Cabibbo–Kobayashi–Maskawa matrix

Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions.

This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks.

[1] Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy,[2] on the effectively rotated nonstrange and strange vector and axial weak currents, which he references.

Other conventions are equally valid: The mass eigenstates u, c, and t of the up-type quarks can equivalently define the matrix in terms of their weak interaction partners u′, c′, and t′.

For the Standard Model case (N = 3), there are three mixing angles and one CP-violating complex phase.

For two generations of quarks, there can be no CP violating phases, as shown by the counting of the previous section.

Since CP violations had already been seen in 1964, in neutral kaon decays, the Standard Model that emerged soon after clearly indicated the existence of a third generation of quarks, as Kobayashi and Maskawa pointed out in 1973.

Note, however, that the specific values that the angles take on are not a prediction of the standard model: They are free parameters.

At present, there is no generally-accepted theory that explains why the angles should have the values that are measured in experiments.

The constraints of unitarity of the CKM-matrix on the diagonal terms can be written as separately for each generation j.

Theoretically it is a consequence of the fact that all SU(2) doublets couple with the same strength to the vector bosons of weak interactions.

The area vanishes for the specific parameters in the Standard Model for which there would be no CP violation.

is doubly antisymmetric, Up to antisymmetry, it only has 9 = 3 × 3 non-vanishing components, which, remarkably, from the unitarity of V, can be shown to be all identical in magnitude, that is, so that Since the three sides of the triangles are open to direct experiment, as are the three angles, a class of tests of the Standard Model is to check that the triangle closes.

For brevity, the cosines and sines of the angles θk are denoted ck and sk, for k = 1, 2, 3 respectively.

A "standard" parameterization of the CKM matrix uses three Euler angles ( θ12, θ23, θ13 ) and one CP-violating phase ( δ13 ).

The approximation to order λ3, good to better than 0.3% accuracy, is: Rates of CP violation correspond to the parameters ρ and η.

Using the values of the previous section for the CKM matrix, as of 2008 the best determination of the Wolfenstein parameter values is:[6] In 2008, Kobayashi and Maskawa shared one half of the Nobel Prize in Physics "for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature".