- Flavour (particle physics)
particle physics, flavour or flavor (see spelling differences) is a quantum numberof elementary particles related to their weak interactions. In the electroweak theorythis symmetry is gauged, and flavour changing processesexist. In quantum chromodynamics, on the other hand, flavour is a global symmetry.
If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. Any (complex) linear combination of these two particles give the same physics, as long as they are
orthogonalor perpendicular to each other. In other words, the theory possesses symmetry transformations such as, where and are the two fields, and is any 2 x 2 unitary matrix with a unit determinant. Such matrices form a Lie groupcalled SU(2) (see special unitary group). This is an example of flavour symmetry.
This symmetry is "global" for
strong interactions, and "gauged" for weak interactions.
The term "flavour" was first coined for use in the
quark modelof hadrons in 1968. A name for the set of quantum numbers related to isospin, hyperchargeand strangenessis said to have been found on the way to lunch by Murray Gell-Mannand Harald Fritzschwhen they passed a Baskin-Robbinsadvertising 31 flavours.Fact|date=February 2007
Flavour quantum numbers
leptons carry a lepton numberL = 1. In addition, leptons carry weak isospin, Tz, which is −½ for the three charged leptons (i.e. e, μ and τ) and ½ for the three associated neutrinos. Each doublet of a charged lepton and a neutrino consisting of opposite Tz are said to constitute one generation of leptons. In addition, one defines a quantum number called weak hypercharge, YW which is −1 for the charged leptons and +1 for the neutrinos. Weak isospinand weak hyperchargeare gauged in the Standard Model.
Leptons may be assigned the six "flavour" quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos. These are conserved in electromagnetic interactions, but violated by weak interactions. Therefore, such "flavour" quantum numbers are not of great use. A quantum number for each generation is more useful. However, neutrinos of different generations can mix; that is, a neutrino of one flavour can transform into another flavour. The strength of such mixings is specified by a matrix called the
quarks carry a baryon numberB = ⅓. In addition they carry weak isospin, Tz = ±½. The positive Tz particles are called "up-type quarks" and the remainder are "down-type quarks". Each doublet of up and down type quarks constitutes one generation of quarks.
Quarks have the following flavour quantum numbers:
Isospinwhich has value Iz = ½ for the up quark and value Iz = −½ for the down quark.
Strangeness(S): a quantum number introduced by Murray Gell-Mann. The strange antiquark is defined to have strangeness +1. This is a down-type quark.
*Charm (C) number which is +1 for the charm quark. This is an up-type quark.
*Bottom (also called beauty) quantum number, B': which is +1 for the down-type bottom antiquark.
*Top (sometimes called truth) quantum number, T: +1 for the up-type top quark.These are useful quantum numbers since they are conserved by both the electromagnetic and strong forces. Out of them can be built the derived quantum numbers:
hypercharge: Y = B+S+C+B'+T and
electric charge: Q = Iz+Y/2.
A quark of a given flavour is an
eigenstateof the weak interactionpart of the Hamiltonian: it will interact in a definite way with the W+, W− and Z bosons. On the other hand, a fermionof a fixed mass (an eigenstate of the kinetic and strong interaction parts of the Hamiltonian) is normally a superposition of various flavours. As a result, the flavour content of a quantum statemay change as it propagates freely. The transformation from flavour to mass basis for quarks is given by the so-called Cabibbo-Kobayashi-Maskawa matrix ( CKM matrix). By definition therefore, this matrix defines the strength of flavour changes under weak interactions of quarks.
The CKM matrix allows for
CP violationif there are at least three generations.
Antiparticles and hadrons
Flavour quantum numbers are additive. Hence
antiparticleshave flavour equal in magnitude to the particle but opposite in sign. Hadrons inherit their flavour quantum number from their valence quarks: this is the basis of the classification in the quark model. The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadrons as well as quarks.
(Flavour symmetry is closely related to chiral symmetry. This part of the article is best read along with the one on
chirality (physics).) Quantum chromodynamicscontains six flavours of quarks. However, their masses differ. As a result, they are not strictly interchangeable with each other. Two of the flavours, called upand down, are close to having equal masses, and the theory of these two quarks possesses an approximate SU(2) symmetry. Under some circumstances one can take Nf flavours to have the same masses and obtain an effective SU(Nf) flavour symmetry.
Under some circumstances, the masses of the quarks can be neglected entirely. In that case, each flavour of quark possesses a chiral symmetry. One can then make flavour transformations independently on the left- and right-handed parts of each quark field. The flavour group is then a chiral group .
If all quarks have equal mass, then this chiral symmetry is broken to the vector symmetry of the "diagonal flavour group" which applies the same transformation to both helicities of the quarks. Such a reduction of the symmetry is called explicit symmetry breaking. The amount of explicit symmetry breaking is controlled by the
current quark masses in QCD.
Even if quarks are massless, chiral flavour symmetry can be spontaneously broken if for some reason the vacuum of the theory contains a
chiral condensate(as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with the valence quark massin QCD.
ymmetries of QCD
Analysis of experiments indicate that the current quark masses of the lighter flavours of quarks are much smaller than the
QCD scale, ΛQCD, hence chiral flavour symmetry is a good approximation to QCD for the up, down and strange quarks. The success of chiral perturbation theoryand the even more naive chiral models spring from this fact. The valence quark masses extracted from the quark modelare much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with the formation of a chiral condensate. Other phases of QCD may break the chiral flavour symmetries in other ways.
Absolutely conserved flavour quantum numbers are
*the difference of the
baryon numberand the lepton number: B−LAll other flavour quantum numbers are violated by the electroweak interactions. Baryon numberand lepton numberare separately violated in the electroweak interactionsthrough the chiral anomaly. Strong interactionsconserve all flavours.
Some of the historical events that lead to the development of flavour symmetry are discussed in the article on
*Field theoretical formulation of the standard model
Weak interactions, flavour changing processesand CP violation
Quantum chromodynamics, strong CP problemand chirality (physics)
Chiral symmetry breakingand quark matter
Quarks, leptons and hadrons.
*Quark flavour tagging is an example of
particle identificationin experimental particle physics.
References and external links
* [http://pdg.lbl.gov/ The particle data group.]
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