Collinear and Soft Divergences in Perturbative Quantum Gravity

TL;DR

This paper investigates collinear and soft divergences in perturbative quantum gravity, demonstrating their cancellation in wide-angle scattering and identifying the specific virtual graviton corrections responsible for soft divergences.

Contribution

It generalizes previous eikonal approximation results by proving collinear divergence cancellation and clarifies which virtual graviton diagrams produce soft logarithmic divergences.

Findings

Collinear singularities cancel when summing over all diagrams.

Only ladder and crossed ladder diagrams contribute to soft divergences.

The gravitational Ward identity decouples unphysical polarizations.

Abstract

Collinear and soft divergences in perturbative quantum gravity are investigated to arbitrary orders in amplitudes for wide-angle scattering, using methods developed for gauge theories. We show that collinear singularities cancel when all such divergent diagrams are summed over, by using the gravitational Ward identity that decouples the unphysical polarizations from the S-matrix. This analysis generalizes a result previously demonstrated in the eikonal approximation. We also confirm that the only virtual graviton corrections that give soft logarithmic divergences are of the ladder and crossed ladder type.