Model independent analysis of $b \to (c,\,u)\,τν$ leptonic and semileptonic decays

Abstract

Latest measurement of the ratio of branching ratios $R_D = \mathcal B(B \to D\,τ\,ν)/\mathcal B(B \to D\,l\,ν)$ and $R_{D^{\ast}} = \mathcal B(B \to D^{\ast}\,τ\,ν)/\mathcal B(B \to D^{\ast}\,l\,ν)$, where $l$ is either an electron or muon, differs from the standard model expectation by $1.9σ$ and $3.3σ$, respectively. Similar tension has been observed in purely leptonic $B \to τν$ decays as well. In this context, we consider the most general effective Lagrangian in the presence of new physics and perform a model independent analysis to explore various new physics couplings. Motivated by the recently proposed new observables $R_D^τ = R_D/\mathcal B(B \to τν)$ and $R_{D^{\ast}}^τ = R_{D^{\ast}}/\mathcal B(B \to τν)$, we impose $2σ$ constraints coming from $R_D^τ$ and $R_{D^{\ast}}^τ$ in addition to the constraints coming from $R_D$, $R_{D^{\ast}}$, and $\mathcal B(B \to τν)$ to constrain the new physics parameter space. We study the impact of new physics on various observables related to $B_s \to (D_s,\,D^{\ast}_s)τν$ and $B \to πτν$ decay processes.