Bs → Ds/B → D semileptonic form-factor ratios and their application to BR(Bs0→μ+μ-)

We calculate form-factor ratios between the semileptonic decays ($) over bar (0) -> D+ l(-) nu(-) and (nu) over bar (0)(s) -> D-s(+) l(-) (nu) over bar 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(B-s(0) -> mu(+)mu(-)). 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 f(0)((s)) (M-pi(2))/ f(0)((d)) (M-K(2)) = 1.046(44)(stat)(15)(syst) and f(0)((s)) (M-pi(2))/ f(0)((d))(M-pi(2)) = 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.