Study of the electromagnetic Dalitz decays $\psi(\Upsilon) \to \eta_{c}(\eta_{b}) l^{+} l^{-}$

We study the electromagnetic Dalitz (EM) decays, $\psi \to \eta_{c} l^{+} l^{-}$ and $\Upsilon \to \eta_{b} l^{+} l^{-}$ ($l = e$ or $\mu$), in which the lepton pair comes from the virtual photon emitted by the M1 transition from $c\bar{c}$ ($b\bar{b}$) spin triplet state to the spin singlet state. We estimate the partial width of $\psi(\Upsilon) \to \eta_{c}(\eta_{b}) l^{+} l^{-}$, based on the simple pole approximation. Besides, based on different QCD models, the partial width of $\psi(\Upsilon) \to \eta_{c}(\eta_{b}) \gamma$ is determined.