Relations between b → cτν 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 → cτν, 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 q2 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 $$ B\to {D}^{\ast}\tau v,{B}_s\to {D}_s^{\ast}\tau v,{B}_c\to J/\psi \tau v $$ B → D ∗ τv , B s → D s ∗ τv , B c → J / ψτv and B → Dτv, Bs → Dsτv, Bc → ηcτv, with implications for R(D(*)), $$ R\left({D}_s^{\left(\ast \right)}\right) $$ R D s ∗ , R(J/ψ), R(ηc), and ℬ(Bc → τv). The slope and curvature of the characteristic q2-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.