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تسجيل مستخدم جديدEmerging $Delta M_{d}$-Anomaly from Tree-Level Determinations of $|V_{cb}|$ and the Angle $gamma$
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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. 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 $|V_{ub}|$.
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