  In previous articles it was demonstrated that the total cross section of the
scattering of two light particles (zero modes of the Kaluza-Klein tower) in the
six-dimensional $\lambda \phi^{4}$ model differs significantly from the cross
section of the same process in the conventional $\lambda \phi^{4}$ theory in
four space-time dimensions even for the energies below the threshold of the
first heavy particle. Here the analytical structure of the cross section in the
same model with torus compactification for arbitrary radii of the
two-dimensional torus is studied. Further amplification of the total cross
section due to interaction of the scalar field with constant background Abelian
gauge potential in the space of extra dimensions is shown.
