Theoretical Review of $\gamma /{\varphi }_3$ Measurements with $B_s$ Decays to Charm

Abstract

We give an overview of various determinations of $\gamma /{\varphi }_3$ with the help of $B_s$ decays into charmed final states, distinguishing between transitions with tree and penguin contributions and pure tree decays. In the corresponding strategies, the $U$-spin flavour symmetry of strong interactions provides a very useful tool, and offers interesting "by-producs" for the $B$-physics programme at the LHC, including the control of the penguin uncertainties in the determinations of the $B_d^0$-${\bar{B}}_d^0$ and $B_s^0$--${\bar{B}}_s^0$ mixing phases ${\varphi }_d$ and ${\varphi }_s$ from $B_d\to J/\psi K_S$ and $B_s\to J/\psi \varphi$, respectively, and an alternative extraction of the latter phase through $B_s\to D_s^{+}{D}_s^{-}$. Finally, we point out that the cleanest determinations of the mixing phases ${\varphi }_s$ and ${\varphi }_d$ are offered by the pure tree decays $B_s\to D_{\pm }{K}_{S(L)}$ and $B_d\to D_{\pm }{\pi }^0,D_{\pm }{\rho }^0,...$, respectively, which are very interesting for the searches of new physics.

Comments: 4 pages, 2 figures, talk given at the 4th International Workshop on the CKM Unitarity Triangle (CKM2006), 12-16 December 2006, Nagoya, Japan, to appear in the proceedings (KEK Report)