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 obtaining 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.