Speaker
Description
We discuss $\gamma^* \gamma^* \to \eta_c(1S)\, , \,\eta_c(2S)$ transition form factor for both virtual photons. The general formula is given. We use different models for the $c \bar c$ wave function obtained from the solution of the Schr\"odinger equation for different $c \bar c$ potentials: harmonic oscillator, Cornell, logarithmic, power-law, Coulomb and Buchm\"uller-Tye. We compare our results to the BaBar experimental data for $\eta_c(1S)$, for one real and one virtual photon. We discuss approaching of $Q_1^2 F(Q_1^2,0)$ or $Q_2^2 F(0,Q_2^2)$ to their asymptotic value $\frac{8}{3}f_{\eta_{c}}$ predicted by Brodsky and Lepage formalism. We discuss applicability of the collinear and/or massless limit and delayed onset of asymptotic behaviour.
We present some examples of two-dimensional distributions for $F_{\gamma^* \gamma^* \to \eta_c}(Q_1^2,Q_2^2)$. A scaling in $\omega = (Q_1^2 = Q_2^2) / (Q_1^2 + Q_2^2)$ was obtained. A factorization breaking measure is proposed and factorization breaking effects are quantified and shown to be weakly model dependent.
