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

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.