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 Bs mixing, in particular we get for the ratio of the V − A Bag parameter in the Bs and Bd 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 ΔMs = (18.5 + 1.2− 1.5 )ps− 1 and ΔMd = (0.547 + 0.035− 0.046 )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 |Vtd/Vts| = 0.2045 + 0.0012− 0.0013 , which is compatible with the results from the CKM fitting groups, but again more precise.
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King, D., Lenz, A. & Rauh, T. Bs mixing observables and |Vtd/Vts| from sum rules. J. High Energ. Phys. 2019, 34 (2019). https://doi.org/10.1007/JHEP05(2019)034
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DOI: https://doi.org/10.1007/JHEP05(2019)034