Model-Independent Prediction of $R(\eta_c)$

Abstract

We present a model-independent prediction for $R(\eta_c) \! \equiv \! \mathcal{BR} (B_c \rightarrow \eta_c \, \tau^+\nu_\tau)/ \mathcal{BR} (B_c \rightarrow \eta_c \, \mu^+\nu_\mu)$. This prediction is obtained from the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing determinations from lattice QCD. The resulting prediction, $R(\eta_c)=0.29(5)$, agrees with the weighted average of previous model predictions, but with reduced uncertainties.