Tests of the Standard Model in $B \to D\ell \nu_\ell$, $B \to D^* \ell \nu_\ell$ and $B_c \to J/\psi \, \ell \nu_\ell$

Abstract

A number of recent experimental measurements suggest the possibility of a breakdown of lepton ($\ell$) universality in exclusive $b \to c \ell \nu_\ell$ semileptonic meson decays. We analyze the full differential decay rates for several such processes, and show how to extract combinations of the underlying helicity amplitudes that are completely independent of $m_\ell$. Ratios of these combinations for different $\ell$ (as well as some combinations for a single value of $\ell$) therefore equal unity in the Standard Model and provide stringent tests of lepton universality. Furthermore, the extractions assume the form of weighted integrals over the differential decay rates and therefore are useful even in situations where data in some regions of allowed phase space may be sparse.