Zero-mode contribution in nucleon-delta transition

Abstract

We investigate the transition form factors between nucleon and $\ensuremath{\Delta}(1232)$ 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 the 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 (${ϵ}_{h=\ifmmode\pm\else\textpm\fi{}}^{+}=0$) with circular polarization in the Drell-Yan-West frame, we find that only the helicity components $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},\ensuremath{-}\frac{1}{2})$ 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 wave functions. The angular condition, which guarantees the full covariance of different schemes, is recovered.