New Strategy to Explore CP Violation with $B_s^0\to K^{-}{K}^{+}$

Abstract

The $U$-spin symmetry provides a powerful tool to extract the angle $\gamma$ of the Unitarity Triangle and the $B_s^0$-${\bar{B}}_s^0$ mixing phase ${\varphi }_s$ from CP violation in the $B_s^0\to K^{-}{K}^{+}$, $B_d^0\to {\pi }^{-}{\pi }^{+}$ system. LHCb has obtained first results with uncertainties at the $7^{\circ }$ level. Due to $U$-spin-breaking corrections, it will be challenging to reduce the uncertainty below $\mathcal{O}(5^{\circ })$ at Belle II and the LHCb upgrade. We propose a new strategy, using $\gamma$ as input and utilizing $B_s^0\to K^{-}{\ell }^{+}{\nu }_{\ell }$, $B_d^0\to {\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ decays, which allows an extraction of ${\varphi }_s$ with a future theoretical precision of up to $\mathcal{O}(0.5^{\circ })$, thereby matching the experimental prospects. Since $B_s^0\to K^{-}{K}^{+}$ is dominated by penguin topologies, new sources of CP violation may be revealed.

Comments: 8 pages, 3 figures