New Physics in $B_q^0-{\bar{B}}_q^0$ Mixing: Present Challenges, Prospects, and Implications for $B_q^0\to {\mu }^{+}{\mu }^{-}$

Abstract

The phenomenon of $B_q^0-{\bar{B}}_q^0$ mixing ($q=d,s$) provides a sensitive probe for physics beyond the Standard Model. We explore the corresponding space for New Physics left through the current data, having a careful look at analyses of the Unitarity Triangle that are needed for the Standard Model predictions of the $B_q$ mixing parameters. In particular, we explore the impact of tensions between inclusive and exclusive determinations of the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$. Moreover, we focus on the angle $\gamma$ of the Unitarity Triangle, comparing measurements from $B\to DK$ and $B\to \pi \pi$, $\rho \pi$, $\rho \rho$ decays, where the latter are typically interpreted in terms of the angle $\alpha$. We discuss various scenarios and present the corresponding state-of-the-art constraints on the New Physics parameters of $B_q^0-{\bar{B}}_q^0$ mixing. We point out that these results have an interesting application in the analysis of rare $B_q^0\to {\mu }^{+}{\mu }^{-}$ decays, allowing us to minimise the impact of CKM parameters in the search for New Physics. In view of the high-precision era, we make future projections. Interestingly, we find that for the extraction of the New Physics parameters in the $B_d$ system the determination of the apex of the Unitarity Triangle results in a key limiting factor. By contrast, the corresponding impact is negligible for the $B_s$ system, making it a promising candidate to reveal sources of New Physics.

Comments: 45 pages, 14 figures and 6 tables. This version matches the published version