The universal psi-prime-prime to psi-prime ratio as unambiguous signature for hard physics in nuclear reactions and in decays of beauty hadrons

We suggest the ratio of the $\psi''(3770)/\psi'(3686)$ production cross sections as an unambiguous probe of the dominance of hard, point-like physics in charmonium production. If hard physics dominates the charmonium production the ratio : ${\sigma(\psi'')\over\sigma(\psi')}\approx {\Gamma(\psi''\to l^+l^-)\over \Gamma(\psi'\to l^+l^-)} \approx 0.1$ is independent of the process. We argue that since the dominant $D\bar D$ decay mode of the $\psi''$-meson can be detected with a high efficiency at the current facilities the effective counting rate for the $\psi''$ production should be comparable to that of the $\psi'$ and hence it could be observed at the $B$-factories. Even in hadron induced processes the ratio will not be changed significantly by final state interactions due to the similar mass and size of these two charmonium states. A possible exception are the charmonium state interactions with low energy particles -- comovers -- which are especially relevant for the heavy ion collisions.