Scrutinizing New Physics in Semi-leptonic $B_c\to J/\psi \tau \nu$ Decay

Abstract

We perform a global analysis of the $b\to c\tau \nu$ data using the recent lattice results on the $B_c\to J/\psi$ vector and axial-vector form factors. To explore the effects from the tensor operator of new physics beyond the standard model, we determine the tensor form factors by using the non-relativistic QCD (NRQCD) relations between tensor and (axial-)vector form factors. Based on the lattice+NRQCD form factors, we fit the Wilson coefficients and the new physics couplings in $R_2$, $S_1$ and $U_1$ leptoquark models by including the recently measured $R({\Lambda }_c)$ and imposing the relaxed constraint $\mathcal{B}(B_c\to J/\psi )<30\%$ in light of the recent studies on LEP1 data and $B_c$ lifetime. We give predictions for the experimental observables including $R(J/\psi )$, $P_{\tau }(J/\psi )$, $F_L(J/\psi )$ and ${\mathcal{A}}_{FB}(J/\psi )$ as well as their $q^2$ distribution in new physics scenarios/models. Our results suggest that the longitudinal $\tau$ polarization fraction $P_{\tau }(J/\psi )$ and the forward-backward asymmetry ${\mathcal{A}}_{FB}(J/\psi )$ are useful for testing the $R_2$ leptoquark model.

Comments: 19 pages, 10 figures and 6 tables