Zooming into CP violation in $B_{(s)}\to hh$ Decays

Abstract

The LHCb collaboration has recently reported the first observation of CP violation in the penguin-dominated $B_s^0\to K^{-}{K}^{+}$ decay and further new measurements, indicating differences between the direct CP asymmetries of both the $B_s^0\to K^{-}{K}^{+}$, $B_d^0\to {\pi }^{-}{K}^{+}$ and the $B_d^0\to {\pi }^{-}{\pi }^{+}$, $B_s^0\to K^{-}{\pi }^{+}$ modes. We show that these puzzling differences can be accommodated through sizeable penguin annihilation and exchange topologies in the Standard Model, and constrain them. Utilising the $U$-spin symmetry, we extract the angle $\gamma$ of the unitarity triangle from the CP asymmetries in the $B_s^0\to K^{-}{K}^{+}$, $B_d^0\to {\pi }^{-}{\pi }^{+}$ system alone, finding $\gamma =(65_{-7}^{+11}{)}^{\circ }$, in perfect agreement with the determination from tree-level $B\to DK$ decays. The $B_s^0$--${\bar{B}}_s^0$ mixing phase ${\varphi }_s$ can be extracted from CP violation measurements in $B_s^0\to K^{-}{K}^{+}$ in a clean way. We present a new strategy and extract ${\varphi }_s=-(3.6\pm 5.4{)}^{\circ }$. This result is in agreement with the determination from $B_s^0\to J/\psi \varphi$ decays. New CP-violating contributions would influence these determinations differently. Hence it is interesting to keep monitoring both as the experimental picture sharpens.

Comments: 18 pages