Phases and Amplitudes in Inclusive $\Psi$ and $\Psi'$ Decays

Abstract

In inclusive decays of the $\Psi$ (3097), electromagnetic and gluonic annihilation amplitudes add incoherently, namely they are 90$^\circ$ out of phase. We argue that this incoherence must persist in each exclusive decay channel. For inclusive $\Psi'$ (3686) decays, we suggest the absence of a significant direct annihilation amplitude into three gluons and propose a new amplitude via QCD anomalies and the $h_c$ (3526) off shell. Phenomenological implications for exclusive decay channels are pointed out.