Cabibbo–Kobayashi–Maskawa matrix

In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix that contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks.

Description

Predecessor: Cabibbo matrix

In 1963, Nicola Cabibbo introduced the Cabibbo angle (θc) to preserve the universality of the weak interaction.

Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy,

on the effectively rotated nonstrange and strange vector and axial weak currents, which he references.

In light of current concepts (quarks had not yet been proposed), the Cabibbo angle is related to the relative probability that down and strange quarks decay into up quarks ( |Vud|2 and |Vus|2 , respectively). In particle physics terminology, the object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks, here denoted by d′.

Mathematically this is:

d

′

=

V

u

d

d

+

V

u

s

s

,

{\displaystyle d'=V_{\mathrm {ud} }\;d~~+~~V_{\mathrm {us} }\;s~,}

or using the Cabibbo angle:

d

′

=

cos

⁡

θ

c

d

+

sin

⁡

θ

c

s

.