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, $O^{++}\to \gamma \gamma$ 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.

25 pages, 3 figures, 6 tables

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Cited by in corpus (9)

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• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• Mass spectra and decay constants of heavy-light axial quarkonia in the framework of Bethe-Salpeter equation
• Radiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
• $E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation
• Study of charm and beauty mass spectra, semileptonic decays of $B_{(s,c)}$ and $B_c\to J/\psi ({\eta }_c)+P(V)$ in a phenomenological potential model
• QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_c\to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Heavy quarkonium decay $V\to ggg$ with both relativistic and QCD radiative corrections