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Unitary matrix containing information on the weak interaction

In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix which 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.

To generalize the matrix, count the number of physically important parameters in this matrix V which appear in experiments. If there are generations of quarks (2 flavours) then

An  ×  unitary matrix (that is, a matrix V such that , where is the conjugate transpose of V and I is the identity matrix) requires 2 real parameters to be specified. 2 − 1 of these parameters are not physically significant, because one phase can be absorbed into each quark field (both of the mass eigenstates, and of the weak eigenstates), but the matrix is independent of a common phase. Hence, the total number of free variables independent of the choice of the phases of basis vectors is 2 − (2 − 1) = ( − 1)2. Of these, ( − 1) are rotation angles called quark mixing angles. The remaining ( − 1)( − 2) are complex phases, which cause CP violation.

For the case  = 2, there is only one parameter, which is a mixing angle between two generations of quarks. Historically, this was the first version of CKM matrix when only two generations were known. It is called the Cabibbo angle after its inventor Nicola Cabibbo.

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

Four independent parameters are required to fully define the CKM matrix. Many parameterizations have been proposed, and three of the most common ones are shown below.

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". Some physicists were reported to harbor bitter feelings about the fact that the Nobel Prize committee failed to reward the work of Cabibbo, whose prior work was closely related to that of Kobayashi and Maskawa. Asked for a reaction on the prize, Cabibbo preferred to give no comment.

at SLAC, California, and at KEK, Japan.