Mass Spectroscopy, Leptonic and Radiative Transitions of Heavy-Light Quarkonia in Framework of Bethe-Salpeter Equation
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Date
9/10/2020
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Addis Ababa University
Abstract
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.
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Keywords
Mass Spectroscopy, Leptonic, Radiative Transitions, Heavy-Light Quarkonia, Framework, Bethe-Salpeter Equation