J/\Psi N and Psi' N total cross sections from photoproduction data: failure of vector dominance

Abstract

Values for the cross sections $\sigma^{\Psi N}_{tot}$ and $\sigma^{\Psi' N}_{tot}$ are of crucial importance, once one wants to understand nuclear suppression of $J/\Psi$($\Psi'$) in a search for the quark gluon plasma. Quoted values are usually extracted from $\gamma N \to J/\Psi(\Psi') N$ data via the vector dominance model (VDM) and are very small compared with expectations from QCD. The validity of QCD is questioned. When the VDM is extended to a multi-channel case, the $\gamma N$ data lead to a value $2.8\pm 0.12 mb <\sigma_{tot}^{\Psi N}(\sqrt{s}= 10 GeV) < 4.1\pm 0.15 mb$, which is a factor 3 larger than the VDM prediction. Errors are due to experimental input, and the corridor shows the theoretical uncertainty. We also derive from the data $\sigma_{tot}^{\Psi' N}/\sigma_{tot}^{J/\Psi N}\approx 4$, where we could not estimate the theoretical uncertainty.