Abstract
A new relativistic definition of the reduced mass () of a pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta , is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of involving the hadron mass is found to produce a natural Regge asymptotic behavior () in the hadron mass spectra, while retaining the property of an asymptotically linear () confinement in the three-dimensional structure of the BS kernel. The relativistic structure of is responsible for a significant improvement in the fits to the ground-state masses of and mesons as compared to its nonrelativistic definition . The leptonic decay constants and the charge radii thus calculated are also in excellent agreement with data () where available, while predictions for mesons have good overlap with recent lattice predictions. Further, the scaling property () of the hadron's electromagnetic form factor at large is a consequence of the "on-shell" form of its null-plane wave function. All these results (which are indicated in the barest outline) are preceded by a perspective summary of the theoretical premises and practical working of the BS equation with a four-fermion interaction kernel as a necessary background on a two-tier basis.
- Received 12 April 1989
DOI:https://doi.org/10.1103/PhysRevD.42.1604
©1990 American Physical Society