## Abstract

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} |.

Original language | English |
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Article number | 159 |

Journal | European Physical Journal C |

Volume | 79 |

Issue number | 2 |

DOIs | |

State | Published - 1 Feb 2019 |

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