Regularizing the Divergent Structure of the Light-Front Currents

Abstract

The divergences appearing in the 3+1 dimensional fermion-loop calculations are often regulated by smearing the vertices in a covariant manner. Performing a parallel light-front calculation, we corroborate the similarity between the vertex-smearing-technique and the Pauli-Villars regularization. In the light-front calculation of the electromagnetic meson current, we find that the persistent end-point singularity that appears in the case of point vertices is removed even if the smeared-vertex is taken to the limit of the point-vertex. Recapitulating the current conservation, we substantiate the finiteness of both valence and non-valence contributions in all components of the current with the regularized bound-state vertex. However, we stress that each contribution, valence or non-valence, depends on the reference-frame even though the sum is always frame-independent. The numerical taxonomy of each contribution including the instantaneous contribution and the zero-mode contribution is presented in the $\pi$, $K$, and $D$-meson form factors.

21 pages including 9 figures, Changes: 1- changed the title; 2-minor revisions are made in the text; 3-removed the Figs.9-12. Version to appear in Phys. Rev. D

References in corpus (3)

• Covariance of Light-Front Models: Pair Current
• Disentangling Intertwined Embedded States and Spin Effects in Light-Front Quantization
• Frame-Independence of Exclusive Amplitudes in the Light-Front Quantization

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