Semileptonic decays of $B_c$ meson to S-wave charmonium states in the perturbative QCD approach

TL;DR

This paper calculates semileptonic decay rates of the $B_c$ meson to S-wave charmonium states using perturbative QCD, providing predictions for branching ratios and polarization contributions that can be tested at LHCb.

Contribution

The study offers the first comprehensive calculation of $B_c$ semileptonic decays to S-wave charmonium states with reduced uncertainties using light-cone wave functions, and compares predictions with experimental data.

Findings

Predicted branching ratios range from 10^{-6} to 10^{-2}.

The ratio of $BR(B_c^+ ightarrow J/ ext{Psi} \pi^+)$ to $BR(B_c^+ ightarrow J/ ext{Psi} \\mu^+ u_{\\mu})$ agrees with experimental data.

Polarization contributions vary with momentum transfer, providing detailed decay dynamics.

Abstract

Inspired by the recent measurement of the ratio of $B_c$ branching fractions to $J/\psi \pi^+$ and $J/\psi \mu^+\nu_{\mu}$ final states at the LHCb detector, we study the semileptonic decays of $B_c$ meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions $B_c\rightarrow P,V$, where $P$ and $V$ denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for $B_c$ meson. It is found that the predicted branching ratios range from $10^{-6}$ up to $10^{-2}$ and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions $\frac{\mathcal {BR}(B_c^+\rightarrow J/\Psi \pi^+)}{\mathcal {BR}(B_c^+\rightarrow J/\Psi \mu^+\nu_{\mu})}$ is in good agreement with the data. For $B_c\rightarrow V l \nu_l$ decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments.