Emerging $\Delta M_{d}$-Anomaly from Tree-Level Determinations of $|V_{cb}|$ and the Angle $\gamma$

Understand

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 roughly by a factor of two larger 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.