New physics in B_q ⁰- B ¯ q 0 mixing: present challenges, prospects, and implications for B q 0 ⃗ μ + μ −

The phenomenon of B⁰_q - B ¯ q 0 mixing (q = d, s) provides a sensitive probe for physics beyond the Standard Model (SM). 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 SM 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 γ of the Unitarity Triangle, comparing measurements from B → DK and B → π π, ρ π, ρ ρ decays, where the latter are typically interpreted in terms of the angle α. We discuss various scenarios and present the corresponding state-of-the-art constraints on the New Physics parameters of B_q ⁰- B ¯ q 0 mixing. We point out that these results have an interesting application in the analysis of rare B q 0 → μ + μ − 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.