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

Abstract

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the $B_s\to D_s\ell \nu$ 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 $B\to D\ell \nu$ form factors, we determine the ratios $f_0^{B_s\to D_s}(M_{\pi }^2)/f_0^{B\to D}(M_K^2)=1.000(62)$ and $f_0^{B_s\to D_s}(M_{\pi }^2)/f_0^{B\to D}(M_{\pi }^2)=1.006(62)$. These results give the fragmentation fraction ratios $f_s/f_d=0.310(30{)}_{stat.}(21{)}_{syst.}(6{)}_{theor.}(38{)}_{latt.}$ and $f_s/f_d=0.307(16{)}_{stat.}(21{)}_{syst.}(23{)}_{theor.}(44{)}_{latt.}$, respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of $B_s$ meson branching fractions at hadron colliders, in particular for the rare decay $\mathcal{B}(B_s\to {\mu }^{+}{\mu }^{-})$. In addition to the form factor results, we make the first prediction of the branching fraction ratio $R(D_s)=\mathcal{B}(B_s\to D_s\tau \nu )/\mathcal{B}(B_s\to D_s\ell \nu )=0.301(6)$, where $\ell$ is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of $B$ mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of $R(D_s)$ may help understand this discrepancy.

21 pages, 15 figures

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• FLAG Review 2024
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• A puzzle in ${\bar{B}}_{(s)}^0\to D_{(s)}^{(\ast )+}\{{\pi }^{-},K^{-}\}$ decays and extraction of the $f_s/f_d$ fragmentation fraction
• Signature of Lepton flavor universality violation in $B_s\to D_s\tau \nu$ semileptonic decays
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• Lepton number violation in $B_s$ meson decays induced by an on-shell Majorana neutrino
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• Form factor ratios for $B_s\to K\ell \nu$ and $B_s\to D_s\ell \nu$ semileptonic decays and $|V_{ub}/V_{cb}|$
• Heavy+light pseudoscalar meson semileptonic transitions
• Measurement of the shape of the $B_s^0\to D_s^{\ast -}{\mu }^{+}{\nu }_{\mu }$ differential decay rate
• Using $B_s^0\to D_s^{\mp }{K}^{\pm }$ Decays as a Portal to New Physics
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• The ratio $\mathcal{R}(D_s)$ for $B_s\to D_s\ell {\nu }_{\ell }$ by using the QCD light-cone sum rules within the framework of heavy quark effective field theory
• Testing Lepton Flavor Universality at the Electron-Ion Collider
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• CP violation in $B_s$ decays mediated by two nearly-degenerate Majorana neutrinos