Bs mixing observables and Vtd/Vts from sum rules

Abstract

We consider the effects of a non-vanishing strange-quark mass in the determination of the full basis of dimension six matrix elements for $B_s$ mixing, in particular we get for the ratio of the $V-A$ Bag parameter in the $B_s$ and $B_d$ system: ${\overline{B}}_{Q_1}^s/{\overline{B}}_{Q_1}^d=0.987_{-0.009}^{+0.007}$. Combining these results with the most recent lattice values for the ratio of decay constants $f_{B_s}/f_{B_d}$ we obtain the most precise determination of the ratio $\xi =f_{B_s}\sqrt{{\overline{B}}_{Q_1}^s}/f_{B_d}\sqrt{{\overline{B}}_{Q_1}^d}=1.2014_{-0.0072}^{+0.0065}$ in agreement with recent lattice determinations. We find $\Delta M_s=(18.5_{-1.5}^{+1.2}){\text{ps}}^{-1}$ and $\Delta M_d=(0.547_{-0.046}^{+0.035}){\text{ps}}^{-1}$ to be consistent with experiments at below one sigma. Assuming the validity of the SM, our calculation can be used to directly determine the ratio of CKM elements $|V_{td}/V_{ts}|=0.2045_{-0.0013}^{+0.0012}$, which is compatible with the results from the CKM fitting groups, but again more precise.

32 pages, 8 figures, journal version

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• Connecting neutral current $B$ anomalies with the heaviness of the third family