Model-Independent Determination of $B_c^+ \to \eta_c\, \ell^+\, \nu$ Form Factors

TL;DR

This paper derives model-independent bounds on the form factors for the decay $B_c^+ o \,eta_c \, \\ell^+ \, u$ using lattice data, leading to precise Standard Model predictions for the ratio of branching fractions involving tau and muon final states.

Contribution

The paper introduces a model-independent approach to bound decay form factors and predicts branching ratio ratios for $B_c^+$ decays, incorporating full mass effects and lattice data.

Findings

Predicted $R(\eta_c) = 0.31^{+0.04}_{-0.02}$ within the Standard Model.

Estimated $R(J/\psi) = 0.26 \pm 0.02$, consistent with other results.

Argued that measuring $R(\eta_c)$ is feasible at LHCb.

Abstract

We derive model-independent bounds on the form factors for the decay $B_c^+ \to \eta_c\, \ell^+\, \nu$ including full mass effects, i.e. $\ell = e,\, \mu, \text{ and } \tau$. The bounds are obtained by using the BGL parameterization for the form factors, and fitting to the preliminary lattice data of the HPQCD Collaboration. Our main result after bounding the form factors is the Standard Model (SM) prediction for the ratio of branching fractions $R(\eta_c) = \mathcal{B}(B_c^+ \to \eta_c\, \tau^+\, \nu_{\tau}) / \mathcal{B}(B_c^+ \to \eta_c\, \mu^+\, \nu_{\mu})$. We find $R(\eta_c)|_{\text{SM}} = 0.31^{+0.04}_{-0.02}$, and argue that a measurement of $R(\eta_c)$ is within the reach of LHCb during the high luminosity run of the LHC. In addition, using the heavy-quark spin symmetry of the $B_c$ meson we relate our results for $B_c^+ \to \eta_c\, \ell^+\, \nu$ to those for $B_c^+ \to J/\psi\, \ell^+\, \nu$ yielding the estimate $R(J/\psi)|_{\text{SM}} = 0.26 \pm 0.02$ in good agreement with other determinations.