$R(J/\ddot{I}ˆ)$ and $B_c^{-}\to J/\ddot{I}ˆ{\ell }^{-}\bar{\hat{I}}{½}_{\ell }$ Lepton Flavor Universality Violating Observables from Lattice QCD

Abstract

We use our lattice QCD computation of the $B_c\to J/\ddot{I}ˆ$ form factors to determine the differential decay rate for the semitauonic decay channel and construct the ratio of branching fractions $R(J/\ddot{I}ˆ)=\mathcal{B}(B_c^{-}\to J/\ddot{I}ˆ\ddot{I}{„}^{-}\bar{\hat{I}}{½}_{\ddot{I}}„)/\mathcal{B}(B_c^{-}\to J/\ddot{I}ˆ\hat{I}{¼}^{-}\bar{\hat{I}}{½}_{\hat{I}}¼)$. We find $R(J/\ddot{I}ˆ)=0.2582(38)$ and give an error budget. We also extend the relevant angular observables, which were recently suggested for the study of lepton flavor universality violating effects in $B\to D^{\ast }\ell \hat{I}½$, to $B_c\to J/\ddot{I}ˆ\ell \hat{I}½$ and make predictions for their values under different new physics scenarios.

6 pages, 4 figures, Version accepted for publication in Phys. Rev. Lett