Zero-Mode Contribution in Nucleon-Delta Transition

TL;DR

This paper studies the nucleon-Delta transition form factors using a covariant quark model, analyzing zero-mode contributions in light-front calculations to ensure covariance and scheme independence.

Contribution

It provides a detailed analysis of zero-mode effects in light-front calculations of nucleon-Delta transitions, ensuring covariance and scheme independence in form factor extraction.

Findings

Zero-mode contributions are present only in specific helicity components.

Including zero-modes restores covariance and scheme independence.

The angular condition is satisfied when zero-modes are properly accounted for.

Abstract

We investigate the transition form factors between nucleon and $\Delta$(1232) particles by using a covariant quark-spectator-diquark field theory model in (3+1) dimensions. Performing a light-front calculation in parallel with the manifestly covariant calculation in light-front helicity basis, we examine the light-front zero-mode contribution to the helicity components of light-front good ("+") current matrix elements. Choosing the light-front gauge ($\epsilon^+_{h=\pm}=0$) with circular polarization in Drell-Yan-West frame, we find that only the helicity components $({1\over 2}, {1\over 2})$ and $({1\over 2},-{1\over 2})$ of the good current receive the zero-mode contribution. Taking into account the zero-mode, we find the prescription independence in obtaining the light-front solution of form factors from any three helicity matrix elements with smeared light-front wavefunctions. The angular condition, which guarantees the full covariance of different schemes, is recovered.