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Quark

2007 Schools Wikipedia Selection. Related subjects: General Physics

   These are the 6 quarks and their most likely decay modes. Mass
   decreases moving from right to left.
   Enlarge
   These are the 6 quarks and their most likely decay modes. Mass
   decreases moving from right to left.

   In particle physics, quarks are one of the two basic constituents of
   matter (the other Standard Model fermions are the leptons).

   Antiparticles of quarks are called antiquarks. Quarks are the only
   fundamental particles that interact through all four of the fundamental
   forces. The word was borrowed by Murray Gell-Mann from the book
   Finnegans Wake by James Joyce, where seabirds give "three quarks", akin
   to three cheers (probably onomatopoetically imitating a seabird call,
   like "quack" for ducks).

   The names of quark flavours ( up, down, strange, charm, bottom, and
   top) were also chosen arbitrarily based on the need to name them
   something that could be easily remembered and used.

   An important property of quarks is called confinement, which states
   that individual quarks are not seen because they are always confined
   inside subatomic particles called hadrons (e.g., protons and neutrons);
   an exception is the top quark, which decays so quickly that it does not
   hadronize, and can therefore be observed more directly via its decay
   products. Confinement began as an experimental observation, and 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 Σc++
   Enlarge
   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
   observables such as mass m and quantum numbers, such as spin J and
   parity P. 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 usually 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

   Each quark is assigned a baryon number, B  =  1/3, and a vanishing
   lepton number L  =  0. They have fractional electric charge, Q, either
   Q  =  +2/3 or Q  =  −1/3. The former are called up-type quarks, the
   latter, down-type quarks. Each quark is assigned a weak isospin: T[z]
   =  +1/2 for an up-type quark and T[z]  =  −1/2 for a down-type quark.
   Each doublet of weak isospin defines a generation of quarks. There are
   three generations, and hence six flavours of quarks — the up-type quark
   flavours are up, charm and top; the down-type quark flavours are down,
   strange, and bottom (each list is in the order of increasing mass).

   The number of generations of quarks and leptons are equal in the
   standard model. The number of generations of leptons with a light
   neutrino is strongly constrained by experiments at the LEP in CERN and
   by observations of the abundance of helium in the universe. Precision
   measurement of the lifetime of the Z boson at LEP constrains the number
   of light neutrino generations to be three. Astronomical observations of
   helium abundance give consistent results. Results of direct searches
   for a fourth generation give limits on the mass of the lightest
   possible fourth generation quark. The most stringent limit comes from
   analysis of results from the Tevatron collider at Fermilab, and shows
   that the mass of a fourth-generation quark must be greater than 190
   GeV. Additional limits on extra quark generations come from
   measurements of quark mixing performed by the experiments Belle and
   BaBar.

   Each flavour defines a quantum number which is conserved under the
   strong interactions, but not the weak interactions. The magnitude of
   flavour changing in the weak interaction is encoded into a structure
   called the CKM matrix. This also encodes the CP violation allowed in
   the Standard Model. The flavour quantum numbers are described in detail
   in the article on flavour.

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 (red, green, and
   blue). 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]   171400 ± 2100

     * Top quark mass from the Tevatron Electroweak Working Group
     * Other quark masses from Particle Data Group; these 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, as an alternative to
       topness and bottomness.

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 quark. Tests of CPT
   symmetry cannot be performed directly on quarks and antiquarks, due to
   confinement, but can be performed on hadrons. Notation of antiquarks
   follows that of antimatter in general: an up quark is denoted by
   \mathrm{u}\, , and an anti-up quark is denoted by \bar{\mathrm{u}} .

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. For more details see the article on preons.

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 a
   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 chose 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 1977 and the top quark in 1996 at the Tevatron collider in Fermilab.

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