ΔMs theory precision confronts flavour anomalies

Based on recent HQET sum rule and lattice calculations we present updated Standard Model predictions for the mass differences of neutral B mesons: Delta M-s(SM) = (18.4(-1.2)(+0.7)) ps(-1) and Delta M-d(SM) = (0.533(-0.036)(+0:.022)) ps(-1) and study their impact on new physics models that address the present hints of anomalous data in b -> sll transitions. We also examine future prospects of further reducing the theory uncertainties and discuss the implications of a 2025 scenario with Delta M-s(SM) =(18.4 +/- 0.5) ps(-1). In particular, the latter yields upper bounds M-Z' less than or similar to 0. 9TeV and M-S3 less than or similar to 30TeV for the minimal Z' and S-3 lepto-quark explanations of the b -> sll anomalies, respectively.