Analytic approach to calculations of mass spectra and decay constants of heavy-light quarkonia in the framework of Bethe-Salpeter equation

Abstract

This work is an extension of the work in \cite{bhatnagar18} to ground and excited states of $0^{++},0^{-+}$, and $1^{--}$ of heavy-light ($c\overline{u},c\overline{s},b\overline{u},b\overline{s}$, and $b\overline{c}$) quarkonia in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure $({\gamma }_{\mu }⨂{\gamma }_{\mu })$ in the interaction kernel, in contrast to the approximate treatment of the same in our previous works \cite{hluf16, bhatnagar18}), which is a substantial improvement over our previous works \cite{hluf16,bhatnagar18}. In this $4\times 4$ BSE framework, the coupled Salpeter equations for $Q\overline{q}$ (that are more involved than the equal mass ($Q\overline{Q}$) mesons) 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 their mass spectral equations. The analytic forms of wave functions obtained from these equations are then used for calculation of leptonic decay constants of ground and excited states of $0^{-+}$, and $1^{--}$ as a test of these wave functions and the over all framework.

31 pages, 5 Tables, 4 figures

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Cited by in corpus (7)

• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• 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
• Spectra and Decay Properties of Higher Lying $B_C$ Meson States
• 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