Bs mixing observables and |Vtd/Vts| from sum rules

Abstract

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: $$ {\overline{B}}_{Q_1}^s/{\overline{B}}_{Q_1}^d={0.987}_{-0.009}^{+0.007} $$ B ¯ Q 1 s / 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 $$ {f}_{B_s}/{f}_{B_d} $$ f B s / f B d we obtain the most precise determination of the ratio $$ \xi ={f}_{B_s}\sqrt{{\overline{B}}_{Q_1}^s}/{f}_{B_d}\sqrt{{\overline{B}}_{Q_1}^d}={1.2014}_{-0.0072}^{+0.0065} $$ ξ = f B s B ¯ Q 1 s / f B d B ¯ Q 1 d = 1.2014 − 0.0072 + 0.0065 in agreement with recent lattice determinations. We find ΔM s  = (18.5 − 1.5 + 1.2 )ps− 1 and ΔM d  = (0.547 − 0.046 + 0.035 )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.