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

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

Jon A. Bailey et al. (Fermilab Lattice and MILC Collaborations)

Phys. Rev. D 85, 114502 – Published 4 June 2012; Erratum Phys. Rev. D 86, 039904 (2012)

Abstract

We calculate form-factor ratios between the semileptonic decays ${\bar{B}}^{0} \to D^{+} ℓ^{-} \bar{ν}$ and ${\bar{B}}_{s}^{0} \to D_{s}^{+} ℓ^{-} \bar{ν}$ 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 $BR (B_{s}^{0} \to μ^{+} μ^{-})$ . 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 $f_{0}^{(s)} (M_{π}^{2}) / f_{0}^{(d)} (M_{K}^{2}) = 1.046 (44)_{stat} (15)_{syst}$ and $f_{0}^{(s)} (M_{π}^{2}) / f_{0}^{(d)} (M_{π}^{2}) = 1.054 (47)_{stat} (17)_{syst}$ . In contrast to a QCD sum-rule calculation, no significant departure from $U$ -spin ( $d \leftrightarrow s$ ) symmetry is observed.