Implication of $b\to c\tau \nu$ flavor anomalies on $B_s\to D_s^{\ast }\tau \nu$ decay observables

Abstract

The experimental predictions of $R_D$, $R_{D^{\ast }}$, $R_{J/\psi }$, $P_{\tau }^{D^{\ast }}$ and $F_L^{D^{\ast }}$ in $B$ decays mediated via $b\to cl\nu$ quark level transition deviate significantly from the standard model expectations. The current world average of the ratio of branching ratios $R_D$ and $R_{D^{\ast }}$ in $B\to D^{(\ast )}l\nu$ ($l\in e,\tau$) show $1.4\sigma$ and $2.5\sigma$ deviation from the SM expectations. Similarly, the $\tau$ polarization fraction $P_{\tau }^{D^{\ast }}$ and the longitudinal polarization fraction of the $D^{\ast }$ meson $F_L^{D^{\ast }}$ in $B\to D^{\ast }\tau \nu$ are found to deviate from the standard model expectations at $1.6\sigma$ and $1.5\sigma$ level, respectively. In addition, the ratio of branching ratio $R_{J/\psi }$ in $B_c\to J/\psi l\nu$ deviates from the standard model prediction at $2\sigma$ level. In this regard, we study the implication of $R_D$, $R_{D^{\ast }}$, $R_{J/\psi }$, $P_{\tau }^{D^{\ast }}$, and $F_L^{D^{\ast }}$ anomalies on $B_s\to D_s^{\ast }\tau \nu$ decay observables in a model independent effective field theory formalism. We give predictions of several physical observables in the standard model and in the presence of various $1D$ and $2D$ new physics scenarios.

Comments: 15 pages, 3 figures, 10 tables