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arXiv · 2211.02084

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

J. A. Oller
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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.

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J. A. Oller. 2022-11-03. Unitarizing infinite-range forces: Graviton-graviton scattering, the graviball, and Coulomb scattering. https://doi.org/10.1051/epjconf/202227408011

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