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Semileptonic decays $B_c\to(η_c,J/Ψ)lν$ in the perturbative QCD approach

In this paper we study the semileptonic decays of $B_c^- \to (η_c,J/ψ)l^-\barν_l$. We firstly evaluate the $B_c \to (η_c,J/Ψ)$ 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 $B_c \to η_c$ and $B_c \to J/Ψ$ 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 $Br\left(B_c^- \toη_c e^-\barν_e(μ^-\barν_μ)\right) =(4.41^{+1.22}_{-1.09})\times10^{-3}$, $Br\left(B_c^- \toη_cτ^-\barν_τ\right) =(1.37^{+0.37}_{-0.34})\times10^{-3}$, $Br(B_c^- \to J/Ψe^-\barν_e(μ^-\barν_μ)) =(10.03^{+1.33}_{-1.18})\times10^{-3}$, and $Br\left(B_c^- \to J/Ψτ^-\barν_τ\right) =(2.92^{+0.40}_{-0.34})\times10^{-3}$; and (c) we also define and calculate two ratios of the branching ratios $R_{η_c}$ and $R_{J/Ψ}$, which will be tested by LHCb and the forthcoming Super-B experiments.