$B_s \to D_s \ell \nu$ Form Factors and the Fragmentation Fraction Ratio $f_s/f_d$

Understand

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the $B_s \rightarrow D_s \ell \nu$ decay over the full physical range of momentum transfer.

• In conjunction with future experimental data, our results will provide a new method to extract $|V_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of this parameter.
• Combining the form factor results at non-zero recoil with recent HPQCD results for the $B \rightarrow D \ell \nu$ form factors, we determine the ratios $f^{B_s \rightarrow D_s}_0(M_\pi^2) / f^{B \rightarrow D}_0(M_K^2) = 1.000(62)$ and $f^{B_s \rightarrow D_s}_0(M_\pi^2) / f^{B \rightarrow D}_0(M_\pi^2) = 1.006(62)$.
• These results give the fragmentation fraction ratios $f_s/f_d = 0.310(30)_{\mathrm{stat.}}(21)_{\mathrm{syst.}}(6)_{\mathrm{theor.}}(38)_{\mathrm{latt.}} $ and $f_s/f_d = 0.307(16)_{\mathrm{stat.}}(21)_{\mathrm{syst.}}(23)_{\mathrm{theor.}}(44)_{\mathrm{latt.}}$, respectively.