$B_{s} \rightarrow D_{s}/B \rightarrow D$ semileptonic form-factor ratios and their application to $\text{BR}(B_{s}^{0} \rightarrow \mu + \mu-)$

Abstract

We calculate form-factor ratios between the semileptonic decays B―0→D+ℓ−ν― and B―s0→Ds+ℓ−ν― with lattice QCD. These ratios are a key theoretical input in a new strategy to determine the fragmentation fractions of neutral B decays, which are needed for measurements of BR(Bs0→μ+μ−). We use the MILC ensembles of gauge configurations with 2+1 flavors of sea-quarks at two s of approximately 0.12 fm and 0.09 fm. We use the model-independent z parametrization to extrapolate our simulation results at small recoil toward maximum recoil. Our results for the form-factor ratios are f0(s)(Mπ2)/f0(d)(MK2)=1.046(44)stat(15)syst and f0(s)(Mπ2)/f0(d)(Mπ2)=1.054(47)stat(17)syst. In contrast to a QCD sum-rule calculation, no significant departure from U-spin (d↔s) symmetry is observed.