An approach to calculation of mass spectra and two-photon decays of $c\overline{c}$ mesons in the framework of Bethe-Salpeter Equation

TL;DR

This paper calculates the mass spectra and two-photon decay widths of various charmonium states using a Bethe-Salpeter Equation framework, providing analytical solutions and comparing results with experimental data.

Contribution

It introduces a decoupling approach within the Bethe-Salpeter Equation for charmonium, incorporating one-gluon exchange perturbatively, and derives analytical wave functions for decay width calculations.

Findings

Mass spectra are in reasonable agreement with experimental data.

Analytical wave functions are obtained for different charmonium states.

Two-photon decay widths are calculated for specific states.

Abstract

In this work we calculate the mass spectrum of charmonium for $1P,...,3P$ states of $0^{++}$ , $1^{++}$, as well as for $1S,...,4S$ states of $0^{-+}$, and $1S, ...,5D$ states of $1^{--}$ along with the two-photon decay widths of ground and first excited state of $0^{++}$ quarkonia for the process, $O^{++}\rightarrow \gamma\gamma$ in the framework of a QCD motivated Bethe-Salpeter Equation. In this $4\times 4$ BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of interaction, under heavy-quark approximation, and analyically solved, and later the one-gluon-exchange interaction is perturbatively incorporated leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for calculation of two-photon decay widths of $\chi_{c0}$. Our results are in reasonable agreement with data (where ever available) and other models.