Mass Spectroscopy, Leptonic and Radiative Transitions of Heavy-Light Quarkonia in Framework of Bethe-Salpeter Equation

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Addis Ababa University


In this thesis, we use the QCD motivated Bethe-Salpeter Equation (BSE) framework for mass spectral calculations of ground and excited states of 0++ (S), 0􀀀+ (P), and 1􀀀􀀀(V) heavy-light as well as equal mass quarkonia by making use of the exact treatment of the spin part (_ _) of the interaction kernel. This work is a substantial improvement over earlier works on equal mass quarkonia in the sense that we have used all Dirac structures contributing in hadronic Bethe- Salpeter wave function for the calculation of mass spectra and leptonic decay constants of heavylight quarkonia. In this 4 _ 4 BSE framework, the coupled integral equations obtained for heavylight mesons through Salpeter equations are much more involved than the corresponding equations of equal mass (QQ) mesons. These equations are first shown to decouple for the confining part of interaction, under heavy-quark approximation, and analyically solved, and later the one-gluonexchange interaction is perturbatively incorporated, leading to their mass spectral equations, which were also used to calculate the algebraic forms of wave functions of various states of 0++; 0􀀀+, and 1􀀀􀀀 heavy-light quarkonia in an approximate harmonic oscillator basis. We have then used the analytic forms of wave functions obtained from these equations to calculate leptonic decay constants of ground and excited states of 0􀀀+, and 1􀀀􀀀. We have further calculated the single photon radiative decay widths for M1 transitions, V ! P, and E1 transitions, V ! S, and S ! V , as a test of the wave functions and the BSE framework. The results of decay widths are in reasonable agreement with data and other models.



Mass Spectroscopy, Leptonic, Radiative Transitions, Heavy-Light Quarkonia, Framework, Bethe-Salpeter Equation