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

Abstract

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 $b\to c\tau \nu$, 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 $B\to D^{\ast }\tau \nu$, $B_s\to D_s^{\ast }\tau \nu$, $B_c\to J/\psi \tau \nu$ and $B\to D\tau \nu$, $B_s\to D_s\tau \nu$, $B_c\to {\eta }_c\tau \nu$, with implications for $R(D^{(\ast )})$, $R(D_s^{(\ast )})$, $R(J/\psi )$, $R({\eta }_c)$, and $\mathcal{B}(B_c\to \tau \nu )$. 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.

30 pages, 1 figure. Additional references and clarifications. Conclusions unchanged