Graviton emission in Einstein-Hilbert gravity

TL;DR

This paper calculates the five-point scattering amplitude involving graviton emission in Einstein-Hilbert gravity, revealing a gauge-invariant structure and connecting it to QCD vertices in the multi-Regge limit.

Contribution

It introduces a new two scalar - two graviton effective vertex and relates graviton emission to QCD gluon emission vertices in a novel way.

Findings

The amplitude satisfies Steinmann relations.

The graviton emission vertex factorizes into QCD vertices in the multi-Regge limit.

The results provide a bridge between gravity and gauge theory amplitudes.

Abstract

The five-point amplitude for the scattering of two distinct scalars with the emission of one graviton in the final state is calculated in exact kinematics for Einstein-Hilbert gravity. The result, which satisfies the Steinmann relations, is expressed in Sudakov variables, finding that it corresponds to the sum of two gauge invariant contributions written in terms of a new two scalar - two graviton effective vertex. A similar calculation is carried out in Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one extra gluon in the final state. The effective vertices which appear in both cases are then evaluated in the multi-Regge limit reproducing the well-known result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex can be written as the product of two QCD gluon emission vertices, up to corrections to preserve the Steinmann relations.