The vector meson form factor analysis in light-front dynamics

Abstract

We study the form factors of vector mesons using a covariant fermion field theory model in $3+1$ dimensions. Performing a light-front (LF) calculation in the ${q}^{+}=0$ frame in parallel with a manifestly covariant calculation, we note the existence of a nonvanishing zero-mode contribution to the light-front current ${J}^{+}$ and find a way of avoiding the zero mode in the form factor calculations. Upon choosing the light-front gauge $({\ensuremath{\epsilon}}_{h=\ifmmode\pm\else\textpm\fi{}}^{+}=0)$ with circular polarization and with spin projection $h=\ensuremath{\uparrow}\ensuremath{\downarrow}=\ifmmode\pm\else\textpm\fi{},$ only the helicity zero-to-zero matrix element of the plus current receives zero-mode contributions. Therefore, one can obtain the exact light-front solution of the form factors using only the valence contribution if only the helicity components, ${(h}^{\ensuremath{'}}h)=(++),(+\ensuremath{-}),$ and $(+0),$ are used. We also compare our results obtained from the light-front gauge in the light-front helicity basis (i.e. $h=\ifmmode\pm\else\textpm\fi{},0)$ with those obtained from the non-LF gauge in the instant form linear polarization basis (i.e. $h=x,y,z)$ where the zero-mode contributions to the form factors are unavoidable.