In the particle physics of quarks, if the eigenstates of the physical Hamiltonian are different from the eigenstates of the weak one, a transformation matrix can be defined for these two bases. This matrix was introduced for six quarks by Kobayashi and Maskawa (cfr. km) and is called the Cabibbo-Kobayashi-Maskawa because one of the parameters was previously introduced by Cabibbo .

The idea of Cabibbo originated from need to explain two phenomena:

1. the transitions , had similar amplitudes.
2. the transitions with variation of strangeness ΔS=1 had amplitudes equal to 1/4 of those with ΔS=0.

where θ_c is called the Cabibbo angle.

A fourth quark was not foreseen by Cabibbo. But taking in account the existence of the charm, the Cabibbo angle can be seen as a mixing angle between two families of quark: 'up' and 'down', 'strange' and 'charm':

where

In 1973, one year before the discovery of the 'charm', the existence of a third family of quarks was introduced by Kobayashi and Maskawa in order to explain the CP-violation phenomena observed in the neutral-kaon system. This was an ad hoc hypothesis, because at that time no component of this third family was observed.

By introducing a mixing for the new family the parameters of the transformation matrix become four: three Euler angles and one phase. It is this phase that can explain CP-violating phenomena in the neutral-kaon system. But other mechanisms have been proposed. Hence it is of great interest to study whether the pattern of CP-violating effects that can be observed in b-decays follows the predictions of the minimal Standard Model, or instead requires the introduction of beyond Standard Model physics.

References

• N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531.
• M. Kobayashi and K. Maskawa, Prog. Theor. Phys. 49 (1973) 652.

See also

• Particle Data Group