Bs→Dsℓν form factors and the fragmentation fraction ratio fs/fd

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the Bs→Dsℓν decay over the full physical range of momentum transfer. In conjunction with future experimental data, our results will provide a new method to extract |Vcb|, which may elucidate the current tension between exclusive and inclusive determinations of this parameter. Combining the form factor results at nonzero recoil with recent HPQCD results for the B→Dℓν form factors, we determine the ratios f0Bs→Ds(Mπ2)/f0B→D(MK2)=1.000(62) and f0Bs→Ds(Mπ2)/f0B→D(Mπ2)=1.006(62). These results give the fragmentation fraction ratios fs/fd=0.310(30)stat(21)syst(6)theor(38)latt and fs/fd=0.307(16)stat(21)syst(23)theor(44)latt, respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of Bs meson branching fractions at hadron colliders, in particular for the rare decay B(Bs→μ+μ−). In addition to the form factor results, we make the first prediction of the branching fraction ratio R(Ds)=B(Bs→Dsτν)/B(Bs→Dsℓν)=0.301(6), where ℓ is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of B mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of R(Ds) may help understand this discrepancy.