Soft Collinear Degeneracies in an Asymptotically Free Theory

TL;DR

This paper investigates soft collinear divergences in asymptotically free theories, demonstrating that certain divergences do not cancel as previously claimed, leading to non-convergent perturbative series.

Contribution

It reveals additional classes of divergences in scalar $$ theory and discusses their implications, challenging existing assumptions about divergence cancellation.

Findings

Soft collinear divergences do not always cancel in asymptotically free theories.

Certain divergences lead to non-convergent perturbative series.

Similar effects are summarized for gauge theories.

Abstract

In asymptotically free theories with collinear divergences it is sometimes claimed that these divergences cancel if one sums over initial and final state degenerate cross-sections and uses an off-shell renormalisation scheme. We show for scalar $\phi^3$ theory in six dimensions that there are further classes of soft collinear divergences and that they do not cancel. Furthermore, they yield a non-convergent series of terms at a fixed order of perturbation theory. Similar effects in gauge theories are also summarised.