Relations between $b\rightarrow c\tau \nu$ Decay Modes in Scalar Models

As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition $b\rightarrow c\tau \nu$, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair $q^2$ in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays $B\rightarrow D^{*}\tau\nu$, $B_s\rightarrow D_s^*\tau\nu$, $B_c\rightarrow J/\psi\tau\nu$ and $B\rightarrow D\tau\nu$, $B_s\rightarrow D_s\tau\nu$, $B_c\rightarrow \eta_c\tau\nu$, with implications for $R(D^{(*)})$, $R(D_s^{(*)})$, $R(J/\psi)$, $R(\eta_c)$, and $\mathcal{B}(B_c\rightarrow \tau\nu)$. The slope and curvature of the characteristic $q^2$-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.