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

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.