Theoretical Review of $γ/ϕ_3$ Measurements with $B_s$ Decays to Charm

Abstract

We give an overview of various determinations of $γ/ϕ_3$ 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 $B^0_d$-$\bar B^0_d$ and $B^0_s$--$\bar B^0_s$ mixing phases $ϕ_d$ and $ϕ_s$ from $B_d\to J/ψK_S$ and $B_s\to J/ψϕ$, 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 $ϕ_s$ and $ϕ_d$ are offered by the pure tree decays $B_s\to D_\pm K_{S(L)}$ and $B_d\to D_\pmπ^0, D_\pmρ^0, ...$, respectively, which are very interesting for the searches of new physics.