Infrared behavior of graviton-graviton scattering

TL;DR

The paper investigates the infrared behavior of graviton–graviton scattering within the quantum gravity effective field theory. It analyzes the one-loop amplitude computed by Dunbar and Norridge, identifying a $1/ epsilon$ infrared piece and showing that soft-graviton bremsstrahlung must be included to yield a finite, model-independent cross section. Through a detailed soft-graviton radiation calculation, the authors demonstrate that all infrared divergences cancel up to ${ O}( appa^6)$, producing a finite result expressed in terms of the on-shell Born amplitude, with a residual scale set by the infrared regulator. This work establishes a robust low-energy theorem for general relativity and confirms the infrared safety of quantum gravity in its effective field theory regime.

Abstract

The quantum effective theory of general relativity, independent of the eventual full theory at high energy, expresses graviton-graviton scattering at one loop order O(E^4) with only one parameter, Newton's constant. Dunbar and Norridge have calculated the one loop amplitude using string based techniques. We complete the calculation by showing that the 1/(d-4) divergence which remains in their result comes from the infrared sector and that the cross section is finite and model independent when the usual bremsstrahlung diagrams are included.

Figures (3)

• Figure 1: The expansion of the cross section in $\kappa$ in graviton-graviton scattering. The quantity ${\cal A}^{tree}$ represents the sum of all tree level diagrams. Solid lines represent hard gravitons, wavy lines are soft gravitons.
• Figure 2: The four Feynman diagrams that contribute to soft graviton radiation at lowest order in hard graviton-graviton scattering.
• Figure 3: The graviton propagator and the triple gluon vertices in harmonic gauge. For an expression of $\tau^{\mu\nu}_{\alpha\beta,\gamma\delta}$ see Eqn. (\ref{['eq:tau3']}).