Null-plane Bethe-salpeter dynamics: mass spectra, decay constants of pseudoscalar mesons, and the pion form factor

A new relativistic definition of the reduced mass (µ12) of a qq̅ pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta qμ, is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of μ12 involving the hadron mass M is found to produce a natural Regge asymptotic behavior (M2˜N) in the hadron mass spectra, while retaining the property of an asymptotically linear (˜r) confinement in the three-dimensional structure of the BS kernel. The relativistic structure of μ12 is responsible for a significant improvement in the fits to the ground-state masses of qq̅ and Qq̅ mesons as compared to its nonrelativistic definition m1m2/(m1+m2). The leptonic decay constants fp and the charge radii thus calculated are also in excellent agreement with data (π,k) where available, while fp predictions for Qq mesons have good overlap with recent lattice predictions. Further, the scaling property (˜kμ-2) of the hadron's electromagnetic form factor at large k2 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