Emerging Δ M _d -anomaly from tree-level determinations of | V _cb | and the angle γ

We point out that the recently increased value of the angle γ in the unitarity triangle (UT), determined in tree-level decays to be γ=(74.0-5.8+5.0)∘ by the LHCb collaboration, combined with the most recent value of | V _cb | implies an enhancement of Δ M _d over the data in the ballpark of 30 %. This is larger by roughly a factor of two than the enhancement of Δ M _s that is independent of γ. This disparity of enhancements is problematic for models with constrained minimal flavour violation (CMFV) and also for U(2) ³ models. In view of the prospects of measuring γ with the precision of ± 1 ^∘ by Belle II and LHCb in the coming years, we propose to use the angles γ and β together with | V _cb | and | V _us | as the fundamental parameters of the CKM matrix until | V _ub | from tree-level decays will be known precisely. Displaying Δ M _{s , d} as functions of γ clearly demonstrates the tension between the value of γ from tree-level decays, free from new physics (NP) contributions, and Δ M _{s , d} calculated in CMFV and U(2) ³ models and thus exhibits the presence of NP contributions to Δ M _{s , d} beyond these frameworks. We calculate the values of | V _ub | and | V _td | as functions of γ and | V _cb | and discuss the implications of our results for ε _K and rare K and B decays. We also briefly discuss a future strategy in which β, possibly affected by NP, is replaced by | V _ub |.