New Strategy to Explore CP Violation with $B^0_s\to K^-K^+$

The $U$-spin symmetry provides a powerful tool to extract the angle $γ$ of the Unitarity Triangle and the $B_s^0$-$\bar{B}_s^0$ mixing phase $ϕ_s$ from CP violation in the $B^0_s\to K^-K^+$, $B^0_d\toπ^-π^+$ 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 ${\cal O}(5^\circ)$ at Belle II and the LHCb upgrade. We propose a new strategy, using $γ$ as input and utilizing $B^0_s\to K^-\ell^+ν_\ell$, $B^0_d\to π^-\ell^+ν_\ell$ decays, which allows an extraction of $ϕ_s$ with a future theoretical precision of up to ${\cal O}(0.5^\circ)$, thereby matching the experimental prospects. Since $B^0_s\to K^-K^+$ is dominated by penguin topologies, new sources of CP violation may be revealed.

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