Soft-collinear gravity

TL;DR

This paper develops an effective field theory for perturbative quantum gravity to analyze collinear and soft singularities, revealing factorization properties and proving the absence of collinear divergences.

Contribution

It introduces a soft-collinear effective theory for gravity, highlighting differences from QCD and providing a proof of no collinear singularities in perturbative quantum gravity.

Findings

Soft sector exhibits factorization similar to SCET

Leading-power collinear effective Lagrangian is trivial

Decoupling of $h_{++}$ confirms absence of collinear divergences

Abstract

We study collinear and soft singularities in perturbative quantum gravity by constructing an effective field theory similar to soft-collinear effective theory for QCD (SCET). We find that the soft sector exhibits factorization properties similar to those of SCET. The collinear sector is, however, quite different. While the leading-power collinear effective Lagrangian is trivial, the presence of the metric field $h_{++}$ with negative scaling dimension allows for collinear divergences in loop diagrams with couplings to non-collinear sources. We provide a compact proof of the well-known fact that there are no collinear singularities in perturbative quantum gravity by demonstrating the decoupling of $h_{++}$ from the sources. We briefly discuss the connection of our approach to recent work by Akhoury et al. (Phys. Rev. D84 (2011) 104040) as well as to the Weinberg's original paper (Phys. Rev. 140 (1965) B516), where the cancellation of the collinear singularities was demonstrated for the first time in the eikonal approximation.