$B_{s} \rightarrow D_{s}/B \rightarrow D$ 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 $\overline{B}^{0} \rightarrow D^{+}\ell^{-}\overline{\nu}$ and $\overline{B}^{0}_{s} \rightarrow D^{+}_{s}\ell^{-}\overline{\nu}$ 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 $\text{BR}(B_{s}^{0} \rightarrow \mu + \mu-)$. 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 $f^{(s)}_{0}(M^{2}_{π})/f^{(d)}_{0}(M^{2}_{K})=1.046(44)_{\text{stat}}(15)_{\text{syst}}$ and $f^{(s)}_{0}(M^{2}_{π})/f^{(d)}_{0}(M^{2}_{\pi})=1.054(47)_{\text{stat}}(17)_{\text{syst}}$. In contrast to a QCD sum-rule calculation, no significant departure from $U$-spin $(d \leftrightarrow s)$ symmetry is observed.