Cancellation of soft and collinear divergences in noncommutative QED

TL;DR

This paper demonstrates the cancellation of soft and collinear divergences in noncommutative QED, ensuring well-defined physical cross sections and extending IR divergence cancellation methods to noncommutative gauge theories.

Contribution

It proves all-order cancellation of IR divergences in noncommutative QED using Weinberg's method and a non-commutative KLN theorem, a novel extension of divergence cancellation techniques.

Findings

Soft IR divergences cancel in noncommutative QED.

Collinear divergences are canceled by the non-commutative KLN theorem.

No mixing occurs between different IR divergence types.

Abstract

In this paper, we investigate the behavior of non-commutative IR divergences and will also discuss their cancellation in the physical cross sections. The commutative IR (soft) divergences existing in the non-planar diagrams will be examined in order to prove an all order cancellation of these divergences using the Weinberg's method. In non-commutative QED, collinear divergences due to triple photon splitting vertex, were encountered, which are shown to be canceled out by the non-commutative version of KLN theorem. This guarantees that there is no mixing between the Collinear, soft and non-commutative IR divergences.