The γ^∗γ^∗ → η_c(1S,2S) transition form factors for two spacelike photons

We discuss γ^∗γ^∗ → η_c(1S), η_c(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 Schrödinger equation for different cc¯ potentials: harmonic oscillator, Cornell, logarithmic, power-law, Coulomb and Buchmüller-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 η_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 Γ_γγ and decay constant f_ηc. We also considered the non-relativistic limit for F(0,0) form factor with the wave function at the origin R(0).