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 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 (${\text{ep}}_{h=\pm }^{+}=0$) with circular polarization and with spin projection $h=\uparrow \downarrow =\pm$, 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, $(h^{\prime }h)=(++),(+-)$, and $(+0)$, are used. We also compare our results obtained from the light-front gauge in the light-front helicity basis (i.e. $h=\pm ,0$) 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.

Comments: 33 pages; typo in Eq.(15) is corrected; comment on Ref.[9] is corrected; version to appear in Phys. Rev. D