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

TL;DR

This paper introduces a novel strategy to measure the $B_s^0$-$ar{B}_s^0$ mixing phase $oldsymbol{\phi_s}$ with high precision by combining $U$-spin symmetry and semileptonic decays, aiming to improve CP violation studies.

Contribution

It proposes a new method using semileptonic decays and $oldsymbol{\gamma}$ as input to extract $oldsymbol{\phi_s}$ with theoretical uncertainty around 0.5°, surpassing current approaches.

Findings

Potential to measure $oldsymbol{\phi_s}$ with ~0.5° precision

Utilizes $B^0_s o K^- uar{ u}$ and $B^0_d o uar{ u}$ decays

Addresses challenges from $U$-spin-breaking corrections

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 $\phi_s$ from CP violation in the $B^0_s\to K^-K^+$, $B^0_d\to\pi^-\pi^+$ 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 ${\cal O}(5^\circ)$ at Belle II and the LHCb upgrade. We propose a new strategy, using $\gamma$ as input and utilizing $B^0_s\to K^-\ell^+\nu_\ell$, $B^0_d\to \pi^-\ell^+\nu_\ell$ decays, which allows an extraction of $\phi_s$ 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.