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

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 σ 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.