Semileptonic decays $B_c\to(\eta_c,J/\Psi)l\nu$ in the perturbative QCD approach

TL;DR

This paper calculates the transition form factors and branching ratios for semileptonic Bc decays to ηc and J/ψ using perturbative QCD, providing predictions consistent with other methods and useful for experimental tests.

Contribution

The study employs the pQCD approach to evaluate form factors and branching ratios for Bc semileptonic decays, offering new theoretical predictions for these processes.

Findings

Form factors agree with other methods.

Predicted branching ratios are provided with uncertainties.

Ratios R_{η_c} and R_{J/Ψ} are calculated for experimental testing.

Abstract

In this paper we study the semileptonic decays of $B_c^- \to (\eta_c,J/\psi)l^-\bar\nu_l$. We firstly evaluate the $B_c \to (\eta_c,J/\Psi)$ transition form factors $F_0(q^2)$, $F_+(q^2)$, $V(q^2)$ and $A_{0,1,2}(q^2)$ by employing the pQCD factorization approach, and then we calculate the branching ratios for all considered semileptonic decays. Based on the numerical results and the phenomenological analysis, we find that: (a) the pQCD predictions for the values of the $B_c \to \eta_c$ and $B_c \to J/\Psi$ transition form factors agree well with those obtained by using other methods; (b) the pQCD predictions for the branching ratios of the considered decays are $Br\left(B_c^- \to\eta_c e^-\bar\nu_e(\mu^-\bar\nu_\mu)\right) =(4.41^{+1.22}_{-1.09})\times10^{-3}$, $Br\left(B_c^- \to\eta_c\tau^-\bar\nu_\tau\right) =(1.37^{+0.37}_{-0.34})\times10^{-3}$, $Br(B_c^- \to J/\Psi e^-\bar\nu_e(\mu^-\bar\nu_\mu)) =(10.03^{+1.33}_{-1.18})\times10^{-3}$, and $Br\left(B_c^- \to J/\Psi\tau^-\bar\nu_\tau\right) =(2.92^{+0.40}_{-0.34})\times10^{-3}$; and (c) we also define and calculate two ratios of the branching ratios $R_{\eta_c}$ and $R_{J/\Psi}$, which will be tested by LHCb and the forthcoming Super-B experiments.