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

This work is an extension of the work in [Phys. Rev. D 97, 034021 (2018)] to ground and excited states of 0++, 0−+, and 1−− of heavy-light (cu¯,cs¯,bu¯,bs¯, and bc¯) quarkonia in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure (γμ⊗γμ) in the interaction kernel, in contrast to the approximate treatment of the same in our previous works [H. Negash and S. Bhatnagar, Int. J. Mod. Phys. E 25, 1650059 (2016)., S. Bhatnagar and L. Alemu, Phys. Rev. D 97, 034021 (2018).]). In this 4×4 BSE framework, the coupled Salpeter equations for Qq¯ (that are more involved than the equal mass (QQ¯) mesons) are first shown to decouple for the confining part of interaction, under heavy-quark approximation, and analytically 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.