- Flavour (particle physics)
In

particle physics ,**flavour**or**flavor**(see spelling differences) is aquantum number ofelementary particle s related to theirweak interactions . In theelectroweak theory this symmetry is gauged, andflavour changing processes exist. Inquantum chromodynamics , on the other hand, flavour is a global symmetry.**Definition**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

orthogonal or perpendicular to each other. In other words, the theory possesses symmetry transformations such as$Mleft(\{uatop\; d\}\; ight)$, where $u$ and $d$are the two fields, and $M$ is any 2 x 2 unitary matrix with a unit determinant. Such matrices form aLie group called SU(2) (seespecial unitary group ). This is an example of flavour symmetry.This symmetry is "global" for

strong interaction s, and "gauged" forweak interaction s.The term "flavour" was first coined for use in the

quark model ofhadron s in 1968. A name for the set of quantum numbers related toisospin ,hypercharge andstrangeness is said to have been found on the way to lunch byMurray Gell-Mann andHarald Fritzsch when they passed aBaskin-Robbins advertising 31 flavours.Fact|date=February 2007**Flavour quantum numbers****Leptons**All

lepton s carry alepton number **L = 1**. In addition, leptons carryweak isospin ,**T**, which is −½ for the three charged leptons (i.e. e, μ and τ) and ½ for the three associated_{z}neutrino s. Each doublet of a charged lepton and a neutrino consisting of opposite**T**are said to constitute one generation of leptons. In addition, one defines a quantum number called_{z}weak hypercharge ,**Y**which is −1 for the charged leptons and +1 for the neutrinos._{W}Weak isospin andweak hypercharge are gauged in theStandard 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

MNS matrix .**Quarks**All

quark s carry abaryon number **B = ⅓**. In addition they carryweak isospin ,**T**. The positive_{z}= ±½**T**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._{z}Quarks have the following flavour quantum numbers:

*Isospin which has value**I**for the up quark and value_{z}= ½**I**for the down quark._{z}= −½

*Strangeness (**S**): a quantum number introduced byMurray 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 = I**._{z}+Y/2A quark of a given flavour is an

eigenstate of theweak interaction part of the Hamiltonian: it will interact in a definite way with the W^{+}, W^{−}and Zboson s. On the other hand, afermion of 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 aquantum state may 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 violation if there are at least three generations.**Antiparticles and hadrons**Flavour quantum numbers are additive. Hence

antiparticles have flavour equal in magnitude to the particle but opposite in sign.Hadron s inherit their flavour quantum number from theirvalence quark s: this is the basis of the classification in thequark model . The relations between the hypercharge, electric charge and other flavour quantum numbers hold forhadron s as well asquark s.**Quantum chromodynamics**(Flavour symmetry is closely related to chiral symmetry. This part of the article is best read along with the one on

chirality (physics) .)Quantum chromodynamics contains six flavours ofquark s. However, their masses differ. As a result, they are not strictly interchangeable with each other. Two of the flavours, calledup anddown , 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 N_{f}flavours to have the same masses and obtain an effective SU(N_{f}) 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 $SU\_L(N\_f)\; imes\; SU\_R(N\_f)$.

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 thecurrent quark mass es in QCD.Even if quarks are massless, chiral flavour symmetry can be

**spontaneously broken**if for some reason the vacuum of the theory contains achiral condensate (as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with thevalence quark mass in 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 ,**Λ**_{QCD}, hence chiral flavour symmetry is a good approximation to QCD for the up, down and strange quarks. The success ofchiral perturbation theory and the even more naivechiral model s spring from this fact. The valence quark masses extracted from thequark model are much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with the formation of achiral condensate . Other phases of QCD may break the chiral flavour symmetries in other ways.**Conservation laws**Absolutely conserved flavour quantum numbers are

*theelectric charge Q

*the difference of thebaryon number and thelepton number :B−L All other flavour quantum numbers are violated by theelectroweak interactions .Baryon number andlepton number are separately violated in theelectroweak interactions through thechiral anomaly .Strong interactions conserve all flavours.**History**Some of the historical events that lead to the development of flavour symmetry are discussed in the article on

isospin .**ee also***Field theoretical formulation of the standard model

*Weak interactions ,flavour changing processes andCP violation

*Quantum chromodynamics ,strong CP problem andchirality (physics)

*Chiral symmetry breaking andquark matter

*Quark s,lepton s andhadron s.

*Quark**flavour tagging**is an example ofparticle identification in experimental particle physics.**References and external links*** [

*http://pdg.lbl.gov/ The particle data group.*]

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