Complete mass spectra of$q\bar q$ and$Q\bar q$ 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 byanm 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$\hat Q_q$ appearing in thebs equation, using the techniques of SO (2, 1) Lie algebra, and (ii) a sharpened definition of theqcd Coulomb term, so as to yield unambiguous values for different flavour sectors. The resulting mass spectra of light$(q\bar q)$ meson towers and semi-heavy$(Q\bar q)$ quarkonia which are most sensitive to the improved treatment of$\hat Q_q$, reveal excellent agreement with experiment, one in which only slight changes in the reduced spring constant$(\tilde \omega )$ 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$q\bar q$ andqqq wave functions. A critical assessment of the strong and weak points of this method is madevis-a-vis other related approaches.