The cabibbo-kobayashi-maskawa quark-mixing matrix

F. J. Gilman, K. Kleinknecht, B. Renk
2000 European Physical Journal C: Particles and Fields  
In the standard model with SU (2) x U(1) as the gauge group of electroweak interactions, both the quarks and leptons are assigned to be left-handed doublets and right-handed singlets. The quark mass eigenstates are not the same as the weak eigenstates, and the matrix relating these bases was defined for six quarks and given an explicit parametrization by Kobayashi and Maskawal in 1973. It generalizes the four-quark case, where the matrix is parametrized by a single angle, the Cabibbo angle.2 By
more » ... convention, the three charge 2/3 quarks (u, c, and t) are unmixed, and all ~-the mixing is expressed in terms of a 3 x 3 unitary matrix V operating on the . . charge -l/3 quarks (d, s, b): (1) -The values of individual matrix elements can in principle all be determined from weak decays of the relevant quarks, or, in some cases, from deep inelastic neutrino scattering. Using the constraints discussed below (in the full-sized edition only), together with unitarity, and assuming only three generations, the 90% confidence limits on the magnitude of the elements of the complete matrix are: 0.9747 to 0.9759 0.218 to 0.224 0.001 to 0.007 0.218 to 0.224 0.9734 to 0.9752 0.030 to 0.058 . (2) 0.003 to 0.019 0.029 to 0.058 0.9983 to 0.9996 The ranges shown are for the individual matrix elements. The constraints of unitarity connect different elements, so choosing a specific value for one element restricts the range of the others.
doi:10.1007/bf02683407 fatcat:mvkadqaqfncvho4olp6r77p4ne