Decay constant of $B_s$ and $B^*_s$ mesons from ${\rm N_f}=2$ lattice QCD}

TL;DR

This study uses two-flavor lattice QCD to estimate the decay constants of $B_s$ and $B^*_s$ mesons, testing the effectiveness of the step scaling in mass strategy with Wilson-Clover fermions for heavy-strange sector extrapolation.

Contribution

It provides new lattice QCD estimates of $f_{B_s}$ and the ratio $f_{B^*_s}/f_{B_s}$, demonstrating the applicability of the step scaling in mass method for bottom quark sector.

Findings

Estimated $f_{B_s}$ as 215 MeV with uncertainties.

Determined the ratio $f_{B^*_s}/f_{B_s}$ as approximately 1.02.

Validated the step scaling in mass approach for heavy-strange mesons.

Abstract

We report on a two-flavor lattice QCD estimate of the $B_s$ and $B^*_s$ leptonic decays parameterized by the decay constants $f_{B_s}$ and $f_{B^*_s}$. In addition to their relevance for phenomenology, their extraction has allowed us to investigate whether the "step scaling in mass" strategy is suitable with Wlilson-Clover fermions to smoothly extrapolate quantities of the heavy-strange sector up to the bottom scale. From the central value of $f_{D_s}$ quoted by FLAG at $N_f=2$ and our ratio $\frac{f_{B_s}}{f_{D_s}}$, we obtain $f_{B_s}=215(10)(2)(^{+2}_{-5})$ MeV and $f_{B^*_s}/f_{B_s}=1.02(2)(^{+2}_{-0})$.