  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.
