On the Regularization of On-Shell Diagrams

TL;DR

This paper introduces a regularization scheme for on-shell diagrams by extending three-particle amplitudes to unphysical helicities, enabling the extraction of four-particle amplitudes at one loop with proper IR divergence handling.

Contribution

It proposes a novel regularization method for on-shell diagrams using extended amplitudes and a specific integration contour, applicable at tree level and one loop.

Findings

Successfully extracts four-particle amplitudes at one loop

Identifies IR divergences as poles in deformation parameters

Provides finite terms consistent with known results

Abstract

In this letter we discuss a regularization scheme for the integration of generic on-shell forms. The basic idea is to extend the three-particle amplitudes to the space of unphysical helicities keeping the dimension of the related coupling constant fixed, and construct on-shell forms out of them. We briefly discuss the analytic structure of the extended on-shell diagrams, both at tree level and one loop. Furthermore, we propose an integration contour which, applied to the relevant on-shell forms, allows to extract the four-particle amplitudes in Lorentz signature at one loop. With this contour at hand, we explicitly apply our procedure to this case obtaining the IR divergences as poles in the deformation parameter space, as well as the correct functional form for the finite term. This procedure provides a natural regularization for generic on-shell diagrams.