Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms

TL;DR

This paper analyzes the high-energy gravitational scattering amplitude, deriving loop expansions and computing leading logarithmic contributions at four loops (5PM) using effective field theory and multi-Regge methods.

Contribution

It introduces a detailed loop expansion framework for high-energy gravitational scattering and computes the 5PM logarithmic contributions with agreement between methods.

Findings

Computed the leading double logarithm at four loops (5PM) in gravitational scattering.

Derived the general loop expansion for Regge logarithms in the high-energy limit.

Extracted the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM.

Abstract

We investigate the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, we derive the general loop expansion that determines how the leading Regge logarithms and their complex structure arise as a power series in $t/s$. Focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior, we compute the leading double logarithm at four loops (5PM) using both effective field theory methods and the multi-Regge expansion, finding complete agreement. Finally, using the aforementioned dispersion relations, we extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.