Graviton emission in Einstein-Hilbert gravity

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.

28 pages, LaTeX, feynmf. v2: typos corrected, reference added. Final version to appear in Journal of High Energy Physics

References in corpus (4)

• xPerm: fast index canonicalization for tensor computer algebra
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Integrability of scattering amplitudes in N=4 SUSY

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• Projectivity of Planar Zeros in Field and String Theory Amplitudes
• Double-logarithms in N=8 supergravity: impact parameter description and mapping to 1-rooted ribbon graphs
• Scattering amplitudes in gauge theories with and without supersymmetry
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism
• Effective gravitational fields in transplanckian scattering