Soft Collinear Degeneracies in an Asymptotically Free Theory

Abstract

In asymptotically free theories with collinear divergences it is sometimes claimed that these divergences are cancelled if one sums over initial and final state degenerate cross-sections and uses an off-shell renormalisation scheme. We show for scalar ϕ3 theory in six dimensions that there are further classes of soft collinear divergences and that they are not cancelled. Furthermore, they yield a nonconvergent series of terms at a fixed order of perturbation theory. Similar effects in gauge theories are also summarised.