Phases and amplitudes in inclusive Ψ and Ψ′ decays

Abstract

In inclusive decays of the Ψ (3097), electromagnetic and gluonic annihilation amplitudes add incoherently, namely they are 90° out of phase. We argue that this incoherence must persist in each exclusive decay channel. For inclusive Ψ′ (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.