimization over rigid-body degrees of freedom with fast Fourier transforms. The runtime of our approach can be amortized at several levels of abstraction, and is particularly favorable for virtual screening settings with a common binding pocket. We benchmark our scoring functions on two simplified docking-related tasks: decoy pose scoring and rigid conformer docking. Our method attains similar but faster performance on crystal structures compared to the widely-used Vina and Gnina scoring functions, and is more robust on computationally predicted structures. Code is available at https://github.com/bjing2016/scalar-fields.

We study the parity-perturbed Hofstadter Q-recursion $ widetilde Q(1)=widetilde Q(2)=1,qquad widetilde Q(n)=widetilde Q(n-widetilde Q(n-1)) +widetilde Q(n-widetilde Q(n-2))+(-1)^n, and the associated two-variable Dirichlet series Z_{widetilde Q}(s,t)=sum_{nge1}n^{-s}widetilde Q(n)^{-t}. The estimate \widetilde Q(n)=n/2+O(n/\log n) gives the exact domain of absolute convergence Re(s+t)>1. With w=s+t, we separate the universal term 2^tζ(w) and derive exact transport, frequency-position, and dyadic renormalization identities. The main result concerns t=-1. For E(n)=2\widetilde Q(n)-n and A(X)=\sum_{n\le X}E(n), the binary-arch clock yields A(X)=Xlog_2X+XΩ!left(log_23X{32}right) +O!left(X{log X}right), where Ω is an explicit continuous periodic function. This continues the normalized correction to Rew>0 and yields a boundary resonance lattice: a double resonance at w=0 and simple resonances at 2πi m/\log2. After subtracting the full-slice order-X skeleton, we analyze the negative-even arch channel. Its companion-forest layers have a weak Gaussian limit, and a canonical subsequence realizes the optimal n/\log n pointwise scale with an explicit signed constant. The negative-arch mass satisfies A_r=512{92π}16^r{sqrt r} left(1-13{16r}+O(r^{-2})right). We do not claim a full-slice continuation across Rew=0$.

Studies of density matrices for random quantum states lead naturally to the fixed trace Laguerre ensemble in random matrix theory. Previous studies have uncovered explicit rational function formulas for moments of purity statistic (trace of the squared density matrix), and also a third order linear differential equation satisfied by the eigenvalue density. We further probe the origin of these results from the viewpoint of integrability, which is taken here to mean wider classes of recursions and differential equations, and give extensions. Prominent in our study are first order linear matrix differential equations. One application given is to the derivation of the third order scalar equation for the density. Another is to obtain the explicit rational function formula for the variance of the purity statistic in the β generalised fixed trace Laguerre ensemble. In the original case (β= 2), the purity cumulants are expressed in terms of the large argument expansion of a particular σ-Painlevé IV transcendent. In a different but related direction, the exact computation of the two-point correlation for the fixed determinant circular unitary ensemble SU(N) is given the Appendix.

scqubits is an open-source Python package for simulating and analyzing superconducting circuits. It provides convenient routines to obtain energy spectra of common superconducting qubits, such as the transmon, fluxonium, flux, cos(2ϕ) and the 0-π qubit. scqubits also features a number of options for visualizing the computed spectral data, including plots of energy levels as a function of external parameters, display of matrix elements of various operators as well as means to easily plot qubit wavefunctions. Many of these tools are not limited to single qubits, but extend to composite Hilbert spaces consisting of coupled superconducting qubits and harmonic (or weakly anharmonic) modes. The library provides an extensive suite of methods for estimating qubit coherence times due to a variety of commonly considered noise channels. While all functionality of scqubits can be accessed programatically, the package also implements GUI-like widgets that, with a few clicks can help users both create relevant Python objects, as well as explore their properties through various plots. When applicable, the library harnesses the computing power of multiple cores via multiprocessing. scqubits further exposes a direct interface to the Quantum Toolbox in Python (QuTiP) package, allowing the user to efficiently leverage QuTiP's proven capabilities for simulating time evolution.

Multi-model LLM systems such as routing, voting, cascades, fusion, and mixture-of-agents are used to beat single-model accuracy. We show that their gain is capped by a quantity the field rarely reports. For any policy whose output is one member model answer, accuracy cannot exceed one minus beta, where beta is the rate at which every model is wrong on the same query. In contrast, the usual diagnostic, average pairwise error correlation rho, cannot identify beta: error laws with identical marginals and pairwise correlations can have different all-wrong rates. A Clopper-Pearson bound on beta gives a finite-sample certificate on the largest gain any router, vote, or cascade could deliver before training a router. Across 67 models from 21 providers, a tetrachoric-calibrated single-factor model still underprices the all-wrong tail: on open-ended mathematics, observed beta is 0.052 versus 0.023 under the full 67-model Gaussian copula, about 2.5 times underpricing, with 90 percent CI 1.7 to 3.4 and k equals 17. The effect recurs on execution-graded code, where beta is 0.079. Re-asking the same GPQA-Diamond questions in free-response rather than multiple-choice form reopens the tail, with beta 0.127 and a five-judge panel with kappa 0.73 to 0.92, locating co-failure in answer format rather than subject. At matched quality, low-rho heterogeneous ensembles beat high-rho Self-MoA, but on checkable tasks in our pool, combining models rarely beats the single best model without a strong query-level routing signal. Gains come from models failing on different questions, not from adding more models.

We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at z to 0, as well as modifications of the geometry in the large z infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable ζ which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable z in AdS space with the impact variable ζ. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.

We introduce an open-source package called QTraj that solves the Lindblad equation for heavy-quarkonium dynamics using the quantum trajectories algorithm. The package allows users to simulate the suppression of heavy-quarkonium states using externally-supplied input from 3+1D hydrodynamics simulations. The code uses a split-step pseudo-spectral method for updating the wave-function between jumps, which is implemented using the open-source multi-threaded FFTW3 package. This allows one to have manifestly unitary evolution when using real-valued potentials. In this paper, we provide detailed documentation of QTraj 1.0, installation instructions, and present various tests and benchmarks of the code.

We study the mixing between a generic axion-like particle (ALP) and the light pseudoscalar mesons within chiral perturbation theory (χPT), and its consequences for low-energy scattering and decay processes. Starting from the most general ALP effective Lagrangian, we derive the ALP-meson kinetic and mass mixing induced at leading order in the ALP decay constant and isospin breaking for arbitrary ALP masses. As a result, we obtain the physical ALP mass to O(F^2/f_a^2), recovering the QCD-axion limit and finding that any ALP with a vanishing bare mass shares the QCD-axion mass. We provide a compact parameterization of every four-body amplitude involving pseudoscalar mesons and an arbitrary number of ALPs. As an illustration, we show the KKto P^0a scattering. The framework applies for general ALP masses and couplings and consistently incorporates isospin breaking, essential for otherwise forbidden processes.

Scientific foundation models hold great promise for advancing nuclear and particle physics by improving analysis precision and accelerating discovery. Yet, progress in this field is often limited by the lack of openly available large scale datasets, as well as standardized evaluation tasks and metrics. Furthermore, the specialized knowledge and software typically required to process particle physics data pose significant barriers to interdisciplinary collaboration with the broader machine learning community. This work introduces a large, openly accessible dataset of 10 million simulated proton-proton collisions, designed to support self-supervised training of foundation models. To facilitate ease of use, the dataset is provided in a common NumPy format. In addition, it includes 70,000 labeled examples spanning three well defined downstream tasks: track finding, particle identification, and noise tagging, to enable systematic evaluation of the foundation model's adaptability. The simulated data are generated using the Pythia Monte Carlo event generator at a center of mass energy of sqrt(s) = 200 GeV and processed with Geant4 to include realistic detector conditions and signal emulation in the sPHENIX Time Projection Chamber at the Relativistic Heavy Ion Collider, located at Brookhaven National Laboratory. This dataset resource establishes a common ground for interdisciplinary research, enabling machine learning scientists and physicists alike to explore scaling behaviors, assess transferability, and accelerate progress toward foundation models in nuclear and high energy physics. The complete simulation and reconstruction chain is reproducible with the sPHENIX software stack. All data and code locations are provided under Data Accessibility.

We conducted a multi-wavelength analysis of the blazar Mrk\,501, utilizing observations from AstroSat (SXT, LAXPC), Swift-UVOT, and Fermi-LAT during the period August 15, 2016 to March 27, 2022. The resulting multi-wavelength light curve revealed relatively low activity of the source across the electromagnetic spectrum. Notably, logparabola and broken power-law models provided a better fit to the joint X-ray spectra from AstroSat-SXT/LAXPC instruments compared to the power-law model. During the low activity state, the source showed the characteristic harder when brighter trend at the X-ray energies. To gain insights into underlying physical processes responsible for the broadband emission, we performed a detailed broadband spectral analysis using the convolved one-zone leptonic model with different forms of particle distributions such as logparabola (LP), broken power-law (BPL), power-law model with maximum energy (ξ_{max}), and energy-dependent acceleration (EDA) models. Our analysis revealed similar reduced-χ^2 values for the four particle distributions. The LP and EDA models exhibited the lowest jet powers. The correlation analyses conducted for the LP and BPL models revealed that there is a positive correlation between jet power and bulk Lorentz factor. Specifically, in the LP model, jet power proved independent of γ_{min}, whereas in the broken power-law model, jet power decreased with an increase in γ_{min}. The jet power in the LP/EDA particle distribution is nearly 10 percent of the Eddington luminosity of a 10^7 M_odot black hole. This result suggests that the jet could potentially be fueled by accretion processes.

We consider N classical particles interacting via the Coulomb potential in spatial dimension d and in the presence of an external trap, at equilibrium at inverse temperature beta. In the large N limit, the particles are confined within a droplet of finite size. We study smooth linear statistics, i.e. the fluctuations of sums of the form {cal L}_N = sum_{i=1}^N f({bf x}_i), where {bf x}_i's are the positions of the particles and where f({bf x}_i) is a sufficiently regular function. There exists at present standard results for the first and second moments of {cal L}_N in the large N limit, as well as associated Central Limit Theorems in general dimension and for a wide class of confining potentials. Here we obtain explicit expressions for the higher order cumulants of {cal L}_N at large N, when the function f({bf x})=f(|{bf x}|) and the confining potential are both rotationnally invariant. A remarkable feature of our results is that these higher cumulants depend only on the value of f'(|{bf x}|) and its higher order derivatives evaluated exactly at the boundary of the droplet, which in this case is a d-dimensional sphere. In the particular two-dimensional case d=2 at the special value beta=2, a connection to the Ginibre ensemble allows us to derive these results in an alternative way using the tools of determinantal point processes. Finally we also obtain the large deviation form of the full probability distribution function of {cal L}_N.

In order to exploit the full potential of the LHC and future colliders, high-precision calculations of a very wide range of observables are crucial. Automated tools for next-to-next-to-leading order calculations of perturbative scattering amplitudes are therefore a highly desirable goal. So far, we have developed several major ingredients of such a tool in the OpenLoops framework. In our approach we split the calculation of scattering amplitudes into three components: loop momentum tensor integrals, the corresponding process-dependent tensor coefficients, and the interplay of (D-4)-dimensional parts of the integrand with divergences of the integrals. In these proceedings, we present a new recursive algorithm to reduce arbitrary two-loop tensor integrals to scalar integrals, which has been implemented into an efficient numerical tool. We also implemented a first version of the subsequent reduction to master integrals, which allows for a full validation of the algorithm. We present a first successful validation computation and discuss its dependence on the precision of the externally computed master integrals.

We propose a unique topological portal between quantum chromodynamics (QCD) and a dark sector characterized by a global symmetry breaking, which connects three QCD to two dark pions. When gauged, it serves as the leading portal between the two sectors, providing an elegant, self-consistent scenario of light thermal inelastic dark matter. The inherent antisymmetrization leads to diminished annihilations at later times and suppressed direct detection. However, novel collider signatures offer tremendous prospects for discovery at Belle II.

We investigate the leading order correction of anomalous magnetic moment (AMM) to the electron in weak magnetic field and find that the magnetic correction is negative and magnetic field dependent, indicating a magnetic catalysis effect for the electron gas. In the laboratory to measure the g-2, the magnitude of the magnetic field B is several T, correspondingly the magnetic correction to the AMM of electron/muon is around 10^{-34}/10^{-42}, therefore the magnetic correction can be safely neglected in current measurement. However, when the magnitude of the magnetic field strength is comparable with the electron mass, the magnetic correction of electron's AMM will become considerable. This general magnetic correction to charged fermion's AMM can be extended to study QCD matter under strong magnetic field.

An amplitude analysis of B^-rightarrow D^- D^0 K_S^0 decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 9,fb^{-1}, collected with the LHCb detector at center-of-mass energies of 7, 8, and 13,Tekern -0.1em V. A resonant structure of spin-parity 0^+ is observed in the D^0 K_S^0 invariant-mass spectrum with a significance of 5.3,sigma. The mass and width of the state, modeled with a Breit-Wigner lineshape, are determined to be 2883pm11pm6,Mekern -0.1em V!/c^2 and 87_{-47}^{+22}pm6,Mekern -0.1em V respectively, where the first uncertainties are statistical and the second systematic. These properties and the quark content are consistent with those of the open-charm tetraquark state T_{cs 0}^{*}(2870)^0 observed previously in the D^+ K^- final state of the B^-rightarrow D^- D^+ K^- decay. This result confirms the existence of the T_{cs 0}^{*}(2870)^0 state in a new decay mode. The T_{cs1}^{*}(2900)^0 state, reported in the B^-rightarrow D^- D^+ K^- decay, is also searched for in the D^0 K_S^0 invariant-mass spectrum of the B^- rightarrow D^- D^0 K_S^0 decay, without finding evidence for it.

We propose a quark flavor model based on modular S'_4 with a general CP symmetry. CP violation in the quark sector is entirely realized by the modulus langle τrangle. We show that the canonical normalization induced by the Kähler metric plays a crucial role in reproducing the observed hierarchies, while maintaining coupling constants of order O(1). The minimal model achieves a great fit to the quark sector data, which we take as the PDG 2024 data extrapolated to the GUT scale.

A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., langle tr M^{2k} rangle ge 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

Standard-Model warm inflation (SMWI) makes QCD the microscopic origin of inflationary dissipation, so the real-time response of the gauge plasma enters the cosmological prediction. We show that a slowly relaxing gauge-helicity response cannot, in general, be absorbed into an effective friction coefficient and must instead remain dynamical. We therefore evolve the quark axial densities and a matched hard-helicity mode, with QCD sphalerons and an effective 2leftrightarrow3 channel generating both charge transfer and correlated stochastic sources in the full perturbation covariance system. The resulting backreaction is substantial but mainly indirect: gauge-helicity screening can reduce the warm dissipation ratio by an order-one fraction on the strong branch, while the 2leftrightarrow3 channel contributes only 0.2%-0.7% of the zero-density sphaleron friction directly, shifting the amplitude-normalized trajectory in both n_s and r_{rm vac}. The relevant trajectories, however, lack a parametrically broad hard-soft hierarchy and extend beyond strict linear response. The predictions should therefore be understood within the stated local Gaussian transport closure; a parameter-free Standard-Model (SM) result requires finite-affinity real-time SU(3) drift, susceptibility, and noise kernels.

We investigate detailed properties of imaginary rotating matter with gluons and quarks at high temperature. Previously, we showed that imaginary rotation induces perturbative confinement of gluons at the rotation center. We perturbatively calculate the Polyakov loop potential and find inhomogeneous confinement above a certain threshold of imaginary angular velocity. We also evaluate the quark contribution to the Polyakov loop potential and confirm that spontaneous chiral symmetry breaking occurs in the perturbatively confined phase.

The μ-parameterization (μP) provides a principled foundation for large language model (LLM) training by prescribing width-independent learning dynamics, which in turn enables predictable scaling behavior and robust hyperparameter transfer across model sizes. A central requirement of μP is the satisfaction of certain spectral conditions on weight matrices, which ensure consistent feature learning and optimization behavior as model width grows. While these conditions are well understood in theory, guaranteeing their validity in practical training for matrix-based optimizers such as Muon is still under studied. Existing works that study Muon under μP exhibit important limitations: they either do not ensure that the spectral conditions hold throughout the entire training horizon, or require repeated spectral normalization (or Newton-Schulz iterations) applied to both weights and updates, leading to significant computational overhead and reduced practicality. In this work, we show how to reliably guarantee the spectral conditions required by μP for Muon during the entire training process. Our key insight is that for moderately large models, maintaining spectral control at the level of optimizer updates alone is sufficient to preserve μP-compatible scaling, eliminating the need for explicit spectral normalization of the weights. Based on this principle, we develop a variant of Muon, namely Muon++, that satisfies spectral condition throughout the training process. Our results bridge the gap between the theoretical promises of μP and the practical deployment of matrix-based optimizers in long-horizon training. We also take the first step towards an adaptive spectral condition by incorporating data-dependent effects, making it better suited for long-horizon LLM training.

Motivated by the recent HAL QCD lattice results on the D - D^* potential at nearly physical point m_π=146.4 MeV, we theoretically examine effects from the two-pion exchange in (semi-)long-range parts of the DD^* system. We employ the framework of heavy-meson chiral perturbation theory with heavy-quark spin symmetry. The pion exchanges up to next-to-next-to-leading order (N^2LO) are taken into account. In order to separate the (semi-)long-range contributions, we apply the dispersion-relation method to one-loop diagrams. As a result, we find that the lattice data on the D - D^* potential in the regime of 0.5, {rm fm} lesssim r is reproduced by adjusting the unknown O(p^2) couplings. In particular, it turns out that contributions from isospin-independent N^2LO triangle diagrams play a central role in reproducing the lattice data of the form V^{DD^*}sim left({rm e}^{-m_πr}/rright)^2 in 1.0, {rm fm} lesssim rlesssim 2.0, {rm fm}. We also present predictions of other D^{(*)} - D^{(*)} potentials, where the similar two-pion exchange tail is predicted. Our findings provide useful information on the (semi-)long-range regime of the D - D^* potential focusing on two-pion exchanges.

This paper presents the first numerical realization of Suzuki's Weil-Quadratic-Form operator, a candidate for the Hilbert--Pólya program linking spectral positivity to the Riemann Hypothesis (RH). Suzuki's 2026 construction was purely theoretical; here, the operator is instantiated via P1 finite-element discretization and Richardson extrapolation. Key results include: (R1) In the prime-free regime, the spectrum follows a closed Archimedean law A_k(a) = log(1/a) + log(k-2) + B_0 + O(a), with B_0 = log q - 2log 2, confirmed to 30-digit precision. (R2) A Mellin double-pole argument proves the head coefficient B(ν) and shows B_0 depends only on the conductor q, independent of the Archimedean parameter. (R2b) The degree d of an L-function appears directly as the logarithmic slope of the spectrum. (R3) Total spectral intensity follows the prime number theorem, S(a) sim (2a)^3/6. (R4) Nontrivial zeros are not eigenvalues but occur in the explicit-formula error term of the prime symbol. (R5) The best-match line σ^*(a) descends toward the critical line. (R6) Weil's positivity criterion is realized in operator form: bounded residual growth corresponds to all zeros on the line, while an injected off-line zero causes exponential blow-up. (R7) The lowest eigenvalue λ_1(a) is strictly positive, decays superexponentially, and passes smoothly through the first prime threshold. (R8) The characteristic function W(a,0;z) is computed for the first time, with all zeros confirmed real. (R9) Indirect traces of GUE statistics appear in the moment structure, even where direct detection is blocked. The authors emphasize that this work does not prove RH. All results are Archimedean and universal, with significance lying in the faithful numerical realization of classical identities rather than new arithmetic.

The early stage of high-energy heavy-ion collisions undergoes transient dynamics, evolving non-perturbatively from a gluon-rich to a chemically equilibrated quark-gluon plasma. We develop an effective hydrodynamic approach that casts the microscopic quark equilibration dynamics as the relaxation evolution of an effective macroscopic bulk viscous pressure. The evolution of this effective bulk viscous pressure captures quark chemical equilibration and the breaking of conformal symmetry, thereby providing a smooth onset of the lattice QCD equation of state after a few fm/c in the hydrodynamic evolution. We investigate phenomenological effects of this macroscopic description on final-state observables in Pb+Pb, O+O, and p+Pb collisions at the Large Hadron Collider.

We generalize the Hamiltonian Monte Carlo algorithm with a stack of neural network layers and evaluate its ability to sample from different topologies in a two dimensional lattice gauge theory. We demonstrate that our model is able to successfully mix between modes of different topologies, significantly reducing the computational cost required to generated independent gauge field configurations. Our implementation is available at https://github.com/saforem2/l2hmc-qcd .

For decades, researchers have developed task-specific models to address scientific challenges across diverse disciplines. Recently, large language models (LLMs) have shown enormous capabilities in handling general tasks; however, these models encounter difficulties in addressing real-world scientific problems, particularly in domains involving large-scale numerical data analysis, such as experimental high energy physics. This limitation is primarily due to BPE tokenization's inefficacy with numerical data. In this paper, we propose a task-agnostic architecture, BBT-Neutron, which employs a binary tokenization method to facilitate pretraining on a mixture of textual and large-scale numerical experimental data. We demonstrate the application of BBT-Neutron to Jet Origin Identification (JoI), a critical categorization challenge in high-energy physics that distinguishes jets originating from various quarks or gluons. Our results indicate that BBT-Neutron achieves comparable performance to state-of-the-art task-specific JoI models. Furthermore, we examine the scaling behavior of BBT-Neutron's performance with increasing data volume, suggesting the potential for BBT-Neutron to serve as a foundational model for particle physics data analysis, with possible extensions to a broad spectrum of scientific computing applications for Big Science experiments, industrial manufacturing and spacial computing. The project code is available at https://github.com/supersymmetry-technologies/bbt-neutron.

Despite the growing application of Large Language Models (LLMs) to theoretical physics, there is little academic exploration into how domain-specific physics reasoning ability develops while training these models. To investigate this, we perform the first academic fine-tuning study of small (7B-parameter) reasoning models dedicated specifically to theoretical physics. Because open-source verifiable training data required to train such capabilities is scarce, we developed a robust data generation pipeline that can both create synthetic problems and make existing human-authored problems suitable for model training. Selecting Quantum Field Theory (QFT) as our primary domain, we generated over 2,500 synthetic problems alongside a curated collection of human-adapted problems sourced from arXiv and standard pedagogical resources. We conduct both Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) experiments, benchmarking performance gains as well as generalization to other physics domains. We perform an extensive analysis of model chains-of-though before and after fine-tuning, to understand how reasoning errors evolve during RL and SFT. Finally, we publicly release our data pipeline, verifiable QFT training data, and sim200M tokens of QFT reasoning traces.

In this work, we explore two classes of density dependent relativistic mean-field models, their predictions of proton fractions at high densities and neutron star structure. We have used a metamodelling approach to these relativistic density functionals. We have generated a large ensemble of models with these classes and then applied constraints from theoretical and experimental nuclear physics and astrophysical observations. We find that both models produce similar equations of state and neutron star mass-radius sequences. But, their underlying compositions, denoted by the proton fraction in this case, are vastly different. This reinstates previous findings that information on composition gets masqueraded in beta-equilibrium. Additional observations of non-equilibrium phenomena are necessary to pin it down.

I propose a Hamiltonian framework for chiral gauge theories (CGT) based on a Euclidean formulation which uses 2n dimensional chiral fermions on the boundary of a 2n+1 dimensional disk. In the original Euclidean formulation, boundary gauge fields were extended into the bulk using 2n + 1 dimensional gauge field equations of motion (EOM) which creates a bottleneck for constructing a Hamiltonian. I present an alternate proposal for extending the gauge fields into the bulk that is compatible with both a Hamiltonian framework and a Euclidean path integral. Applying this to Abelian gauge fields produces exact expressions of interior fields as a functional of the boundary fields, which can be directly used in a Hamiltonian formulation. Euclidean analysis of the new gauge field extension shows that it can preserve the non-perturbative content of the original construction, including the behavior of topological charge, associated chiral fermion zero modes and an absence of the strong CP problem when applied to the Standard Model. This construction opens up a route to a Hamiltonian treatment and future quantum simulation of CGTs on a disk boundary.

We present a novel method for measuring |V_{cb}| at the LHC using an advanced boosted-jet tagger to identify "bc signatures". By associating boosted W rightarrow bc signals with bc-matched jets from top-quark decays, we enable an in-situ calibration of the tagger. This approach significantly suppresses backgrounds while reducing uncertainties in flavor tagging efficiencies -- key to improving measurement precision. Our study is enabled by the development of realistic, AI-based large- and small-radius taggers, Sophon and the newly introduced SophonAK4, validated to match ATLAS and CMS's state-of-the-art taggers. The method complements the conventional small radius jet approach and enables a ~30% improvement in |V_{cb}| precision under HL-LHC projections. As a byproduct, it enhances H^{pm} rightarrow bc search sensitivity by a factor of 2--5 over the recent ATLAS result based on Run 2 data. Our work offers a new perspective for the precision |V_{cb}| measurement and highlights the potential of using advanced tagging models to probe unexplored boosted regimes at the LHC.

Energy-energy correlators are constructed by averaging the number of charged particle pairs within jets, weighted by the product of their transverse momenta, as a function of the angular separation of the particles within a pair. They are sensitive to a multitude of perturbative and nonperturbative quantum chromodynamics phenomena in high-energy particle collisions. Using lead-lead data recorded with the CMS detector, energy-energy correlators inside high transverse momentum jets are measured in heavy ion collisions for the first time. The data are obtained at a nucleon-nucleon center-of-mass energy of 5.02 TeV and correspond to an integrated luminosity of 1.70 nb^{-1}. A similar analysis is done for proton-proton collisions at the same center-of-mass energy to establish a reference. The ratio of lead-lead to proton-proton energy-energy correlators reveals significant jet substructure modifications in the quark-gluon plasma. The results are compared to different models that incorporate either color coherence or medium response effects, where the two effects predict similar substructure modifications.

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the φ^{4} scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the φ^{4} theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the φ^{4} machine learning algorithms and target probability distributions.

We present a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural networks to approximate the solution to the differential equations satisfied by the Feynman integrals. This approach relies neither on a canonical form of the differential equations, which is often a bottleneck for the analytical techniques, nor on the availability of a large dataset, and after training yields essentially instantaneous evaluation times. We provide a proof-of-concept implementation within the PyTorch framework, and apply it to a number of one- and two-loop examples, achieving a mean magnitude of relative difference of around 1% at two loops in the physical phase space with network training times on the order of an hour on a laptop GPU.

We analyse three KV cache quantization schemes under a fair bit budget: KV (scalar MSE baseline), KQV (WHT + MSE on K; WHT + MSE + QJL on V), and QKQV (WHT + MSE + QJL on both). Starting from the Beta distribution on the hypersphere, we trace how QJL on K inflates inner product variance by π/2, which softmax amplifies nonlinearly via Jensen's inequality, and we present statistical inference and information metrics to highlight practical differences. Three empirical findings emerge. (1)~At n=4 (the practically dominant budget), KQV wins on every measure -- KL divergence, geometric K error, and 6D distance -- across all distributions and ranks tested. (2)~The K--V asymmetry is unconditional: QKQV is consistently worse than KQV in KL divergence at every budget and distribution. (3)~A budget-dependent crossover exists: QKQV achieves better geometric K reconstruction at n in {2,3,5}, KQV at n in {4,6}, invariant to rank and tail weight -- an open rate-distortion problem. KL(p_{ref} | p_{quant}), K-only by construction, bridges K direction error to routing corruption and output collapse. We present a sufficient condition when the Jensen mechanism amplifies superlinearly through the softmax. At n in {2,3,5}, QKQV wins geometrically because this assumption does not bind. At n=4, elevated K error and KL divergence for QKQV strongly suggest the Jensen mechanism is the operative cause of the crossover, providing a new perspective and explanation.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

The largest machine learning models in particle physics are also the most expensive to train, yet the return on scaling a given architecture cannot be estimated before that compute is spent. Scaling laws have been fit for jets, but none has yet been shown to predict the performance of models it was not fit on. We show that, for a generic transformer pretrained on collider jets, it can be forecast. Fitting a joint model-and-data scaling law on small models alone, spanning three orders of magnitude of training compute, we predict the loss of models trained afterward with more than one hundred times more compute to within one percent. We then connect the forecast to downstream physics performance: across two standard tagging benchmarks, lower pretraining loss yields systematically lower fine-tuning loss and higher background rejection after fine-tuning. Within this model family and these tasks, a compute budget can therefore be translated into expected physics performance before any large model is trained. The final frontier model is consistent with the published numbers for current state-of-the-art physics-aware foundation models trained on the same corpus, on accuracy, AUC, and quark/gluon rejection, with a residual edge for the physics-aware model only in the high-purity tail of top tagging. We release five pretrained models spanning multiple sizes, together with the complete training recipe and code.

Coexistent phase of kaon condensates and hyperons [(Y+K) phase] in beta equilibrium with electrons and muons is investigated as a possible form of dense hadronic phase with multi-strangeness. The effective chiral Lagrangian for kaon-baryon and kaon-kaon interactions is utilized within chiral symmetry approach in combination with the interaction model between baryons. For the baryon-baryon interactions, we adopt the minimal relativistic mean-field theory with exchange of scalar mesons and vector mesons between baryons without including the nonlinear self-interacting meson field terms. In addition, the universal three-baryon repulsion and the phenomenological three-nucleon attraction are introduced as density-dependent effective two-body potentials. The repulsive effects leading to stiff equation of state at high densities consist of both the two-baryon repulsion via the vector-meson exchange and the universal three-baryon repulsion. Interplay of kaon condensates with hyperons through chiral dynamics in dense matter is clarified, and resulting onset mechanisms of kaon condensation in hyperon-mixed matter and the equation of state with the (Y+K) phase and characteristic features of the system are presented. It is shown that the slope L of the symmetry energy controls the two-baryon repulsion beyond the saturation density and resulting stiffness of the equation of state. The stiffness of the equation of state in turn controls admixture of hyperons and the onset and development of kaon condensates as a result of competing effect between kaon condensates and hyperons. The equation of state with the (Y+K) phase becomes stiff enough to be consistent with recent observations of massive neutron stars. Static properties of neutron stars with the (Y+K) phase are discussed.

We update predictions for observables in the "delicate" D3/anti-D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the zeta power spectrum often cannot be modelled as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction fNL ~ -(5/12)(ns-1) if nt << 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNLeq| ~ 75 at kt/3 = 0.002/Mpc. It has been suggested that the quasi-single field inflation ("QSFI") mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of "shape" running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.

We explore a generative machine learning-based approach for estimating multi-dimensional probability density functions (PDFs) in a target sample using a statistically independent but related control sample - a common challenge in particle physics data analysis. The generative model must accurately reproduce individual observable distributions while preserving the correlations between them, based on the input multidimensional distribution from the control sample. Here we present a conditional normalizing flow model (CNF) based on a chain of bijectors which learns to transform unpaired simulation events to data events. We assess the performance of the CNF model in the context of LHC Higgs to diphoton analysis, where we use the CNF model to convert a Monte Carlo diphoton sample to one that models data. We show that the CNF model can accurately model complex data distributions and correlations. We also leverage the recently popularized Modified Differential Multiplier Method (MDMM) to improve the convergence of our model and assign physical meaning to usually arbitrary loss-function parameters.

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g phi^3 QFT, by using the retarded/advanced (R/A) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping d<4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Sigma_{F}(p_0) does not vanish when |p_0|rightarrowinfty and cannot be split to retarded and advanced parts. In the Glaser--Epstein approach, the causality is repaired in the composite object G_F(p_0)Sigma_{F}(p_0). In the FTP approach, after repairing the vertices, the corresponding composite objects are G_R(p_0)Sigma_{R}(p_0) and Sigma_{A}(p_0)G_A(p_0). In the limit drightarrow 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition langle 0|phi|0rangle =0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit trightarrow infty .

Detector simulation and event reconstruction will be computationally expensive for future e^+e^- collider programs and are currently critical bottlenecks for accurate feasibility studies. To address this challenge, we build a Parnassus model for the CLD detector concept. Parnassus is a framework for automatically tuning a surrogate model, in our case, a conditional flow matching neural network, to emulate a full detector simulation and reconstruction. We train on e^+e^-to Zto qbar q events at s=91.2 GeV processed through a Geant4 simulation of the CLD detector concept and the Pandora particle-flow reconstruction and reproduce single-particle kinematics, particle-IDs, and impact-parameter distributions. We also examine jet- and event-level features, inclusively and split by flavor, and find excellent fidelity, significantly better than the parameterized program Delphes. Furthermore, we train a transformer-based flavor tagger on the reconstructed particle-flow constituents and show that the surrogate preserves the b/c/s/q discrimination of the full CLD reconstruction. The Parnassus CLD model achieves a generation cost of about 1.2 ms (40 ms) per event on a single GPU (CPU), over three (two) orders of magnitude faster than full simulation and reconstruction. Our model is publicly available for feasibility and design studies.

We establish a unified framework for understanding the results on the Weil quadratic form obtained by Yoshida (1992), Bombieri (2001, 2003), Connes--Consani (2023), and Connes--Consani--Moscovici (2025+) from the perspective of the screw function introduced in Suzuki (2023). An advantage of the approach via the screw function is that it provides a method to study the Weil quadratic form, which is originally defined in terms of distributions, by means of continuous functions. Based on this framework, we formulate a conjecture stating that a self-adjoint operator whose eigenvalues are the imaginary parts of the nontrivial zeros of the Riemann zeta function can be obtained as the limit, as a to infty, of self-adjoint operators arising from nonlocal realizations of the first-order differential operator on the finite interval [-a,a]. All these results are obtained without assuming the Riemann Hypothesis. This conjecture may be compared with the limit formula for the Riemann zeta function expressed in terms of zeta-regularized products proposed by Connes, Consani, and Moscovici, and it sheds new light on the spectral-theoretic interpretation of the nontrivial zeros of the Riemann zeta function.

Single-minus tree-level n-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into n-1 plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.

Neural scaling laws describe how model performance improves as a power law in compute, model size, and dataset size. While well-established for large language models, these relationships are emerging for large models in particle physics. As with language, empirical studies show that the performance scales as a power law. However, unlike natural language or image domains, fundamental physics has high-fidelity simulators that produce synthetic data cheaply. This favors scaling regimes where additional data is cheaper than additional parameters, and allows the pretraining dataset itself to be engineered to influence the scaling. For the task of classifying hadronic jets produced in collisions of high-energy particle beams, we show that the scaling behavior can be engineered towards requiring more data rather than larger models by inclusion of pretraining data which is more diverse and better aligned with the downstream classification task.