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

TL;DR

This paper investigates the phases of decay amplitudes in $ ext{Psi}$ and $ ext{Psi'}$ decays, proposing that electromagnetic and gluonic contributions are incoherent and introducing a new amplitude mechanism for $ ext{Psi'}$ decays.

Contribution

It presents the novel idea that decay amplitudes are incoherent in inclusive decays and introduces a new amplitude via QCD anomalies for $ ext{Psi'}$ decays.

Findings

Electromagnetic and gluonic amplitudes are 90° out of phase in $ ext{Psi}$ decays.

In $ ext{Psi'}$ decays, direct three-gluon annihilation is negligible.

A new amplitude involving QCD anomalies and the $h_c$ off shell is proposed.

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.