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

Abstract

Latest measurement of the ratio of branching ratios $R_D=\mathcal{B}(B\to D\tau \nu )/\mathcal{B}(B\to Dl\nu )$ and $R_{D^{\ast }}=\mathcal{B}(B\to D^{\ast }\tau \nu )/\mathcal{B}(B\to D^{\ast }l\nu )$, where $l$ is either an electron or muon, differs from the standard model expectation by $1.9\sigma$ and $3.3\sigma$, respectively. Similar tension has been observed in purely leptonic $B\to \tau \nu$ 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 $R_D^{\tau }=R_D/\mathcal{B}(B\to \tau \nu )$ and $R_{D^{\ast }}^{\tau }=R_{D^{\ast }}/\mathcal{B}(B\to \tau \nu )$, we impose $2\sigma$ constraints coming from $R_D^{\tau }$ and $R_{D^{\ast }}^{\tau }$ in addition to the constraints coming from $R_D$, $R_{D^{\ast }}$, and $\mathcal{B}(B\to \tau \nu )$ to constrain the new physics parameter space. We study the impact of new physics on various observables related to $B_s\to (D_s,D_s^{\ast })\tau \nu$ and $B\to \pi \tau \nu$ decay processes.

24 pages, 7 figures, typos corrected, references added