PoS - Proceedings of Science
Volume 364 - European Physical Society Conference on High Energy Physics (EPS-HEP2019) - QCD and Hadronic Physics
The ${\gamma^* \gamma^* \to \eta_c (1S,2S)}$ transition form factors for two spacelike photons
I. Babiarz,* V. Goncalves, R. Pasechnik, W. Schaefer, A. Szczurek
*corresponding author
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Pre-published on: June 10, 2020
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We discuss $\gamma^* \gamma^* \to \eta_c(1S)\, , \,\eta_c(2S)$ transition form factors
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 showed some examples of wave functions in the Light Front
representation as well as in the rest frame of $c \bar c$ pair. We compare our results to
the BaBar experimental data for $\eta_c(1S)$, for one real and one virtual photon,
and to the values collected by the Particle Data Group for $F(0,0)$, decay width
$\Gamma_{\gamma \gamma}$ and decay constant $f_{\eta_c}$.
We also considered the non-relativistic limit for $F(0,0)$ form factor with
the wave function at the origin $R(0)$.
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