Finite energy sum rules for gravitational Regge amplitudes

• DOI: 10.1007/jhep06(2023)032
• Publication Date: 2023-06-07T15:02:17Z
• Authors: Toshifumi Noumi; Junsei Tokuda
• Keywords: High Energy Physics - Theory; Cosmology and Nongalactic Astrophysics (astro-ph.CO); FOS: Physical sciences; Effective Field Theories; QC770-798; General Relativity and Quantum Cosmology (gr-qc); 01 natural sciences; General Relativity and Quantum Cosmology; High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Scattering Amplitudes; Astrophysics - Cosmology and Nongalactic Astrophysics

Abstract We develop a framework to derive consistency constraints on gravitational Regge amplitudes based on the finite energy sum rules (FESRs), which directly connect gravitational Regge amplitudes at a finite ultraviolet scale with infrared physics without suffering from super-Planckian physics. For illustration, we consider four-point scattering of an identical massless scalar coupled to gravity. First, we derive multiple FESRs without relying on the s-t-u permutation invariance. We then make use of FESRs, crossing symmetry, and other principles such as unitarity, to derive bounds on the Regge parameters. The bounds result in infrared finite gravitational positivity bounds in four spacetime dimensions.