Unitarizing infinite-range forces: Graviton-graviton scattering, the graviball, and Coulomb scattering

TL;DR

This paper unitarizes graviton-graviton scattering amplitudes to identify a new resonance called the graviball and applies similar techniques to Coulomb scattering, revealing insights into nonperturbative effects and infrared divergences.

Contribution

It introduces a novel unitarization method for graviton scattering that removes infrared divergences and predicts a scalar resonance, the graviball, in a nonperturbative framework.

Findings

Discovery of the graviball resonance as a pole in the S-wave amplitude.

Infrared divergence removal via phase factor subtraction.

Agreement of unitarized Coulomb scattering with exact solutions.

Abstract

We study graviton-graviton scattering in partial-wave amplitudes after unitarizing their Born terms. In order to apply $S$-matrix techniques, based on unitarity and analyticity, we introduce an $S$-matrix associated to this resummation that is free of infrared divergences. This is achieved by removing the diverging phase factor calculated by Weinberg that multiplies the $S$ matrix, and that stems from the virtual infrared gravitons. A scalar graviton-graviton resonance with vacuum quantum numbers is obtained as a pole in the nonperturbative $S$-wave amplitude, which is called the graviball. Its resonant effects along the physical real $s$-axis may peak at values substantially lower than the UV cutoff squared of the theory, similarly to the $\sigma$ resonance in QCD. These techniques are also applied to study nonrelativistic Coulomb scattering up to next-to-leading order in the unitarization program. A comparison with the exact known solution is very illuminating.