The ${\eta }_c\gamma {\gamma }^{\ast }$ 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

Abstract

The Dalitz distribution and the effective mass spectrum of the lepton pair produced in the decay ${\eta }_c\to \gamma {\ell }^{+}{\ell }^{-}$, as well as the differential 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 sole electromagnetic transition form factor for the vertex ${\eta }_c\to \gamma {\gamma }^{\ast }$, where ${\gamma }^{\ast }$ is a virtual photon with a space-like (for $\gamma e^{-}\to {\eta }_c{e}^{-}$) or a time-like (for $e^{+}{e}^{-}\to {\eta }_c\gamma$ and ${\eta }_c\to \gamma {\ell }^{+}{\ell }^{-}$) four-momentum. Explicit parametrisations of the transition form factor are found in two different approaches, namely in Vector Dominance 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 the annihilating quarks.

Comments: 20 pages, 9 figures