CP violation and the CKM angle $γ$ from angular distributions of untagged $B_s$ decays governed by $\bar b\to\bar c u\bar s$

Abstract

We demonstrate that time-dependent studies of angular distributions for $B_s$ decays caused by $\bar b\to\bar cu\bar s$ quark-level transitions extract cleanly and model-independently the CKM angle $γ$. This CKM angle could be cleanly determined from untagged $B_s$ decays alone, if the lifetime difference between the $B_s$ mass eigenstates $B_s^L$ and $B_s^H$ is sizable. The time-dependences for the relevant tagged and untagged observables are given both in a general notation and in terms of linear polarization states and should exhibit large CP-violating effects. These observables may furthermore provide insights into the hadronization dynamics of the corresponding exclusive $B_s$ decays thereby allowing tests of the factorization hypothesis.