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The Dalitz distribution and the effective mass spectrum of the lepton pairproduced in the decay $\eta_c\to \gamma \ell^+ \ell^-$, as well as thedifferential cross sections for the crossed channels $\gamma e^-\to \eta_c e^-$ and $e^+ e^-\to \eta_c \gamma$, are calculated in terms of the soleelectromagnetic transition form factor for the vertex $\eta_c\to\gamma\gamma^*$, where $\gamma^*$ is a virtual photon with a space-like (for $\gammae^- \to \eta_c e^- $) or a time-like (for $e^+ e^-\to \eta_c \gamma$ and$\eta_c\to\gamma \ell^+\ell^-$) four-momentum. Explicit parametrisations of thetransition form factor are found in two different approaches, namely in VectorDominance Model and in a QCD-inspired consideration on the basis of the process$c \bar{c}\to \gamma \ell^+ \ell^-$, with zero relative three-momentum of theannihilating quarks.Comment: 20 pages, 9 figure

european physical journal. c, particles and fields

The $\eta_c\gamma \gamma ^*$ transition form factor in the decay $\eta_c\to \gamma \ell^+\ell^-$ and in the crossed channels $\gamma e^-\to \eta_c e^- $ and $e^+e^-\to\eta_c\gamma$