Nonvanishing zero modes in the light-front current

We find that the zero mode($q^{+}=0$ mode of a continuum theory) contribution is crucial to obtain the correct values of the light-front current $J^{-}$ in the Drell-Yan($q^{+}=0$) frame. In the exactly solvable model of (1+1)-dimensional scalar field theory interacting with gauge fields, we quantify the zero mode contribution and observe that the zero mode effects are very large for the light meson form factors even though they are substantially reduced for the heavy meson cases.