\ga\ga and g g decay rates for equal mass heavy quarkonia

TL;DR

This paper calculates the two-photon and two-gluon decay widths for specific heavy quarkonium states using a relativistic approach and wave functions derived from the Bethe-Salpeter equation.

Contribution

It introduces a relativistic calculation method for decay widths of heavy quarkonia using wave functions from the Bethe-Salpeter equation.

Findings

Decay widths for charmonium and upsilon states are computed.

Relativistic effects are incorporated via the full $q\bar{q}\to\ga\ga$ amplitude.

Wave functions from spectral fits are used for integral evaluations.

Abstract

We present a calculation of the two-photon and two-gluon widths for the equal mass quarkonium states $^1S_0$, $^3P_0$ and $^3P_2$ of the charmonium and upsilon systems. The approach taken is based on using the full relativistic $q\bar{q}\to\ga\ga$ amplitude together with a wave function derived from the instantaneous Bethe-Salpeter equation. Momentum space radial wave functions obtained from an earlier fit of the charmonium and upsilon spectra are used to evaluate the necessary integrals.