$\chi_{QJ} \to\ell^+\ell^-$ within and beyond the Standard Model

We revisit $\chi_{QJ}\to \ell^+\ell^-$ (with $J=0,1,2$ and $Q=b,c$) within the Standard Model (SM). The electro-magnetic contributions are given in color-singlet model with non-vanishing lepton masses at the leading order of $v$. Numerically, the branching ratios of $\chi_{QJ}\to\ell^{+}\ell^{-}$ predicted within the SM are so small that such decays are barely possible to be detected at future BESIII and SuperB experiments, but may be possible to be observed at the LHC. We investigate $\chi_{b0}\to\ell^+\ell^-$ in Type-II 2HDM with large $\tan\beta$, and $\chi_{b2}\to\ell^+\ell^-$ in the Randall-Sundrum model, to see their chance to be observed in future experiments.