# EPS-HEP2019

10-17 July 2019
Ghent
Europe/Brussels timezone

## The ${\gamma^* \gamma^* \to \eta_c (1S,2S)}$ transition form factor from quarkonium wave functions

11 Jul 2019, 15:15
15m
ICC - Baeckeland 3 (Ghent)

### ICC - Baeckeland 3

#### Ghent

Parallel talk QCD and Hadronic Physics

### Speaker

Ms Izabela Babiarz (Institute of Nuclear Physics, Polish Academy of Sciences)

### 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.

### Primary authors

Prof. Antoni Szczurek (Institute of Nuclear Physics, Polish Academy of Sciences) Prof. Victor P. Goncalves (Instituto de Fisica e Matematica --Universidade Federal de Pelotas (UFPel)) Dr Roman Pasechnik (Department of Astronomy and Theoretical Physics, Lund University) Dr Wolfgang Sch\"afer (Institute of Nuclear Physics, Polish Academy of Sciences) Ms Izabela Babiarz (Institute of Nuclear Physics, Polish Academy of Sciences)