New Physics in B_q ⁰B_q ⁰ mixing: Present challenges, prospects, and implications for B_q ⁰??⁺?^-

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