Validity of the Color Dipole Approximation for Diffractive Production of Heavy Quarkonium

We study the diffractive photo- and leptoproductions of $J / psi$ and $psi $ on the proton, and examine the validity of the small-size color dipole approximation to the production of radially excited heavy quarkonium. The dipole model predicts a small ratio of $psi $ to $J / psi$ photoproduction cross sections, which does not agree with experimental data. We show that this discrepancy originates from a large transverse size of $psi $ which makes the convergence of the transverse size expansion questionable, and the calculation without the dipole approximation turns out to be consistent with the data. Productions of $Upsilon (2S,3S)$ are also discussed, and the dipole approximation is found to be reasonable for the $Upsilon$-family.