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21,900 | Because Higgs boson production in a particle collision is likely to be very rare (1 in 10 billion at the LHC), | https://en.wikipedia.org/wiki?curid=20556903 |
21,901 | and many other possible collision events can have similar decay signatures, the data of hundreds of trillions of collisions needs to be analysed and must "show the same picture" before a conclusion about the existence of the Higgs boson can be reached. To conclude that a new particle has been found, particle physicists... | https://en.wikipedia.org/wiki?curid=20556903 |
21,902 | To find the Higgs boson, a powerful particle accelerator was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a high luminosity in order to ensure enough collisions were seen for conclusions to be drawn. Finally, advanced computing facilities were needed to process... | https://en.wikipedia.org/wiki?curid=20556903 |
21,903 | The first extensive search for the Higgs boson was conducted at the Large Electron–Positron Collider (LEP) at CERN in the 1990s. At the end of its service in 2000, LEP had found no conclusive evidence for the Higgs. | https://en.wikipedia.org/wiki?curid=20556903 |
21,904 | The search continued at Fermilab in the United States, where the Tevatron the collider that discovered the top quark in 1995 – had been upgraded for this purpose. There was no guarantee that the Tevatron would be able to find the Higgs, but it was the only supercollider that was operational since the Large Hadron Colli... | https://en.wikipedia.org/wiki?curid=20556903 |
21,905 | The Large Hadron Collider at CERN in Switzerland, was designed specifically to be able to either confirm or exclude the existence of the Higgs boson. Built in a 27 km tunnel under the ground near Geneva originally inhabited by LEP, it was designed to collide two beams of protons, initially at energies of per beam (7 Te... | https://en.wikipedia.org/wiki?curid=20556903 |
21,906 | Data collection at the LHC finally commenced in March 2010. By December 2011 the two main particle detectors at the LHC, ATLAS and CMS, had narrowed down the mass range where the Higgs could exist to around (ATLAS) and (CMS). There had also already been a number of promising event excesses that had "evaporated" and pro... | https://en.wikipedia.org/wiki?curid=20556903 |
21,907 | On 22 June 2012 CERN announced an upcoming seminar covering tentative findings for 2012, and shortly afterwards (from around 1 July 2012 according to an analysis of the spreading rumour in social media) rumours began to spread in the media that this would include a major announcement, but it was unclear whether this wo... | https://en.wikipedia.org/wiki?curid=20556903 |
21,908 | On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery: CMS of a previously unknown boson with mass and ATLAS of a boson with mass . Using the combined analysis of two interaction types (known as 'channels'), both experiments independently reached a local significance of 5 ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,909 | The two teams had been working 'blinded' from each other from around late 2011 or early 2012, meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle. This level of evidence, confirmed independently by two separate teams and... | https://en.wikipedia.org/wiki?curid=20556903 |
21,910 | On 31 July 2012, the ATLAS collaboration presented additional data analysis on the "observation of a new particle", including data from a third channel, which improved the significance to 5.9 sigma (1 in 588 million chance of obtaining at least as strong evidence by random background effects alone) and mass , and CMS i... | https://en.wikipedia.org/wiki?curid=20556903 |
21,911 | Following the 2012 discovery, it was still unconfirmed whether the particle was a Higgs boson. On one hand, observations remained consistent with the observed particle being the Standard Model Higgs boson, and the particle decayed into at least some of the predicted channels. Moreover, the production rates and branchin... | https://en.wikipedia.org/wiki?curid=20556903 |
21,912 | In November 2012, in a conference in Kyoto researchers said evidence gathered since July was falling into line with the basic Standard Model more than its alternatives, with a range of results for several interactions matching that theory's predictions. Physicist Matt Strassler highlighted "considerable" evidence that ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,913 | These findings meant that as of January 2013, scientists were very sure they had found an unknown particle of mass ~, and had not been misled by experimental error or a chance result. They were also sure, from initial observations, that the new particle was some kind of boson. The behaviours and properties of the parti... | https://en.wikipedia.org/wiki?curid=20556903 |
21,914 | In January 2013, CERN director-general Rolf-Dieter Heuer stated that based on data analysis to date, an answer could be possible 'towards' mid-2013, and the deputy chair of physics at Brookhaven National Laboratory stated in February 2013 that a "definitive" answer might require "another few years" after the . In early... | https://en.wikipedia.org/wiki?curid=20556903 |
21,915 | CMS and ATLAS have compared a number of options for the spin-parity of this particle, and these all prefer no spin and even parity [two fundamental criteria of a Higgs boson consistent with the Standard Model]. This, coupled with the measured interactions of the new particle with other particles, strongly indicates tha... | https://en.wikipedia.org/wiki?curid=20556903 |
21,916 | In July 2017, CERN confirmed that all measurements still agree with the predictions of the Standard Model, and called the discovered particle simply "the Higgs boson". As of 2019, the Large Hadron Collider has continued to produce findings that confirm the 2013 understanding of the Higgs field and particle. | https://en.wikipedia.org/wiki?curid=20556903 |
21,917 | The LHC's experimental work since restarting in 2015 has included probing the Higgs field and boson to a greater level of detail, and confirming whether less common predictions were correct. In particular, exploration since 2015 has provided strong evidence of the predicted direct decay into fermions such as pairs of b... | https://en.wikipedia.org/wiki?curid=20556903 |
21,918 | In July 2018, the ATLAS and CMS experiments reported observing the Higgs boson decay into a pair of bottom quarks, which makes up approximately 60% of all of its decays. | https://en.wikipedia.org/wiki?curid=20556903 |
21,919 | Gauge invariance is an important property of modern particle theories such as the Standard Model, partly due to its success in other areas of fundamental physics such as electromagnetism and the strong interaction (quantum chromodynamics). However, before Sheldon Glashow extended the electroweak unification models in 1... | https://en.wikipedia.org/wiki?curid=20556903 |
21,920 | W and Z bosons are observed to have mass, but a boson mass term contains terms which clearly depend on the choice of gauge, and therefore these masses too cannot be gauge invariant. Therefore, it seems that "none" of the standard model fermions "or" bosons could "begin" with mass as an inbuilt property except by abando... | https://en.wikipedia.org/wiki?curid=20556903 |
21,921 | Additionally, solutions based on spontaneous symmetry breaking appeared to fail, seemingly an inevitable result of Goldstone's theorem. Because there is no potential energy cost to moving around the complex plane's "circular valley" responsible for spontaneous symmetry breaking, the resulting quantum excitation is pure... | https://en.wikipedia.org/wiki?curid=20556903 |
21,922 | A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone's theorem, | https://en.wikipedia.org/wiki?curid=20556903 |
21,923 | that under certain conditions it "might" theoretically be possible for a symmetry to be broken "without" disrupting gauge invariance and "without" any new massless particles or forces, and having "sensible" (renormalisable) results mathematically. This became known as the Higgs mechanism. | https://en.wikipedia.org/wiki?curid=20556903 |
21,924 | The Standard Model hypothesises a field which is responsible for this effect, called the Higgs field (symbol: formula_1), which has the unusual property of a non-zero amplitude in its ground state; i.e., a non-zero vacuum expectation value. It can have this effect because of its unusual "Mexican hat" shaped potential w... | https://en.wikipedia.org/wiki?curid=20556903 |
21,925 | The proposed Higgs mechanism arose as a result of theories proposed to explain observations in superconductivity. A superconductor does not allow penetration by external magnetic fields (the Meissner effect). This strange observation implies that somehow, the electromagnetic field becomes short ranged during this pheno... | https://en.wikipedia.org/wiki?curid=20556903 |
21,926 | In these theories, superconductivity is interpreted as arising from a charged condensate field. Initially, the condensate value does not have any preferred direction, implying it is scalar, but its phase is capable of defining a gauge, in gauge based field theories. To do this, the field must be charged. A charged scal... | https://en.wikipedia.org/wiki?curid=20556903 |
21,927 | Once attention was drawn to this theory within particle physics, the parallels were clear. A change of the usually long range electromagnetic field to become short ranged, within a gauge invariant theory, was exactly the needed effect sought for the weak force bosons (because a long range force has massless gauge boson... | https://en.wikipedia.org/wiki?curid=20556903 |
21,928 | The Minimal Standard Model as described above is the simplest known model for the Higgs mechanism with just one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector f... | https://en.wikipedia.org/wiki?curid=20556903 |
21,929 | The key method to distinguish between these different models involves study of the particles' interactions ("coupling") and exact decay processes ("branching ratios"), which can be measured and tested experimentally in particle collisions. In the Type-I 2HDM model one Higgs doublet couples to up and down quarks, while ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,930 | In other models the Higgs scalar is a composite particle. For example, in technicolour the role of the Higgs field is played by strongly bound pairs of fermions called techniquarks. Other models feature pairs of top quarks (see top quark condensate). In yet other models, there is no Higgs field at all and the electrowe... | https://en.wikipedia.org/wiki?curid=20556903 |
21,931 | The Standard Model leaves the mass of the Higgs boson as a parameter to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions with virtual particles) should apparently cause the Higgs particle to have a mass immensel... | https://en.wikipedia.org/wiki?curid=20556903 |
21,932 | There are also issues of quantum triviality, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles. However, if quantum triviality is avoided, triviality constraints may set bounds on the Higgs Boson mass. | https://en.wikipedia.org/wiki?curid=20556903 |
21,933 | In the Standard Model, the Higgs field is a scalar tachyonic field "scalar" meaning it does not transform under Lorentz transformations, and "tachyonic" meaning the field (but not the particle) has imaginary mass, and in certain configurations must undergo symmetry breaking. It consists of four components: Two neutral ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,934 | Mathematically, the Higgs field has imaginary mass and is therefore a "tachyonic" field. While tachyons (particles that move faster than light) are a purely hypothetical concept, "fields" with imaginary mass have come to play an important role in modern physics. Under no circumstances do any excitations ever propagate ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,935 | Although the notion of imaginary mass might seem troubling, it is only the field, and not the mass itself, that is quantised. Therefore, the field operators at spacelike separated points still commute (or anticommute), and information and particles still do not propagate faster than light. Tachyon condensation drives a... | https://en.wikipedia.org/wiki?curid=20556903 |
21,936 | Since the Higgs field is scalar, the Higgs boson has no spin. The Higgs boson is also its own antiparticle, is CP-even, and has zero electric and colour charge. | https://en.wikipedia.org/wiki?curid=20556903 |
21,937 | The Standard Model does not predict the mass of the Higgs boson. If that mass is between (consistent with empirical observations of ), then the Standard Model can be valid at energy scales all the way up to the Planck scale (). It should be the only particle in the Standard Model that remains massive even at high energ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,938 | The highest possible mass scale allowed for the Higgs boson (or some other electroweak symmetry breaking mechanism) is 1.4 TeV; beyond this point, the Standard Model becomes inconsistent without such a mechanism, because unitarity is violated in certain scattering processes. | https://en.wikipedia.org/wiki?curid=20556903 |
21,939 | It is also possible, although experimentally difficult, to estimate the mass of the Higgs boson indirectly: In the Standard Model, the Higgs boson has a number of indirect effects; most notably, Higgs loops result in tiny corrections to masses of the W and Z bosons. Precision measurements of electroweak parameters, suc... | https://en.wikipedia.org/wiki?curid=20556903 |
21,940 | The LHC cannot directly measure the Higgs boson's lifetime, due to its extreme brevity. It is predicted as based on the predicted decay width of . However it can be measured indirectly, based upon comparing masses measured from quantum phenomena occurring in the on shell production pathways and in the, much rarer, off ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,941 | If Higgs particle theories are valid, then a Higgs particle can be produced much like other particles that are studied, in a particle collider. This involves accelerating a large number of particles to extremely high energies and extremely close to the speed of light, then allowing them to smash together. Protons and l... | https://en.wikipedia.org/wiki?curid=20556903 |
21,942 | Quantum mechanics predicts that if it is possible for a particle to decay into a set of lighter particles, then it will eventually do so. This is also true for the Higgs boson. The likelihood with which this happens depends on a variety of factors including: the difference in mass, the strength of the interactions, etc... | https://en.wikipedia.org/wiki?curid=20556903 |
21,943 | Since it interacts with all the massive elementary particles of the SM, the Higgs boson has many different processes through which it can decay. Each of these possible processes has its own probability, expressed as the "branching ratio"; the fraction of the total number decays that follows that process. The SM predict... | https://en.wikipedia.org/wiki?curid=20556903 |
21,944 | One way that the Higgs can decay is by splitting into a fermion–antifermion pair. As general rule, the Higgs is more likely to decay into heavy fermions than light fermions, because the mass of a fermion is proportional to the strength of its interaction with the Higgs. By this logic the most common decay should be int... | https://en.wikipedia.org/wiki?curid=20556903 |
21,945 | Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 21.5% of the time for a Higgs boson with a mass of . The W bosons can subsequently decay either into a q... | https://en.wikipedia.org/wiki?curid=20556903 |
21,946 | Decay into massless gauge bosons (i.e., gluons or photons) is also possible, but requires intermediate loop of virtual heavy quarks (top or bottom) or massive gauge bosons. The most common such process is the decay into a pair of gluons through a loop of virtual heavy quarks. This process, which is the reverse of the g... | https://en.wikipedia.org/wiki?curid=20556903 |
21,947 | In 2021 the extremely rare Dalitz decay was tentatively observed, into two leptons (electrons or muons) and a photon (ℓℓγ), via virtual photon decay. This can happen in three ways; Higgs to virtual photon to ℓℓγ in which the virtual photon (γ*) has very small but nonzero mass, Higgs to Z boson to ℓℓγ, or Higgs to two l... | https://en.wikipedia.org/wiki?curid=20556903 |
21,948 | The name most strongly associated with the particle and field is the Higgs boson and Higgs field. For some time the particle was known by a combination of its PRL author names (including at times Anderson), for example the Brout–Englert–Higgs particle, the Anderson–Higgs particle, or the Englert–Brout–Higgs–Guralnik–Ha... | https://en.wikipedia.org/wiki?curid=20556903 |
21,949 | Higgs himself prefers to call the particle either by an acronym of all those involved, or "the scalar boson", or "the so-called Higgs particle". | https://en.wikipedia.org/wiki?curid=20556903 |
21,950 | A considerable amount has been written on how Higgs' name came to be exclusively used. Two main explanations are offered. The first is that Higgs undertook a step which was either unique, clearer or more explicit in his paper in formally predicting and examining the particle. Of the PRL papers' authors, only the paper ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,951 | Physicist and author Frank Close and physicist-blogger Peter Woit both comment that the paper by GHK was also completed after Higgs and Brout–Englert were submitted to Physical Review Letters, | https://en.wikipedia.org/wiki?curid=20556903 |
21,952 | and that Higgs alone had drawn attention to a predicted massive "scalar" boson, while all others had focused on the massive "vector" bosons. | https://en.wikipedia.org/wiki?curid=20556903 |
21,953 | In this way, Higgs' contribution also provided experimentalists with a crucial "concrete target" needed to test the theory. | https://en.wikipedia.org/wiki?curid=20556903 |
21,954 | However, in Higgs' view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work, while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whose mathematical rigour is absent from the other two papers, and a massive p... | https://en.wikipedia.org/wiki?curid=20556903 |
21,955 | The alternative explanation is that the name was popularised in the 1970s due to its use as a convenient shorthand or because of a mistake in citing. Many accounts including Higgs' own credit the "Higgs" name to physicist Benjamin Lee. | https://en.wikipedia.org/wiki?curid=20556903 |
21,956 | Lee was a significant populariser of the theory in its early days, and habitually attached the name "Higgs" as a "convenient shorthand" for its components from 1972. | https://en.wikipedia.org/wiki?curid=20556903 |
21,957 | and in at least one instance from as early as 1966. Although Lee clarified in his footnotes that "'Higgs' is an abbreviation for Higgs, Kibble, Guralnik, Hagen, Brout, Englert", | https://en.wikipedia.org/wiki?curid=20556903 |
21,958 | his use of the term (and perhaps also Steven Weinberg's mistaken cite of Higgs' paper as the first in his seminal 1967 paper | https://en.wikipedia.org/wiki?curid=20556903 |
21,959 | ) meant that by around 1975–1976 others had also begun to use the name 'Higgs' exclusively as a shorthand. | https://en.wikipedia.org/wiki?curid=20556903 |
21,960 | In 2012, physicist Frank Wilczek, who was credited for naming the elementary particle, the axion (over an alternative proposal "Higglet", by Weinberg), endorsed the "Higgs boson" name, stating "History is complicated, and wherever you draw the line, there will be somebody just below it." | https://en.wikipedia.org/wiki?curid=20556903 |
21,961 | The Higgs boson is often referred to as the "God particle" in popular media outside the scientific community. | https://en.wikipedia.org/wiki?curid=20556903 |
21,962 | The nickname comes from the title of the 1993 book on the Higgs boson and particle physics, "" by Physics Nobel Prize winner and Fermilab director Leon Lederman. | https://en.wikipedia.org/wiki?curid=20556903 |
21,963 | Lederman wrote it in the context of failing US government support for the Superconducting Super Collider, a partially constructed titanic | https://en.wikipedia.org/wiki?curid=20556903 |
21,964 | competitor to the Large Hadron Collider with planned collision energies of that was championed by Lederman since its 1983 inception | https://en.wikipedia.org/wiki?curid=20556903 |
21,965 | and shut down in 1993. The book sought in part to promote awareness of the significance and need for such a project in the face of its possible loss of funding. | https://en.wikipedia.org/wiki?curid=20556903 |
21,966 | Lederman, a leading researcher in the field, writes that he wanted to title his book "The Goddamn Particle: If the Universe is the Answer, What is the Question?" Lederman's editor decided that the title was too controversial and convinced him to change the title to "The God Particle: If the Universe is the Answer, What... | https://en.wikipedia.org/wiki?curid=20556903 |
21,967 | the particle also has nothing to do with any God, leaves open numerous questions in fundamental physics, and does not explain the ultimate origin of the universe. Higgs, an atheist, was reported to be displeased and stated in a 2008 interview that he found it "embarrassing" because it was "the kind of misuse ... which ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,968 | Science writer Ian Sample stated in his 2010 book on the search that the nickname is "universally hate[d]" by physicists and perhaps the "worst derided" in the history of physics, but that (according to Lederman) the publisher rejected all titles mentioning "Higgs" as unimaginative and too unknown. | https://en.wikipedia.org/wiki?curid=20556903 |
21,969 | Lederman begins with a review of the long human search for knowledge, and explains that his tongue-in-cheek title draws an analogy between the impact of the Higgs field on the fundamental symmetries at the Big Bang, and the apparent chaos of structures, particles, forces and interactions that resulted and shaped our pr... | https://en.wikipedia.org/wiki?curid=20556903 |
21,970 | Today ... we have the standard model, which reduces all of reality to a dozen or so particles and four forces ... It's a hard-won simplicity [...and...] remarkably accurate. But it is also incomplete and, in fact, internally inconsistent ... This boson is so central to the state of physics today, so crucial to our fina... | https://en.wikipedia.org/wiki?curid=20556903 |
21,971 | Lederman asks whether the Higgs boson was added just to perplex and confound those seeking knowledge of the universe, and whether physicists will be confounded by it as recounted in that story, or ultimately surmount the challenge and understand "how beautiful is the universe [God has] made". | https://en.wikipedia.org/wiki?curid=20556903 |
21,972 | A renaming competition by British newspaper "The Guardian" in 2009 resulted in their science correspondent choosing the name "the champagne bottle boson" as the best submission: "The bottom of a champagne bottle is in the shape of the Higgs potential and is often used as an illustration in physics lectures. So it's not... | https://en.wikipedia.org/wiki?curid=20556903 |
21,973 | The name "Higgson" was suggested as well, in an opinion piece in the Institute of Physics' online publication "physicsworld.com". | https://en.wikipedia.org/wiki?curid=20556903 |
21,974 | There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass, | https://en.wikipedia.org/wiki?curid=20556903 |
21,975 | including coverage of explanatory attempts in their own right and a competition in 1993 for the best popular explanation by then-UK Minister for Science Sir William Waldegrave | https://en.wikipedia.org/wiki?curid=20556903 |
21,976 | An educational collaboration involving an LHC physicist and a High School Teachers at CERN educator suggests that dispersion of light responsible for the rainbow and dispersive prism is a useful analogy for the Higgs field's symmetry breaking and mass-causing effect. | https://en.wikipedia.org/wiki?curid=20556903 |
21,977 | The Higgs field's effect on particles was famously described by physicist David Miller as akin to a room full of political party workers spread evenly throughout a room: The crowd gravitates to and slows down famous people but does not slow down others. | https://en.wikipedia.org/wiki?curid=20556903 |
21,978 | He also drew attention to well-known effects in solid state physics where an electron's effective mass can be much greater than usual in the presence of a crystal lattice. | https://en.wikipedia.org/wiki?curid=20556903 |
21,979 | Analogies based on drag effects, including analogies of "syrup" or "molasses" are also well known, but can be somewhat misleading since they may be understood (incorrectly) as saying that the Higgs field simply resists some particles' motion but not others' a simple resistive effect could also conflict with Newton's th... | https://en.wikipedia.org/wiki?curid=20556903 |
21,980 | There was considerable discussion prior to late 2013 of how to allocate the credit if the Higgs boson is proven, made more pointed as a Nobel prize had been expected, and the very wide basis of people entitled to consideration. These include a range of theoreticians who made the Higgs mechanism theory possible, the the... | https://en.wikipedia.org/wiki?curid=20556903 |
21,981 | Englert's co-researcher Robert Brout had died in 2011 and the Nobel Prize is not ordinarily given posthumously. | https://en.wikipedia.org/wiki?curid=20556903 |
21,982 | Additionally Physical Review Letters' 50-year review (2008) recognised the 1964 PRL symmetry breaking papers and Weinberg's 1967 paper "A model of Leptons" (the most cited paper in particle physics, as of 2012) "milestone Letters". | https://en.wikipedia.org/wiki?curid=20556903 |
21,983 | Following reported observation of the Higgs-like particle in July 2012, several Indian media outlets reported on the supposed neglect of credit to Indian physicist Satyendra Nath Bose after whose work in the 1920s the class of particles "bosons" is named | https://en.wikipedia.org/wiki?curid=20556903 |
21,984 | In the Standard Model, the Higgs field is a four-component scalar field that forms a complex doublet of the weak isospin SU(2) symmetry: | https://en.wikipedia.org/wiki?curid=20556903 |
21,985 | where formula_4 and formula_5 are the gauge bosons of the SU(2) and U(1) symmetries, formula_6 and formula_7 their respective coupling constants, formula_8 are the Pauli matrices (a complete set generators of the SU(2) symmetry), and formula_9 and formula_10, so that the ground state breaks the SU(2) symmetry (see figu... | https://en.wikipedia.org/wiki?curid=20556903 |
21,986 | The ground state of the Higgs field (the bottom of the potential) is degenerate with different ground states related to each other by a SU(2) gauge transformation. It is always possible to pick a gauge such that in the ground state formula_11. The expectation value of formula_12 in the ground state (the vacuum expectat... | https://en.wikipedia.org/wiki?curid=20556903 |
21,987 | with their ratio determining the Weinberg angle, formula_18, and leave a massless U(1) photon, formula_19. The mass of the Higgs boson itself is given by | https://en.wikipedia.org/wiki?curid=20556903 |
21,988 | where formula_22 are left-handed and right-handed quarks and leptons of the th generation, formula_23 are matrices of Yukawa couplings where h.c. denotes the hermitian conjugate of all the preceding terms. In the symmetry breaking ground state, only the terms containing formula_12 remain, giving rise to mass terms for ... | https://en.wikipedia.org/wiki?curid=20556903 |
21,989 | where the masses of the fermions are formula_26, and formula_27 denote the eigenvalues of the Yukawa matrices. | https://en.wikipedia.org/wiki?curid=20556903 |
21,990 | Economics () is the social science that studies the production, distribution, and consumption of goods and services. | https://en.wikipedia.org/wiki?curid=9223 |
21,991 | Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, fi... | https://en.wikipedia.org/wiki?curid=9223 |
21,992 | Other broad distinctions within economics include those between positive economics, describing "what is", and normative economics, advocating "what ought to be"; between economic theory and applied economics; between rational and behavioural economics; and between mainstream economics and heterodox economics. | https://en.wikipedia.org/wiki?curid=9223 |
21,993 | Economic analysis can be applied throughout society, including business, finance, health care, engineering and government. It is also applied to such diverse subjects as crime, education, the family, feminism, law, philosophy, politics, religion, social institutions, war, science, and the environment. | https://en.wikipedia.org/wiki?curid=9223 |
21,994 | The earlier term for the discipline was 'political economy', but since the late 19th century, it has commonly been called 'economics'. The term is derived from the Ancient Greek ("oikonomikos"), "practiced in the management of a household or family" and therefore "frugal, thrifty", which in turn comes from ("oikonomia"... | https://en.wikipedia.org/wiki?curid=9223 |
21,995 | There are a variety of modern definitions of economics; some reflect evolving views of the subject or different views among economists. Scottish philosopher Adam Smith (1776) defined what was then called political economy as "an inquiry into the nature and causes of the wealth of nations", in particular as: | https://en.wikipedia.org/wiki?curid=9223 |
21,996 | Jean-Baptiste Say (1803), distinguishing the subject from its public-policy uses, defined it as the science "of" production, distribution, and consumption of wealth. On the satirical side, Thomas Carlyle (1849) coined "the dismal science" as an epithet for classical economics, in this context, commonly linked to the pe... | https://en.wikipedia.org/wiki?curid=9223 |
21,997 | Alfred Marshall provided a still widely cited definition in his textbook "Principles of Economics" (1890) that extended analysis beyond wealth and from the societal to the microeconomic level: | https://en.wikipedia.org/wiki?curid=9223 |
21,998 | Lionel Robbins (1932) developed implications of what has been termed "[p]erhaps the most commonly accepted current definition of the subject": | https://en.wikipedia.org/wiki?curid=9223 |
21,999 | Robbins described the definition as not "classificatory" in "pick[ing] out certain "kinds" of behaviour" but rather "analytical" in "focus[ing] attention on a particular "aspect" of behaviour, the form imposed by the influence of scarcity." He affirmed that previous economists have usually centred their studies on the ... | https://en.wikipedia.org/wiki?curid=9223 |
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