Semileptonic decays $B_c\to ({\eta }_c,J/\Psi )l\nu$ in the perturbative QCD approach

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 $Br\left(B_c^{-}\to {\eta }_c{e}^{-}{\bar{\nu }}_e({\mu }^{-}{\bar{\nu }}_{\mu })\right)=(4.41_{-1.09}^{+1.22})\times 10^{-3}$, $Br\left(B_c^{-}\to {\eta }_c{\tau }^{-}{\bar{\nu }}_{\tau }\right)=(1.37_{-0.34}^{+0.37})\times 10^{-3}$, $Br(B_c^{-}\to J/\Psi e^{-}{\bar{\nu }}_e({\mu }^{-}{\bar{\nu }}_{\mu }))=(10.03_{-1.18}^{+1.33})\times 10^{-3}$, and $Br\left(B_c^{-}\to J/\Psi {\tau }^{-}{\bar{\nu }}_{\tau }\right)=(2.92_{-0.34}^{+0.40})\times 10^{-3}$; 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.

Comments: 12 pages, 2 figures, typos removed, some modifications in content and the numerical results. To be published in Chinese Physics C