Soft-collinear gravity

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.

16 pages, 2 figures

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