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

Abstract

We present a model-independent bound on $R(J/\psi )\equiv \mathcal{B}\mathcal{R}(B_c^{+}\to J/\psi {\tau }^{+}{\nu }_{\tau })/\mathcal{B}\mathcal{R}(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })$. This bound is constructed by constraining the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing 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 rules out some previously suggested model form factors.

Comments: 19 pages, 4 figures, JHEP format, revised to match published version