Extracting CKM Phases and $B_s - \bar{B}_s$ Mixing Parameters from Angular Distributions of Non-Leptonic B Decays

Abstract

Suggestions for efficiently determining the lifetimes and mass difference of the light and heavy $B_s$ mesons ($B_s^L, B_s^H$) from $B_s \to J/ \psi \phi, D_s^{*+}D_s^{*-}$ decays are given. Using appropriate weighting functions for the angular distributions of the decay products (moment analysis), one can extract $(\Gamma_H, \Gamma_L, \Delta m)_{B_s}$. Such a moment analysis allows the determination of the relative magnitudes and phases of the CP-odd and CP-even decay amplitudes. Efficient determinations of CP-violating effects occuring in $B_s \to J/\psi \phi, D_s^{*+} D_s^{*-}$ are discussed in the light of a possible width difference $(\Delta \Gamma)_{B_s}$, and the utility of this method for $B \to J/\psi K^*, D^{\ast +}_s \bar D^{\ast}$ decays is noted. Since our approach is very general, it can in principle be applied to all kinds of angular distributions and allows the determination of all relevant observables, including fundamental CKM (Cabibbo-Kobayashi-Maskawa) parameters, as well as tests of various aspects of the factorization hypothesis. Explicit angular distributions and weighting functions are given, and the general method that can be used for any angular distribution is indicated.