Flavour (particle physics)

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Electron.svg Muon.svg Tau lepton.svg
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Six flavours of leptons

In particle physics, flavour or flavor refers to a species of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles, including composite ones. For hadrons, these quantum numbers depend on the numbers of constituent quarks of each particular flavour.

Intuitive description[edit]

Elementary particles are not eternal and indestructible. Unlike in classical mechanics, where forces only change a particle's momentum, the weak force can alter the essence of a particle, even an elementary particle. This means that it can convert one quark to another quark with different mass and electric charge, and the same for leptons. From the point of view of quantum mechanics, changing the flavour of a particle by the weak force is no different in principle from changing its spin by electromagnetic interaction, and should be described with quantum numbers as well. In particular, flavour states may undergo quantum superposition.

In atomic physics the principal quantum number of an electron specifies the electron shell in which it resides, which determines the energy level of the whole atom. In an analogous way, the five flavour quantum numbers[which?] of a quark specify which of six flavours (u, d, s, c, b, t) it has, and when these quarks are combined this results in different types of baryons and mesons with different masses, electric charges, and decay modes.

Flavour symmetry[edit]




Flavour quantum numbers[edit]





All quarks carry a baryon number B = 1/3. They also all carry weak isospin, T3 = ±1/2. The positive-T3 quarks (up, charm, and top quarks) are called up-type quarks and negative-T3 quarks (down, strange, and bottom quarks) are called down-type quarks. Each doublet of up and down type quarks constitutes one generation of quarks.

For all the quark flavour quantum numbers (strangeness, charm, topness and bottomness) the convention is that the flavour charge and the electric charge of a quark have the same sign. Thus any flavour carried by a charged meson has the same sign as its charge. Quarks have the following flavour quantum numbers:

  • Isospin, less ambiguously known as "isobaric spin", which has value I3 = 1/2 for the up quark and I3 = −1/2 for the down quark.
  • Strangeness (S): Defined as S = −(nsn), where ns represents the number of strange quarks (
    ) and n represents the number of strange antiquarks (
  • Charm (C): Defined as C = (ncn), where nc represents the number of charm quarks (
    ) and n represents the number of charm antiquarks. Is +1 for the charm quark.
  • Bottomness (B′): Also called 'beauty'. Defined as B′ = −(nbn), where nb represents the number of bottom quarks (
    ) and n represents the number of bottom antiquarks.
  • Topness (T): Also called 'truth'. Defined as T = (ntn), where nt represents the number of top quarks (

These five quantum numbers, together with baryon number (which is not a flavour quantum number), completely specify numbers of all 6 quark flavours separately (as nqn, i.e. an antiquark is counted with the minus sign). They are conserved by both the electromagnetic and strong interactions (but not the weak interaction). From them can be built the derived quantum numbers:


For first-order weak decays, that is processes involving only one quark decay, these quantum numbers (e.g. charm) can only vary by 1 (| C | = ±1); ΔB′ = ±1. Since first-order processes are more common than second-order processes (involving two quark decays), this can be used as an approximate "selection rule" for weak decays.

A quark of a given flavour is an eigenstate of the weak interaction part of the Hamiltonian: it will interact in a definite way with the W and Z bosons. On the other hand, a fermion 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 a quantum state may change as it propagates freely. The transformation from flavour to mass basis for quarks is given by the Cabibbo–Kobayashi–Maskawa matrix (CKM matrix). This matrix is analogous to the PMNS matrix for neutrinos, and defines the strength of flavour changes under weak interactions of quarks.


Antiparticles and hadrons[edit]


Quantum chromodynamics[edit]

Flavour symmetry is closely related to chiral symmetry. This part of the article is best read along with the one on chirality.


Under some circumstances, the masses of the quarks can be neglected entirely. 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 SUL(Nf) × SUR(Nf).

If all quarks had non-zero but equal masses, then this chiral symmetry is broken to the vector symmetry of the "diagonal flavour group" SU(Nf), 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.


Symmetries of QCD[edit]


Conservation laws[edit]

All of the various charges discussed above are conserved by the fact that the charge operator is best understood as the generator of a symmetry that commutes with the Hamiltonian. Thus, the eigenvalues of the various charge operators are conserved.

Absolutely conserved flavour quantum numbers are:

In some theories, the individual baryon and lepton number conservation can be violated, if the difference between them (BL) is conserved (see chiral anomaly). All other flavour quantum numbers are violated by the electroweak interactions. Strong interactions conserve all flavours.


Some of the historical events that led to the development of flavour symmetry are discussed in the article on isospin.

See also[edit]



Further reading[edit]

External links[edit]