On Testing Unitarity of the Quark Mixing Matrix

Abstract

Unitarity triangles and characteristic measurables of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix are discussed. Beyond the $3\times 3$ CKM scheme we make a rephasing-invariant generalization of the Gronau-Wyler-Dunietz approach to determine the weak phase shift in $B_u^{\pm }\to D{K}^{\pm }$ or $B_d^0\to D{K}^{\ast 0}$ vs ${\bar{B}}_d^0\to D{\bar{K}}^{\ast 0}$, which is only sensitive to the underlying new physics in $D^0-{\bar{D}}^0$ mixing. We also show that the weak angle $\gamma \equiv \arg (-V_{ub}^{\ast }{V}_{cd}^{\ast }{V}_{ud}{V}_{cb})$ is possible to be determined from the $CP$ asymmetries of some $B_d$ decays, even in a non-standard model with an extended quark sector. Brief comments are given on tests of unitarity of the $3\times 3$ CKM matrix.

Comments: Postscript file 15 pages. A talk given at the Conference on Production and Decay of Hyperons, Charm and Beauty Hadrons, Strasbourg, France, September 5 - 8, 1995 (to appear in the conference proceedings)