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

Abstract

Model-independent bounds on $R(J/\psi )\equiv \mathcal{B}\mathcal{R}(B_c^{+}\to J/\psi {\tau }^{+}{\nu }_{\tau })/$ $\mathcal{B}\mathcal{R}(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })$ 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, $0.20\le R(J/\psi )\le 0.39$, 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.

Comments: Talk presented CIPANP2018. 7 pages, LaTeX, 3 figures