Footprints of New Physics in $b\to c\tau\nu$ Transitions

In this work, we perform a combined analysis of the $R(D)$, $R(D^*)$, and $R(J/\psi)$ anomalies in a model-independent manner based on the general framework of the four-fermion effective field theory, paying special attention to the use of the hadronic form factors. For the $B\to D(D^*)$ transition form factors, we use the HQET parametrization that includes the higher order corrections of $\mathcal{O}(\alpha_s,\Lambda_{\mathrm{QCD}}/m_{b,c})$ and was determined recently from a fit to lattice QCD and light-cone sum rule results in complementary kinematical regions of the momentum transfer. For the $B_c\to J/\psi(\eta_c)$ transitions, we use the form factors calculated in the covariant light-front quark model, which are found to be well consistent with the preliminary lattice results. With this particular treatment of hadronic matrix elements, in our analysis the two classes of vector operators are shown to be the most favored single new physics (NP) operators by the current experimental constraints within $2\sigma$ and the LEP1 data on $Br(B_c\to \tau\nu)$ as well as the minimum $\chi^2$ fit, while the tensor operator is also allowed but severely constrained, and the scalar ones are excluded. Using the favored ranges and fitted values of the Wilson coefficients of the single NP operators, we also give a prognosis for the physical observables such as the ratios of decay rates ($R(D(D^*)), R(J/\psi(\eta_c))$) and other polarized observables as well as the $q^2$ distributions.