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

Francesco Alessio1,*, Vittorio Del Duca1,†, Riccardo Gonzo2,3,‡, Emanuele Rosi1,4,§, Ira Z. Rothstein5,∥, and Michael Saavedra5,6,¶

  • *Contact author: Francesco.Alessio@lnf.infn.it
  • †Contact author: delduca@lnf.infn.it
  • ‡Contact author: r.gonzo@qmul.ac.uk
  • §Contact author: emanuele.rosi@uniroma1.it
  • ∥Contact author: izr@andrew.cmu.edu
  • Contact author: msaavedra@physics.ucla.edu
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Phys. Rev. D 113, 105013 – Published 18 May, 2026

DOI: https://doi.org/10.1103/2qtg-6msp

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 (or equivalently fifth post-Minkowskian order, 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.

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Phys. Rev. D 113, 105013– Published 18 May, 2026
  • Received 15 December 2025
  • Accepted 16 April 2026
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