Emerging $$Δ M_{d}$$ ΔMd -anomaly from tree-level determinations of $$|V_{cb}|$$ |Vcb| and the angle $$γ $$ γ - Monika Blanke; Andrzej J. Buras (European Physical Journal C: Particles and Fields, 2019)
Abstract We point out that the recently increased value of the angle $$γ $$ γ in the unitarity triangle (UT), determined in tree-level decays to be $$γ =(74.0^{+5.0}_{-5.8})^° $$ γ=(74.0-5.8+5.0)∘ by the LHCb collaboration, combined with the most recent value of $$|V_{cb}|$$ |Vcb| implies an enhancement of $$Δ M_{d}$$ ΔMd over the data in the ballpark of $$30%$$ 30% . This is larger by roughly a factor of two than the enhancement of $$Δ M_{s}$$ ΔMs that is independent of $$γ $$ γ . This disparity of enhancements is problematic for models with constrained minimal flavour violation (CMFV) and also for $$U(2)^3$$ U(2)3 models. In view of the prospects of measuring $$γ $$ γ with the precision of $$± 1^° $$ ±1∘ by Belle II and LHCb in the coming years, we propose to use the angles $$γ $$ γ and $$β $$ β together with $$|V_{cb}|$$ |Vcb| and $$|V_{us}|$$ |Vus| as the fundamental parameters of the CKM matrix until $$|V_{ub}|$$ |Vub| from tree-level decays will be known precisely. Displaying $$Δ M_{s,d}$$ ΔMs,d as functions of $$γ $$ γ clearly demonstrates the tension between the value of $$γ $$ γ from tree-level decays, free from new physics (NP) contributions, and $$Δ M_{s,d}$$ ΔMs,d calculated in CMFV and $$U(2)^3$$ U(2)3 models and thus exhibits the presence of NP contributions to $$Δ M_{s,d}$$ ΔMs,d beyond these frameworks. We calculate the values of $$|V_{ub}|$$ |Vub| and $$|V_{td}|$$ |Vtd| as functions of $$γ $$ γ and $$|V_{cb}|$$ |Vcb| and discuss the implications of our results for $$ε _K$$ εK and rare K and B decays. We also briefly discuss a future strategy in which $$β $$ β , possibly affected by NP, is replaced by $$|V_{ub}|$$ |Vub| .