Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Universality of ultra-relativistic gravitational scattering

Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano

TL;DR

The paper establishes that in ultra-relativistic gravitational scattering at 3PM, the real part of the eikonal correction $\operatorname{Re}(\delta_2)$ is universal across two-derivative gravity theories and remains connected to the massless Amati–Ciafaloni–Veneziano result. It employs two complementary approaches: a dispersion-relation analysis based on analyticity and crossing that links $\operatorname{Re}(\delta_2)$ to the high-energy imaginary part of the two-loop amplitude, and a direct computation of loop integrals in the full soft region (demonstrated explicitly in ${\cal N}=8$ supergravity) to show that the universal behavior emerges once the soft contributions are fully included. The results show that $\operatorname{Im}(\delta_2)$ acquires a single $\log s$ enhancement, and, with $p=1$ in the dispersion relation, $\operatorname{Re}(2\delta_2)$ is determined by $\operatorname{Im}(\delta_2)$ and $\delta_0$, with IR divergences canceling in physical observables. The authors conjecture that this universality persists to all orders in the PM expansion, and provide explicit expressions for the massive and massless cases, clarifying prior discrepancies and underscoring the pivotal role of the soft region in achieving ultra-relativistic finiteness.

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.

Universality of ultra-relativistic gravitational scattering

TL;DR

The paper establishes that in ultra-relativistic gravitational scattering at 3PM, the real part of the eikonal correction is universal across two-derivative gravity theories and remains connected to the massless Amati–Ciafaloni–Veneziano result. It employs two complementary approaches: a dispersion-relation analysis based on analyticity and crossing that links to the high-energy imaginary part of the two-loop amplitude, and a direct computation of loop integrals in the full soft region (demonstrated explicitly in supergravity) to show that the universal behavior emerges once the soft contributions are fully included. The results show that acquires a single enhancement, and, with in the dispersion relation, is determined by and , with IR divergences canceling in physical observables. The authors conjecture that this universality persists to all orders in the PM expansion, and provide explicit expressions for the massive and massless cases, clarifying prior discrepancies and underscoring the pivotal role of the soft region in achieving ultra-relativistic finiteness.

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.

Paper Structure

This paper contains 5 sections, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The analyticity/crossing argument revisited
  3. Direct calculation of $\operatorname{Re} \delta_2$
  4. Asymptotic $\rho \equiv \frac{\operatorname{Re} A}{\operatorname{Im} A}$ from analyticity and crossing
  5. Summary of the soft integrals

Figures (1)

  • Figure 1: The lines in bold represent energetic massive states, while the others represent massless states. The process depicted inside the dashed bubbles should not be interpreted as a specific Feynman diagram contribution, but just as a visual aid to recall the definition of the kinematic variables $q_i$. We are interested in the full$2\to 3$ tree level process, see \ref{['ampli']} as an explicit example.