Complete mass spectra of qq̅ and Qq̅ mesons with improved Bethe-Salpeter dynamics of confinementmesons with improved Bethe-Salpeter dynamics of confinement

Abstract

The Bethe-Salpeter (BS) dynamics of harmonic confinement developed by ANM and collaborators over the last three years and already applied with considerable experimental success to various hadron spectra and coupling structures has been significantly improved through (i) a more exact treatment of a certain momentum-dependent operator Q^{^}_q appearing in the BS equation, using the techniques of SO(2, 1) Lie algebra, and (ii) a sharpened definition of the QCD Coulomb term, so as to yield unambiguous values for different flavour sectors. The resulting mass spectra of light (qq̅) meson towers and semi-heavy (Qq̅) quarkonia which are most sensitive to the improved treatment of Q^{^}_q, reveal excellent agreement with experiment, one in which only slight changes in the reduced spring constant (ω˜)and quark masses (m_q) over the earlier parametrizations are involved. These changes are however found to have a negligible effect on the (already good) numerical values of the other predictions (electroweak and pionic couplings) depending on the qq̅ and qqq wave functions. A critical assessment of the strong and weak points of this method is made vis-a-vis other related approaches.