MarKov-Yukawa Transversality On Covariant Null Plane: Pion Form Factor, Gauge Invariance And Lorentz Completion

Abstract

The Markov-Yukawa Transversality Principle (MYTP) on a 2-body Bethe-Salpeter kernel is formulated on a covariant Null Plane (NP) to reconstruct the 4D BS wave function for 2 fermion quarks in terms of 3D entities that satisfy a 3D BSE. This result is the null-plane counterpart of a 3D-4D interconnection for the 2-body BS wave functions found earlier by imposing MYTP covariantly in the instantaneous rest frame (termed CIA) of the composite. This formulation yields a 3D BSE which is formally identical to its Covariant Instantaneity form, thus fully preserving its spectral results, while ensuring full covariance. More importantly, the reconstructed 4D vertex functions in the covariant null-plane ensure that 4D quark-loops are now free from ill-defined time-like momentum integrations (which had plagued the earlier CIA vertex functions), while a simple prescription of `Lorentz completion' in the new description yields a manifestly Lorentz-invariant result.This is illustrated for the pion and kaon form factors with full QED gauge-invariance, showing a $k^{-2}$ behaviour at large $k^2$, and `correct' slopes at small $k^2$. This method is compared with the Kadychevsky-Karmanov light-front formalism.