They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles.
In particular, the action of the weak force is such that it allows the conversion of quantum numbers describing mass and electric charge of both quarks and leptons from one discrete type to another.
Analogously, the five flavour quantum numbers (isospin, strangeness, charm, bottomness or topness) can characterize the quantum state of quarks, by the degree to which it exhibits six distinct flavours (u, d, c, s, t, b).
Composite particles can be created from multiple quarks, forming hadrons, such as mesons and baryons, each possessing unique aggregate characteristics, such as different masses, electric charges, and decay modes.
, where u and d are the two fields (representing the various generations of leptons and quarks, see below), and M is any 2×2 unitary matrix with a unit determinant.
In the electroweak theory, on the other hand, this symmetry is broken, and flavour changing processes exist, such as quark decay or neutrino oscillations.
In addition, one defines a quantum number called weak hypercharge, YW, which is −1 for all left-handed leptons.
Strangeness was introduced to explain the rate of decay of newly discovered particles, such as the kaon, and was used in the Eightfold Way classification of hadrons and in subsequent quark models.
Hence antiparticles have flavour equal in magnitude to the particle but opposite in sign.
The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadrons as well as quarks.
These free parameters - the fermion masses and their mixing angles - appear to be specifically tuned.
There are very fundamental questions involved in this puzzle such as why there are three generations of quarks (up-down, charm-strange, and top-bottom quarks) and leptons (electron, muon and tau neutrino), as well as how and why the mass and mixing hierarchy arises among different flavours of these fermions.
The simplified behavior of flavour transformations can then be successfully modeled as acting independently on the left- and right-handed parts of each quark field.
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.
The strength of explicit symmetry breaking is controlled by the current quark masses in QCD.
The first of those quantum numbers, Isospin, was introduced as a concept in 1932 by Werner Heisenberg,[5] to explain symmetries of the then newly discovered neutron (symbol n): Protons and neutrons were grouped together as nucleons and treated as different states of the same particle, because they both have nearly the same mass and interact in nearly the same way, if the (much weaker) electromagnetic interaction is neglected.
The Gell-Mann–Nishijima formula was identified in 1953, which relates strangeness and hypercharge with isospin and electric charge.
[6] Once the kaons and their property of strangeness became better understood, it started to become clear that these, too, seemed to be a part of an enlarged symmetry that contained isospin as a subgroup.
The larger symmetry was named the Eightfold Way by Murray Gell-Mann, and was promptly recognized to correspond to the adjoint representation of SU(3).
To explain the observed absence of flavor-changing neutral currents, the GIM mechanism was proposed in 1970, which introduced the charm quark and predicted the J/psi meson.