Emerging Δ Md Δ M d -anomaly from tree-level determinations of |Vcb| | V cb | and the angle γ 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+5.0-5.8)^∘ by the LHCb collaboration, combined with the most recent value of |Vcb| implies an enhancement of Δ Md over the data in the ballpark of $$30%$$ . This is larger by roughly a factor of two than the enhancement of Δ Mₛ 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 |Vcb| and |Vᵤₛ| as the fundamental parameters of the CKM matrix until |Vub| from tree-level decays will be known precisely. Displaying Δ Ms,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 Ms,d calculated in CMFV and U(2)³ models and thus exhibits the presence of NP contributions to Δ Ms,d beyond these frameworks. We calculate the values of |Vub| and |Vtd| as functions of γ and |Vcb| 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 |Vub| .