Rephasing-invariant parametrizations of generalized Kobayashi-Maskawa matrices

We discuss a simple rephase-invariant parametrization of the Kobayashi-Maskawa mixing matrix V which easily generalizes to more than three generations and which we believe to be suitable as a phenomenological standard. Our independent parameters are the magnitudes ‖$V_{i\alpha }$‖ with i<α and the phase of plaquettes, ${\mathrm{V}}_{\mathit{a}\mathrm{\alpha }}$ ${\mathrm{V}}_{\mathit{j}\mathrm{\beta }}$V${\mathrm{*}}_{\mathit{j}\mathrm{\alpha }}$), where j=i+1, β=α+1, β=α+1, and j<β. The detailed discussion includes consequences of unitarity constraints, modifications in cases of degenerate quark masses, and the relation of Jarlskog’s invariant functions of mass matrices. We reexpress the CP-violation phenomenology of the K-K¯ and B-B¯ systems in this rephase-invariant formalism. We exhibit a fourth-generation scenario where the top-quark mass need not be large even in the presence of large $B_d$-B${¯}_d$ mixing.