Annihilation Rate of Heavy 0^{++} P-wave Quarkonium in Relativistic Salpeter Method

TL;DR

This paper estimates two-photon and two-gluon annihilation rates of P-wave scalar charmonium and bottomonium states using the relativistic Salpeter method, providing decay width predictions for various excited states.

Contribution

It applies the relativistic Salpeter equation with a well-defined wave function to calculate annihilation rates of heavy P-wave quarkonium states, including excited states, using the Mandelstam formalism.

Findings

Decay widths for two-photon annihilation are estimated for several states.

Total decay widths via two-gluon channels are provided for multiple states.

Results offer theoretical predictions for heavy quarkonium decay processes.

Abstract

Two-photon and two-gluon annihilation rates of P-wave scalar charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. We solved the full Salpeter equation with a well defined relativistic wave function and calculated the transition amplitude using the Mandelstam formalism. Our model dependent estimates for the decay widths: $\Gamma(\chi_{c0} \to 2\gamma)=3.78$ keV, $\Gamma(\chi'_{c0} \to 2\gamma)=3.51$ keV, $\Gamma(\chi_{b0} \to 2\gamma)=48.8$ eV and $\Gamma(\chi'_{b0} \to 2\gamma)=50.3$ eV. We also give estimates of total widths by the two-gluon decay rates: $\Gamma_{tot}(\chi_{c0})=10.3$ MeV, $\Gamma_{tot}(\chi'_{c0})=9.61$ MeV, $\Gamma_{tot}(\chi_{b0})=0.887$ MeV and $\Gamma_{tot}(\chi'_{b0})=0.914$ MeV.