B s mixing observables and |V td /V ts | 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: B¯Q1s/B¯Q1d=0.987−0.009+0.007. Combining these results with the most recent lattice values for the ratio of decay constants fBs/fBd we obtain the most precise determination of the ratio ξ=fBsB¯Q1s/fBdB¯Q1d=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.