B_s->D_s/B->D Semileptonic Form-Factor Ratios and Their Application to BR(B^0_s->\mu^+\mu^-)

Abstract

We calculate form-factor ratios between the semileptonic decays \bar{B}->D^+\ell^-\bar{\nu} and \bar{B}_s->D_s^+\ell^-\bar{\nu} with lattice QCD. These ratios are a key theoretical input in a new strategy to determine the fragmentation fractions of the neutral B decays, which are needed for measurements of BR(B^0_s-> \mu^+\mu^-). We use the MILC ensembles of gauge configurations with 2+1 flavors of sea quarks at two lattice spacings 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.

Comments: 30 pages, 11 figures. Fig. 1 updated. Table II added. Conforms with version published in Physical Review D, except typos fixed, as in the PRD Erratum, in Table V (previously Table IV in arXiv v1). Results unchanged