The ${\gamma^* \gamma^* \to \eta_c (1S,2S)}$ transition form factors for two spacelike photons

Abstract

We discuss γ∗γ∗ → ηc(1S), ηc(2S) transition form factors for both virtual photons. The general formula is given. We use different models for the cc¯ wave function obtained from the solution of the Schrodinger equation for different cc¯ potentials: harmonic oscillator, Cornell, logarithmic, power-law, Coulomb and Buchmuller-Tye. We showed some examples of wave functions in the Light Front representation as well as in the rest frame of cc¯ pair. We compare our results to the BaBar experimental data for ηc(1S), for one real and one virtual photon, and to the values collected by the Particle Data Group for F(0,0), decay width Γγγ and decay constant fηc. We also considered the non-relativistic limit for F(0,0) form factor with the wave function at the origin R(0). (Less)