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

TL;DR

This paper derives relations between differential decay rates of semileptonic $b ightarrow c au u$ decays in scalar models, enabling extraction of new physics parameters from decay distributions.

Contribution

It establishes decay-rate relations based on the Ward identity, linking measurable decay modes to scalar new physics without relying on form factor uncertainties.

Findings

Relations between decay rates for different modes are derived.

A universal function for decay modes is identified, independent of specific channels.

The $q^2$-dependence slope and curvature directly relate to scalar new physics parameters.

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 $b\rightarrow c\tau \nu$, 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.