Quark

Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. (The others are leptons.) Antiparticles of quarks are called antiquarks. Quarks and antiquarks are the only fundamental particles that interact through all four of the fundamental forces.

The single most important property of quarks is called confinement. This is the experimentally determined fact that except for the top quark, which decays too rapidly, individual quarks are not seen — they are always confined inside subatomic particles called hadrons, such as protons, neutrons, and mesons. This fundamental property is expected to follow from the modern theory of strong interactions, called quantum chromodynamics (QCD). Although there is no mathematical derivation of confinement in QCD, it is easy to show using lattice gauge theory.

Free quarks

1974 discovery photograph of a possible charmed baryon, now identified as the Σ_c⁺⁺

No search for free quarks or fractional electric charges has returned convincing evidence. The absence of free quarks has therefore been incorporated into the notion of confinement, which, it is believed, the theory of quarks must possess. However, it may be possible to change the volume of confinement by creating dense or hot quark matter. These new phases of QCD matter have been predicted theoretically, and experimental searches for them have now started.

Confinement and quark properties

Every subatomic particle is completely described by a small set of quantum numbers such as its spin J, parity P, and mass m. Usually these properties are directly determined by experiments. However, confinement makes it impossible to measure these properties of quarks. Instead, they must be inferred from measurable properties of the composite particles which are made up of quarks. Such inferences are most easily made for certain additive quantum numbers called flavours.

The composite particles made of quarks and antiquarks are the hadrons. These include the mesons which get their quantum numbers from a quark and an antiquark, and the baryons, which get theirs from three quarks. The quarks (and antiquarks) which impart quantum numbers to hadrons are called valence quarks. Apart from these, any hadron may contain an indefinite number of virtual quarks, antiquarks and gluons which together contribute nothing to their quantum numbers. Such virtual quarks are called sea quarks.

Flavour

Flavour in particle physics

Flavour quantum numbers

Lepton number: L
Baryon number: B
Electric charge: Q
Weak hypercharge: Y_W
Weak isospin: T_z
Isospin: I, I_z
Hypercharge: Y
Strangeness: S
Charm: C
Bottomness: B'
Topness: T

Y=B+S+C+B'+T
Q=I_z+Y/2
Q=T_z+Y_W/2
B−L

Spin

Quantum numbers corresponding to non-Abelian symmetries like rotations require more care in extraction, since they are not additive. In the quark model one builds mesons out of a quark and an antiquark, whereas baryons are built from three quarks. Since mesons are bosons (having integer spins) and baryons are fermions (having half-integer spins), the quark model implies that quarks are fermions. Further, the fact that the lightest baryons have spin-1/2 implies that each quark can have spin J = 1/2. The spins of excited mesons and baryons are completely consistent with this assignment.

Colour

Since quarks are fermions, the Pauli exclusion principle implies that the three valence quarks must be in an antisymmetric combination in a baryon. However, the charge Q = 2 baryon, Δ⁺⁺ (which is one of four isospin I_z = 3/2 baryons) can only be made of three u quarks with parallel spins. Since this configuration is symmetric under interchange of the quarks, it implies that there exists another internal quantum number, which would then make the combination antisymmetric. This is given the name " colour", although it has nothing to do with the perception of the frequency (or wavelength) of light, which is the usual meaning of colour. This quantum number is the charge involved in the gauge theory called quantum chromodynamics (QCD).

The only other coloured particle is the gluon, which is the gauge boson of QCD. Like all other non-Abelian gauge theories (and unlike quantum electrodynamics) the gauge bosons interact with one another by the same force that affects the quarks.

Colour is a gauged SU(3) symmetry. Quarks are placed in the fundamental representation, 3, and hence come in three colours. Gluons are placed in the adjoint representation, 8, and hence come in eight varieties. For more on this, see the article on colour charge.

Quark masses

Although one speaks of quark mass in the same way as the mass of any other particle, the notion of mass for quarks is complicated by the fact that quarks cannot be found free in nature. As a result, the notion of a quark mass is a theoretical construct, which makes sense only when one specifies exactly the procedure used to define it.

Current quark mass

The approximate chiral symmetry of QCD, for example, allows one to define the ratio between various (up, down and strange) quark masses through combinations of the masses of the pseudo-scalar meson octet in the quark model through chiral perturbation theory, giving

$\frac{m_u}{m_d}=0.56\qquad{\rm and}\qquad\frac{m_s}{m_d}=20.1.$

The fact that m_u ≠ 0 is important, since there would be no strong CP problem if m_u were to vanish. The absolute values of the masses are currently determined from QCD sum rules (also called spectral function sum rules) and lattice QCD. Masses determined in this manner are called current quark masses. The connection between different definitions of the current quark masses needs the full machinery of renormalization for its specification.

Valence quark mass

Another, older, method of specifying the quark masses was to use the Gell-Mann-Nishijima mass formula in the quark model, which connect hadron masses to quark masses. The masses so determined are called constituent quark masses, and are significantly different from the current quark masses defined above. The constituent masses do not have any further dynamical meaning.

Heavy quark masses

The masses of the heavy charm and bottom quarks are obtained from the masses of hadrons containing a single heavy quark (and one light antiquark or two light quarks) and from the analysis of quarkonia. Lattice QCD computations using the heavy quark effective theory (HQET) or non-relativistic quantum chromodynamics (NRQCD) are currently used to determine these quark masses.

The top quark is sufficiently heavy that perturbative QCD can be used to determine its mass. Before its discovery in 1995, the best theoretical estimates of the top quark mass are obtained from global analysis of precision tests of the Standard Model. The top quark, however, is unique amongst quarks in that it decays before having a chance to hadronize. Thus, its mass can be directly measured from the resulting decay products. This can only be done at the Tevatron which is the only particle accelerator energetic enough to produce top quarks in abundance.

Properties of quarks

The following table summarizes the key properties of the six known quarks:

Generation	Weak Isospin	Flavour	Name	Symbol	Charge / e	Mass / MeV. c^-2
1	+ ¹/₂	I_z=+1/2	Up	u	+ ²/₃	1.5 to 4.0
1	− ¹/₂	I_z=−1/2	Down	d	− ¹/₃	4 to 8
2	− ¹/₂	S=−1	Strange	s	− ¹/₃	80 to 130
2	+ ¹/₂	C=1	Charm	c	+ ²/₃	1150 to 1350
3	− ¹/₂	B′=−1	Bottom	b	− ¹/₃	4100 to 4400
3	+ ¹/₂	T=1	Top	t	+ ²/₃	172700 ± 2900

Top quark mass from the Tevatron Electroweak Working Group
Other quark masses from Particle Data Group. Quark masses are given in the MS-bar scheme.
The quantum numbers of the top and bottom quarks are sometimes known as truth and beauty respectively.

Antiquarks

The additive quantum numbers of antiquarks are equal in magnitude and opposite in sign to those of the quarks. CPT symmetry forces them to have the same spin and mass as the corresponding antiquark. Tests of CPT symmetry cannot be performed directly on quarks and antiquarks, due to confinement, but can be performed on hadrons.

Substructure

Some extensions of the Standard Model begin with the assumption that quarks and leptons have substructure. In other words, these models assume that the elementary particles of the Standard Model are in fact composite particles, made of some other elementary constituents. Such an assumption is open to experimental tests, and these theories are severely constrained by data. At present there is no evidence for such substructure.

History

The notion of quarks evolved out of a classification of hadrons developed independently in 1961 by Murray Gell-Mann and Kazuhiko Nishijima, which nowadays goes by the name of the quark model. The scheme grouped together particles with isospin and strangeness using an unitary symmetry derived from current algebra, which we today recognise as part of the approximate chiral symmetry of QCD. This is a global flavour SU(3) symmetry, which should not be confused with the gauge symmetry of QCD.

In this scheme the lightest mesons (spin-0) and baryons (spin-½) are grouped together into octets, 8, of flavour symmetry. A classification of the spin-3/2 baryons into the representation 10 yielded a prediction of a new particle, Ω⁻, the discovery of which in 1964 led to wide acceptance of the model. The missing representation 3 was identified with quarks.

This scheme was called the eightfold way by Gell-Mann, a clever conflation of the octets of the model with the eightfold way of Buddhism. He also invented the name quark and attributed it to the sentence “Three quarks for Muster Mark” in James Joyce's Finnegans Wake. The negative results of quark search experiments caused Gell-Mann to hold that quarks were mathematical fiction.

Analysis of certain properties of high energy reactions of hadrons led Richard Feynman to postulate substructures of hadrons, which he called partons (since they form part of hadrons). A scaling of deep inelastic scattering cross sections derived from current algebra by James Bjorken received an explanation in terms of partons. When Bjorken scaling was verified in an experiment in 1969, it was immediately realized that partons and quarks could be the same thing. With the proof of asymptotic freedom in QCD in 1973 by David Gross, Frank Wilczek and David Politzer the connection was firmly established.

The charm quark was postulated by Sheldon Glashow, Iliopoulos and Maiani in 1973 to prevent unphysical flavour changes in weak decays which would otherwise occur in the standard model. The discovery in 1975 of the meson which came to be called the J/ψ led to the recognition that it was made of a charm quark and its antiquark.

The existence of a third generation of quarks was predicted by Kobayashi and Maskawa who realized that the observed violation of CP symmetry by neutral kaons could not be accommodated into the Standard Model with two generations of quarks. The bottom quark was discovered in 1980 and the top quark in 1996 at the Tevatron collider in Fermilab.