Cancellation of spectator interactions in the Drell-Yan and deep inelastic processes

We present an explicit calculation of the one-gluon soft interactions involving one spectator quark in the Drell-Yan and in the deep inelastic processes. We verify that these interactions are suppressed in the high energy limit. The gluon has a wavelength ranging from infinity to a value that is much smaller than the wavelength of the high energy photon. This includes a subregion, ranging from the meson size to values much bigger than the meson size, that has not been explicitly considered in the previous calculations.