Measurement of the ratio of the B$_\mathrm{c}^+$ $\to$ J/$\psi$$\tau^+\nu_\tau$ and B$_\mathrm{c}^+$ $\to$ J/$\psi$ $\mu^+\nu_\mu$ branching fractions using three-prong $\tau$ lepton decays

Abstract

The ratio between the B$_\mathrm{c}^+$ $\to$ J/$\psi$$\tau^+\nu_\tau$ and B$_\mathrm{c}^+$ $\to$ J/$\psi$$\mu^+\nu_\mu$ branching fractions is measured using a data sample of proton-proton collisions collected by CMS at a center-of-mass energy of 13 TeV in the years 2016$-$2018 and corresponding to an integrated luminosity of 138 fb$^{-1}$. The J$/\psi$ meson is identified through its J$/\psi$ $\to$ $\mu^+\mu^-$ decay and the tau lepton is reconstructed in the hadronic three-prong final state. The measured ratio of branching fractions in this tau decay mode, $\mathcal{R}^\text{had}_{\mathrm{J}/\psi}$ = 1.04 $_{-0.44}^{+0.50}$, is combined with the previous analysis based on the $\tau^+$ $\to$ $\mu^+\nu_\mu\bar{\nu}_\tau$ leptonic decay channel, leading to $\mathcal{R}_{\mathrm{J}/\psi}$ = 0.49 $\pm$ 0.26. As this result is consistent with the standard model prediction of 0.258 $\pm$ 0.004, no evidence of lepton flavor universality violation is found.