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

Model-independent bounds on $R(J/ψ) \! \equiv \!\mathcal{BR} (B_c^+ \rightarrow J/ψ\, τ^+ν_τ)/$ $\mathcal{BR} (B_c^+ \rightarrow J/ψ\, μ^+ν_μ)$ 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, $0.20\leq R(J/ψ)\leq0.39$, agrees with the recent LHCb result at $1.3 \, σ$, and removes the dominant model-dependent uncertainty from theory predictions. Using the same techniques, a prediction of $R(η_c)=0.29(5)$ is obtained.