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.

Unitarized one-loop graviton-graviton scattering

“…Starting from the tree level amplitude the authors of [20][21][22][23] found a pole in the J = 0 channel at s 0 = πxM 2 p ≈ (0.22 − i0.63)M 2 P with x = 0.07 − i0.2 which they claim is a pure gravitational resonance (graviball). This particular x value corresponds to some arbitrary but reasonable choice of an UV cut-off Λ which is needed for their unitarization method (in fact the position of the pole depends logarithmically on Λ).…”