The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c(1S,2S)$ transition form factors for spacelike photons

Abstract

We derive the light-front wave function (LFWF) representation of the ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c(1S),{\eta }_c(2S)$ transition form factor $F(Q_1^2,Q_2^2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schrödinger equation for a variety of $c\bar{c}$ potentials. We compare our results to the BaBar experimental data for the ${\eta }_c(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massless limit. We present some examples of two-dimensional distributions for $F(Q_1^2,Q_2^2)$. A factorization breaking measure is proposed and factorization breaking effects are quantified and shown to be almost model independent. Factorization is shown to be strongly broken, and a scaling of the form factor as a function of ${\bar{Q}}^2=(Q_1^2+Q_2^2)/2$ is obtained.

Comments: 22 pages, 9 figs