Model-Independent Bounds on $R(J/\psi)$ via Dispersive Relations

TL;DR

This paper derives model-independent bounds on the ratio R(J/ψ) for Bc+ decays using dispersive relations and lattice QCD, providing a reliable theoretical range that aligns with experimental data and reduces uncertainties.

Contribution

It introduces a novel approach combining dispersive relations, heavy-quark symmetry, and lattice QCD to bound R(J/ψ) without relying on specific models.

Findings

Bound on R(J/ψ): 0.20 to 0.39 at 95% CL

Agreement with LHCb measurement within 1.3 sigma

Predicted R(η_c)=0.29(5)

Abstract

Model-independent bounds on $R(J/\psi) \! \equiv \!\mathcal{BR} (B_c^+ \rightarrow J/\psi \, \tau^+\nu_\tau)/$ $\mathcal{BR} (B_c^+ \rightarrow J/\psi \, \mu^+\nu_\mu)$ are obtained through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing form factor determinations from lattice QCD. The resulting 95% confidence-level bound, $0.20\leq R(J/\psi)\leq0.39$, agrees with the recent LHCb result at $1.3 \, \sigma$, and removes the dominant model-dependent uncertainty from theory predictions. Using the same techniques, a prediction of $R(\eta_c)=0.29(5)$ is obtained.