Zero-Mode Contribution in Nucleon-Delta Transition

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.