Universality of ultra-relativistic gravitational scattering

TL;DR

This paper demonstrates that the real part of the eikonal, which determines the deflection angle in ultra-relativistic gravitational scattering, is universal across various gravitational theories at the 3PM level, connecting with the massless case.

Contribution

It shows the universality of the deflection angle in ultra-relativistic scattering at two-loop order across different gravitational theories, using amplitude analysis and explicit calculations.

Findings

Universality of the deflection angle in ultra-relativistic scattering.

Inelastic graviton emission explains the universality.

Soft region contributions are crucial for finiteness and universality.

Abstract

We discuss the ultra-relativistic gravitational scattering of two massive particles at two-loop (3PM) level. We find that in this limit the real part of the eikonal, determining the deflection angle, is universal for gravitational theories in the two derivative approximation. This means that, regardless of the number of supersymmetries or the nature of the probes, the result connects smoothly with the massless case discussed since the late eighties by Amati, Ciafaloni and Veneziano. We analyse the problem both by using the analyticity and crossing properties of the scattering amplitudes and, in the case of the maximally supersymmetric theory, by explicit evaluation of the 4-point 2-loop amplitude using the results for the integrals in the full soft region. The first approach shows that the observable we are interested in is determined by the inelastic tree-level amplitude describing the emission of a graviton in the high-energy double-Regge limit, which is the origin of the universality property mentioned above. The second approach strongly suggests that the inclusion of the whole soft region is a necessary (and possibly sufficient) ingredient for recovering ultra relativistic finiteness and universality at the 3PM level. We conjecture that this universality persists at all orders in the PM expansion.