In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann, who dubbed them "quarks" in a concise paper, and George Zweig, who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation. Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, dubbed the Standard Model.
Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the quantum numbers of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the Poincaré symmetry—JPC, where J, P and C stand for the total angular momentum, P-symmetry, and C-symmetry, respectively.
The remaining are flavor quantum numbers such as the isospin, strangeness, charm, and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet.
All quarks are assigned a baryon number of ⅓. Up, charm and top quarks have an electric charge of +⅔, while the down, strange, and bottom quarks have an electric charge of −⅓. Antiquarks have the opposite quantum numbers. Quarks are spin-½ particles, and thus fermions. Each quark or antiquark obeys the Gell-Mann−Nishijima formula individually, so any additive assembly of them will as well.
Mesons are made of a valence quark−antiquark pair (thus have a baryon number of 0), while baryons are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor SU(3) symmetry). There are generalizations to larger number of flavors.
Developing classification schemes for hadrons became a timely question after new experimental techniques uncovered so many of them, that it became clear that they could not all be elementary. These discoveries led Wolfgang Pauli to exclaim "Had I foreseen that, I would have gone into botany." and Enrico Fermi to advise his student Leon Lederman: "Young man, if I could remember the names of these particles, I would have been a botanist." These new schemes earned Nobel prizes for experimental particle physicists, including Luis Alvarez, who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the "zoo" at hand. Several early proposals, such as the ones by Enrico Fermi and Chen-Ning Yang (1949), and the Sakata model (1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data.
The Gell-Mann–Nishijima formula, developed by Murray Gell-Mann and Kazuhiko Nishijima, led to the Eightfold Way classification, invented by Gell-Mann, with important independent contributions from Yuval Ne'eman, in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The Gell-Mann–Okubo mass formula systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the explicit symmetry breaking of SU(3).
baryon, a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at Brookhaven National Laboratory, Gell-Mann received a Nobel prize in physics for his work on the Eightfold Way, in 1969.
Finally, in 1964, Gell-Mann, and, independently, George Zweig, discerned what the Eightfold Way picture encodes. They posited elementary fermionic constituents, unobserved, and possibly unobservable in a free form, underlying and elegantly encoding the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks.
It would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See Quarks). Counter-intuitively, they cannot ever be observed in isolation (color confinement), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of quantum chromodynamics, the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them.
The Eightfold Way classification is named after the following fact. If we take three flavors of quarks, then the quarks lie in the fundamental representation, 3 (called the triplet) of flavor SU(3). The antiquarks lie in the complex conjugate representation 3. The nine states (nonet) made out of a pair can be decomposed into the trivial representation, 1 (called the singlet), and the adjoint representation, 8 (called the octet). The notation for this decomposition is
Figure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory includes consideration of the symmetry breaking induced by the quark mass differences, and considerations of mixing between various multiplets (such as the octet and the singlet).
N.B. Nevertheless, the mass splitting between the
is larger than the quark model can accommodate, and this "
puzzle" has its origin in topological peculiarities of the strong interaction vacuum, such as instanton configurations.
If P = (−1)J, then it follows that S = 1, thus PC= 1. States with these quantum numbers are called natural parity states; while all other quantum numbers are thus called exotic (for example the state JPC = 0−−).
Since quarks are fermions, the spin-statistics theorem implies that the wavefunction of a baryon must be antisymmetric under exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is
The decuplet is symmetric in flavor, the singlet antisymmetric and the two octets have mixed symmetry. The space and spin parts of the states are thereby fixed once the orbital angular momentum is given.
It is sometimes useful to think of the basis states of quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor SU(6). In terms of this, the decomposition is
The 56 states with symmetric combination of spin and flavour decompose under flavor SU(3) into
where the superscript denotes the spin, S, of the baryon. Since these states are symmetric in spin and flavor, they should also be symmetric in space—a condition that is easily satisfied by making the orbital angular momentum L = 0. These are the ground state baryons.
The S = 1⁄2 octet baryons are the two nucleons (
), the three Sigmas (
), the two Xis (
), and the Lambda (
). The S = 3⁄2 decuplet baryons are the four Deltas (
), three Sigmas (
), two Xis (
), and the Omega (
For example, the constituent quark model wavefunction for the proton is
Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully.
Color quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin S = 3⁄2 baryon, the
, required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wave function, (due to the Pauli exclusion principle), unless there were a hidden quantum number. Oscar Greenberg noted this problem in 1964, suggesting that quarks should be para-fermions.
Instead, six months later, Moo-Young Han and Yoichiro Nambu suggested the existence of three triplets of quarks to solve this problem, but flavor and color intertwined in that model: They did not commute.
While the quark model is derivable from the theory of quantum chromodynamics, the structure of hadrons is more complicated than this model allows. The full quantum mechanical wave function of any hadron must include virtual quark pairs as well as virtual gluons, and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the glueballs (which contain only valence gluons), hybrids (which contain valence quarks as well as gluons) and "exotic hadrons" (such as tetraquarks or pentaquarks).
In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was awarded the 2008 Nobel prize in physics for describing this phenomenon ("for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics").Constituent quark
A constituent quark is a current quark with a notional "covering" induced by the renormalization group.
In the low energy limit of QCD, a description by means of perturbation theory is not possible: Here, no asymptotic freedom exists, but collective interactions between valence quarks and sea quarks gain strongly in significance. Part of the effects of virtual quarks and virtual gluons in the 'sea' can be assigned to a quark so well, that the term 'constituent quark' can serve as an effective description of the low energy system.
Constituent quarks appear like 'dressed' current quarks, i.e. current quarks surrounded by a cloud of virtual quarks and gluons. This cloud, in the end, underlies the large constituent-quark masses.
Definition: Constituent quarks are valence quarks for which the correlations for the description of hadrons by means of gluons and sea-quarks are put into effective quark masses of these valence quarks.
The effective quark mass is called constituent quark mass. Hadrons consist of 'glued' constituent quarks.Delta baryon
The Delta baryons (or Δ baryons, also called Delta resonances) are a family of subatomic particle made of three up or down quarks (u or d quarks).
Four closely related Δ baryons exist: Δ++ (constituent quarks: uuu), Δ+ (uud), Δ0 (udd), and Δ− (ddd), which respectively carry an electric charge of +2 e, +1 e, 0 e, and −1 e. The Δ baryons have a mass of about 1232 MeV/c2, a spin of 3⁄2, and an isospin of 3⁄2. Ordinary protons and neutrons (nucleons (symbol N)), by contrast, have a mass of about 939 MeV/c2, a spin of 1⁄2, and an isospin of 1⁄2. The Δ+ (uud) and Δ0 (udd) particles are the higher-mass excitations of the proton (N+, uud) and neutron (N0, udd), respectively. However, the Δ++ and Δ− have no direct nucleon analogues.
The states were established experimentally at the University of Chicago cyclotron and the Carnegie Institute of Technology synchro-cyclotron in the mid-1950s using accelerated positive pions on hydrogen targets. The existence of the Δ++, with its unusual +2 charge, was a crucial clue in the development of the quark model.
The Delta states discussed here are only the lowest-mass quantum excitations of the proton and neutron. At higher masses, additional Delta states appear, all defined by having 3⁄2 units of isospin, but with a spin quantum numbers including 1⁄2, 3⁄2, 5⁄2, ... 11⁄2. A complete listing of all properties of all these states can be found in Beringer et al (2013).There also exist antiparticle Delta states with opposite charges, made up of the corresponding antiquarks.Down quark
The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up quarks, one down quark) of atomic nuclei. It is part of the first generation of matter, has an electric charge of −1/3 e and a bare mass of 4.7+0.5−0.3 MeV/c2. Like all quarks, the down quark is an elementary fermion with spin 1/2, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong interactions. The antiparticle of the down quark is the down antiquark (sometimes called antidown quark or simply antidown), which differs from it only in that some of its properties have equal magnitude but opposite sign.
Its existence (along with that of the up and strange quarks) was postulated in 1964 by Murray Gell-Mann and George Zweig to explain the Eightfold Way classification scheme of hadrons. The down quark was first observed by experiments at the Stanford Linear Accelerator Center in 1968.Eightfold way (physics)
In physics, the eightfold way is an organizational scheme for a class of subatomic particles known as hadrons that led to the development of the quark model. American physicist Murray Gell-Mann and Israeli physicist Yuval Ne'eman both proposed the idea in 1961. The name comes from Gell-Mann's 1961 paper and is an allusion to the Noble Eightfold Path of Buddhism.Exotic meson
Non-quark model mesons include:
exotic mesons, which have quantum numbers not possible for mesons in the quark model;
glueballs or gluonium, which have no valence quarks at all;
tetraquarks, which have two valence quark-antiquark pairs; and
hybrid mesons, which contain a valence quark-antiquark pair and one or more gluons.All of these can be classed as mesons, because they are hadrons and carry zero baryon number. Of these, glueballs must be flavor singlets; that is, have zero isospin, strangeness, charm, bottomness, and topness. Like all particle states, they are specified by the quantum numbers which label representations of the Poincaré symmetry, q.e., JPC (where J is the angular momentum, P is the intrinsic parity, and C is the charge conjugation parity) and by the mass. One also specifies the isospin I of the meson. Typically, every quark model meson comes in SU(3) flavor nonet: an octet and a flavor singlet. A glueball shows up as an extra (supernumerary) particle outside the nonet.
In spite of such seemingly simple counting, the assignment of any given state as a glueball, tetraquark, or hybrid remains tentative even today. Even when there is agreement that one of several states is one of these non-quark model mesons, the degree of mixing, and the precise assignment is fraught with uncertainties. There is also the considerable experimental labor of assigning quantum numbers to each state and crosschecking them in other experiments. As a result, all assignments outside the quark model are tentative. The remainder of this article outlines the situation as it stood at the end of 2004.George Zweig
George Zweig (; born May 30, 1937) is a Russian-American physicist. He was trained as a particle physicist under Richard Feynman. He introduced, independently of Murray Gell-Mann, the quark model (although he named it "aces"). He later turned his attention to neurobiology. He has worked as a Research Scientist at Los Alamos National Laboratory and MIT, and in the financial services industry.GlueX
GlueX is a particle physics experiment located at the Thomas Jefferson National Accelerator Facility (JLab) accelerator. Its primary purpose is to better understand the nature of confinement in quantum chromodynamics (QCD) by identifying a spectrum of hybrid and exotic mesons generated by the excitation of the gluonic field binding the quarks. Such mesonic states are predicted to exist outside of the well-established quark model, but none have been definitively identified by previous experiments. A broad high-statistics survey of known light mesons up to and including the is also underway.Henry Way Kendall
Henry Way Kendall (December 9, 1926 – February 15, 1999) was an American particle physicist who won the Nobel Prize in Physics in 1990 jointly with Jerome Isaac Friedman and Richard E. Taylor "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics."Kaon
In particle physics, a kaon , also called a K meson and denoted K, is any of a group of four mesons distinguished by a quantum number called strangeness. In the quark model they are understood to be bound states of a strange quark (or antiquark) and an up or down antiquark (or quark).
Kaons have proved to be a copious source of information on the nature of fundamental interactions since their discovery in cosmic rays in 1947. They were essential in establishing the foundations of the Standard Model of particle physics, such as the quark model of hadrons and the theory of quark mixing (the latter was acknowledged by a Nobel Prize in Physics in 2008). Kaons have played a distinguished role in our understanding of fundamental conservation laws: CP violation, a phenomenon generating the observed matter–antimatter asymmetry of the universe, was discovered in the kaon system in 1964 (which was acknowledged by a Nobel Prize in 1980). Moreover, direct CP violation was discovered in the kaon decays in the early 2000s by the NA48 experiment at CERN and the KTeV experiment at Fermilab.Neutron magnetic moment
The neutron magnetic moment is the intrinsic magnetic dipole moment of the neutron, symbol μn. Protons and neutrons, both nucleons, comprise the nucleus of atoms, and both nucleons behave as small magnets whose strengths are measured by their magnetic moments. The neutron interacts with normal matter through either the nuclear force or its magnetic moment. The neutron's magnetic moment is exploited to probe the atomic structure of materials using scattering methods and to manipulate the properties of neutron beams in particle accelerators. The neutron was determined to have a magnetic moment by indirect methods in the mid 1930s. Luis Alvarez and Felix Bloch made the first accurate, direct measurement of the neutron's magnetic moment in 1940. The existence of the neutron's magnetic moment indicates the neutron is not an elementary particle. For an elementary particle to have an intrinsic magnetic moment, it must have both spin and electric charge. The neutron has spin 1/2 ħ, but it has no net charge. The existence of the neutron's magnetic moment was puzzling and defied a correct explanation until the quark model for particles was developed in the 1960s. The neutron is composed of three quarks, and the magnetic moments of these elementary particles combine to give the neutron its magnetic moment.Nucleon
In chemistry and physics, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines an isotope's mass number (nucleon number).
Until the 1960s, nucleons were thought to be elementary particles, not made up of smaller parts. Now they are known to be composite particles, made of three quarks bound together by the so-called strong interaction. The interaction between two or more nucleons is called internucleon interaction or nuclear force, which is also ultimately caused by the strong interaction. (Before the discovery of quarks, the term "strong interaction" referred to just internucleon interactions.)
Nucleons sit at the boundary where particle physics and nuclear physics overlap. Particle physics, particularly quantum chromodynamics, provides the fundamental equations that explain the properties of quarks and of the strong interaction. These equations explain quantitatively how quarks can bind together into protons and neutrons (and all the other hadrons). However, when multiple nucleons are assembled into an atomic nucleus (nuclide), these fundamental equations become too difficult to solve directly (see lattice QCD). Instead, nuclides are studied within nuclear physics, which studies nucleons and their interactions by approximations and models, such as the nuclear shell model. These models can successfully explain nuclide properties, as for example, whether or not a particular nuclide undergoes radioactive decay.
The proton and neutron are both fermions, hadrons and baryons. The proton carries a positive net charge and the neutron carries a zero net charge; the proton's mass is only about 0.13% less than the neutron's. Thus, they can be viewed as two states of the same nucleon, and together form an isospin doublet (I = 1⁄2). In isospin space, neutrons can be transformed into protons via SU(2) symmetries, and vice versa. These nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space. According to the Noether theorem, isospin is conserved with respect to the strong interaction.Quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation; they can be found only within hadrons, which include baryons (such as protons and neutrons) and mesons. For this reason, much of what is known about quarks has been drawn from observations of hadrons.
Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. They are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known particles whose electric charges are not integer multiples of the elementary charge.
There are six types, known as flavors, of quarks: up, down, strange, charm, bottom, and top. Up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay: the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions (such as those involving cosmic rays and in particle accelerators). For every quark flavor there is a corresponding type of antiparticle, known as an antiquark, that differs from the quark only in that some of its properties (such as the electric charge) have equal magnitude but opposite sign.
The quark model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964. Quarks were introduced as parts of an ordering scheme for hadrons, and there was little evidence for their physical existence until deep inelastic scattering experiments at the Stanford Linear Accelerator Center in 1968. Accelerator experiments have provided evidence for all six flavors. The top quark, first observed at Fermilab in 1995, was the last to be discovered.Richard E. Taylor
Richard Edward Taylor, (2 November 1929 – 22 February 2018), was a Canadian physicist and Stanford University professor. He shared the 1990 Nobel Prize in Physics with Jerome Friedman and Henry Kendall "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics."Sakata model
In particle physics, the Sakata model of hadrons was a precursor to the quark model. It proposed that the proton, neutron, and Lambda baryon were elementary particles (sometimes referred to as sakatons), and that all other known hadrons were made of them. The model was proposed by Shoichi Sakata in 1956. The model was successful in explaining many features of hadrons, but was supplanted by the quark model as the understanding of hadrons progressed.Strange quark
The strange quark or s quark (from its symbol, s) is the third lightest of all quarks, a type of elementary particle. Strange quarks are found in subatomic particles called hadrons. Example of hadrons containing strange quarks include kaons (K), strange D mesons (Ds), Sigma baryons (Σ), and other strange particles.
According to the IUPAP the symbol s is the official name, while strange is to be considered only as a mnemonic. The name sideways has also been used because the s quark has a I3 value of 0 while the u (“up”) and d (“down”) quarks have values of +1/2 and −1/2 respectively.Along with the charm quark, it is part of the second generation of matter, and has an electric charge of −1/3 e and a bare mass of 95+9−3 MeV/c2. Like all quarks, the strange quark is an elementary fermion with spin 1/2, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong interactions. The antiparticle of the strange quark is the strange antiquark (sometimes called antistrange quark or simply antistrange), which differs from it only in that some of its properties have equal magnitude but opposite sign.
The first strange particle (a particle containing a strange quark) was discovered in 1947 (kaons), but the existence of the strange quark itself (and that of the up and down quarks) was only postulated in 1964 by Murray Gell-Mann and George Zweig to explain the Eightfold Way classification scheme of hadrons. The first evidence for the existence of quarks came in 1968, in deep inelastic scattering experiments at the Stanford Linear Accelerator Center. These experiments confirmed the existence of up and down quarks, and by extension, strange quarks, as they were required to explain the Eightfold Way.Tetraquark
A tetraquark, in particle physics, is an exotic meson composed of four valence quarks. A tetraquark state has long been suspected to be allowed by quantum chromodynamics, the modern theory of strong interactions. A tetraquark state is an example of an exotic hadron which lies outside the conventional quark model classification.Up quark
The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quarks, one down quark) of atomic nuclei. It is part of the first generation of matter, has an electric charge of +2/3 e and a bare mass of 2.2+0.5−0.4 MeV/c2.. Like all quarks, the up quark is an elementary fermion with spin 1/2, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong interactions. The antiparticle of the up quark is the up antiquark (sometimes called antiup quark or simply antiup), which differs from it only in that some of its properties, such as charge have equal magnitude but opposite sign.
Its existence (along with that of the down and strange quarks) was postulated in 1964 by Murray Gell-Mann and George Zweig to explain the Eightfold Way classification scheme of hadrons. The up quark was first observed by experiments at the Stanford Linear Accelerator Center in 1968.X(3872)
The X(3872) is an exotic meson candidate with a mass of 3871.68 MeV/c2 which does not fit into the quark model because of its quantum numbers. It was first discovered in 2003 by the Belle experiment in Japan and later confirmed by several other experimental collaborations. Several theories have been proposed for its nature, such as a mesonic molecule or a diquark-antidiquark pair (tetraquark).
The quantum numbers of X(3872) have been determined by the LHCb Experiment at CERN in March 2013. The values for JPC is 1++.