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

Abstract

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 q_μ, 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 f_p and the charge radii thus calculated are also in excellent agreement with data (π,k) where available, while f_p predictions for Qq mesons have good overlap with recent lattice predictions. Further, the scaling property (˜k_μ^-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.