Scrutinizing New Physics in Semi-leptonic $B_{c}\rightarrow J/\psi \tau\nu$ Decay

TL;DR

This paper analyzes $b o c au u$ decay data using lattice and NRQCD form factors, fitting new physics models with leptoquarks, and predicts observables to test these models.

Contribution

It provides a comprehensive global analysis incorporating recent lattice results and explores tensor operators in new physics models for $B_c$ decays.

Findings

Constraints on leptoquark models from $R(\Lambda_c)$ and $B_c$ lifetime.

Predictions for $R(J/\psi)$, $P_ au(J/\psi)$, $F_L(J/\psi)$, and $\mathcal{A}_{FB}(J/\psi)$.

Identification of $P_ au(J/\psi)$ and $\mathcal{A}_{FB}(J/\psi)$ as key tests for $R_2$ leptoquark model.

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.