Towards New Frontiers in the Exploration of Charmless Non-Leptonic $B$ Decays

TL;DR

This paper proposes a novel method to precisely determine the $B_s^0$-$ar{B}_s^0$ mixing phase using charmless non-leptonic $B$ decays, enhancing the search for new CP violation sources.

Contribution

It introduces a new approach combining semileptonic and non-leptonic decays to improve theoretical precision in measuring CP-violating phases.

Findings

Potential to achieve 0.5° precision in $\,\phi_s$ measurement

Probes penguin, exchange, and annihilation topologies

Enhances future CP violation searches

Abstract

Non-leptonic $B$ decays into charmless final states offer an important laboratory to study CP violation and the dynamics of strong interactions. Particularly interesting are $B^0_s\to K^-K^+$ and $B^0_d\to\pi^-\pi^+$ decays, which are related by the $U$-spin symmetry of strong interactions, and allow for the extraction of CP-violating phases and tests of the Standard Model. The theoretical precision is limited by $U$-spin-breaking corrections and innovative methods are needed in view of the impressive future experimental precision expected in the era of Belle II and the LHCb upgrade. We have recently proposed a novel method to determine the $B_s^0$-$\bar{B}_s^0$ mixing phase $\phi_s$ from the $B_s^0\to K^-K^+$, $B_d^0\to \pi^-\pi^+$ system, where semileptonic $B^0_s\to K^-\ell^+\nu_\ell$, $B^0_d\to \pi^-\ell^+\nu_\ell$ decays are a new ingredient and the theoretical situation is very favourable. We discuss this strategy in detail, with a focus on penguin contributions as well as exchange and penguin-annihilation topologies which can be probed by a variety of non-leptonic $B$ decays into charmless final states. We show that a theoretical precision as high as ${\cal O}(0.5^\circ)$ for $\phi_s$ can be attained in the future, thereby offering unprecedented prospects for the search for new sources of CP violation.