Emerging Delta M_{d}-anomaly from tree-level determinations of |V_{cb}| and the angle gamma

Abstract

We point out that the recently increased value of the angle gamma in the unitarity triangle (UT), determined in tree-level decays to be gamma =(74.0^{+5.0}_{-5.8})^circ by the LHCb collaboration, combined with the most recent value of |V_{cb}| implies an enhancement of Delta M_{d} over the data in the ballpark of 30%. This is larger by roughly a factor of two than the enhancement of Delta M_{s} that is independent of gamma . 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 gamma with the precision of pm 1^circ by Belle II and LHCb in the coming years, we propose to use the angles gamma and beta 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 Delta M_{s,d} as functions of gamma clearly demonstrates the tension between the value of gamma from tree-level decays, free from new physics (NP) contributions, and Delta M_{s,d} calculated in CMFV and U(2)^3 models and thus exhibits the presence of NP contributions to Delta M_{s,d} beyond these frameworks. We calculate the values of |V_{ub}| and |V_{td}| as functions of gamma and |V_{cb}| and discuss the implications of our results for varepsilon _K and rare K and B decays. We also briefly discuss a future strategy in which beta , possibly affected by NP, is replaced by |V_{ub}|.