Exploring the timelike region for the elastic form factor in the light-front quantization

Even though the Drell-Yan-West formulation is the most rigorous and well-established framework to compute the exclusive processes, its utility has been limited only to the spacelike region because of the intrinsic kinematic constraint $q^+=0$. We present an explicit example demonstrating how one may obtain the necessary information (i.e. nonvalence or so called Z-graph contribution) in the timelike region of exclusive process without encountering a formidable task of direct calculation that has hindered so far the progress in this area. In the analysis of $q\bar{Q}$ bound state form factors using an exactly solvable model of $(3+1)$ dimensional scalar field theory interacting with gauge fields, the results analytically continued from the spacelike region coincide exactly with the direct results in the timelike region. This example verifies that the method of analytic continuation is capable of yielding the effect of complicate nonvalence contributions. The meson peaks analogous to the vector meson dominance(VMD) phenomena are also generated at the usual VMD positions.