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

TL;DR

This paper provides a model-independent prediction for the ratio of branching fractions of Bc decays to eta_c with tau and mu neutrinos, using form factors and existing lattice QCD data, resulting in a precise estimate.

Contribution

It introduces a novel, model-independent method to predict R(eta_c) combining dispersive relations, heavy-quark symmetry, and lattice QCD, reducing uncertainties compared to previous models.

Findings

Predicted R(eta_c)=0.29(5) with reduced uncertainty.

Prediction aligns with previous models but is more precise.

Method can be applied to other semileptonic decay ratios.

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.