Semileptonic form factor ratio B_s->D_s/B->D and its application to BR(B^0_s->\mu^+\mu^-)

TL;DR

This paper reports a lattice QCD calculation of the ratio of semileptonic form factors for B_s and B decays, providing crucial input for determining B meson fragmentation and rare decay branching ratios.

Contribution

The study introduces a precise lattice QCD computation of the form factor ratio for B_s and B decays, aiding in the accurate determination of B meson fragmentation fractions.

Findings

Preliminary form factor ratio at specific momentum transfer is reported.

High-statistics lattice simulations with small lattice spacings were used.

Results support improved theoretical inputs for B_s to mu+mu- decay measurements.

Abstract

We present a (2+1)-flavor lattice QCD calculation of the form factor ratio between the semileptonic decays $\bar{B}^0_s \to D^+_sl^-\bar{\nu} $ and $\bar{B}^0 \to D^+l^-\bar{\nu} $. This ratio is an important theoretical input to the hadronic determination of the $B$ meson fragmentation fraction ratio $f_s/f_d$ which enters in the measurement of $\mathrm{BR}(B^0_s\to \mu^+\mu^-)$. Small lattice spacings and high statistics enable us to simulate the decays with a dynamic final $D$ meson of small momentum and reliably extract the hadronic matrix elements at nonzero recoil. We report our preliminary result for the form factor ratio at the corresponding momentum transfer of the two decays $f_0^{(s)}(M^2_\pi)/f_0^{(d)}(M^2_K)$.