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.
The cross section for the $e^+ e^- \to e^+ e^- \eta_c$ reaction are given for double
tagging ($e^{+}$ and $e^{-}$) case and the effect of $(Q_1^2,Q_2^2)$ dependence of the
transition form factor is quantified.
I. Babiarz, V. Goncalves, R. Pasechnik, W. Schafer and A. Szczurek,
a paper in print i Phys. Rev. D (see also arXiv)
