Gravitational scattering amplitudes in collinear and high-energy limits
Abstract
In this thesis we study the high-energy and collinear behaviour of gravitational scattering amplitudes and their relation to classical scattering and radiation observables. Multi-Regge kinematics, characterised by a strong rapidity ordering, provides the factorised building blocks governing the leading logarithmic structure. Relaxing this ordering to next-to-multi-Regge kinematics allows two neighbouring particles to have comparable rapidities and provides the real emission building blocks entering at next-to-leading logarithmic accuracy. We extract the next-to-multi-Regge impact factor from tree-level MHV amplitudes for pure gravitons and derive its gravitational splitting functions. We then use BCFW recursion relations to reconstruct the five-point tree amplitude for two massive scalars scattering with the emission of one graviton. Its high-energy limit yields the massive scalar--graviton impact factor and, through the KMOC formalism, a representation of the leading high-energy collinear waveform. Finally, by sewing the relevant vertices across unitarity cuts, we construct the elastic H kernel, its radiative extension and a classical next-to-multi-Regge kernel. The latter reproduces the standard H kernel in the multi-Regge limit and the universal Weinberg current in the soft limit.
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BibTeX
@misc{pietrini2026gravitational,
title = {{Gravitational scattering amplitudes in collinear and high-energy limits}},
author = {Lorenzo Pietrini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08860},
eprint = {2610.08860},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08860},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational scattering amplitudes in collinear and high-energy limits
AU - Lorenzo Pietrini
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.08860
UR - https://arxiv.org/abs/2610.08860
AB - In this thesis we study the high-energy and collinear behaviour of gravitational scattering amplitudes and their relation to classical scattering and radiation observables. Multi-Regge kinematics, characterised by a strong rapidity ordering, provides the factorised building blocks governing the leading logarithmic structure. Relaxing this ordering to next-to-multi-Regge kinematics allows two neighbouring particles to have comparable rapidities and provides the real emission building blocks entering at next-to-leading logarithmic accuracy. We extract the next-to-multi-Regge impact factor from tree-level MHV amplitudes for pure gravitons and derive its gravitational splitting functions. We then use BCFW recursion relations to reconstruct the five-point tree amplitude for two massive scalars scattering with the emission of one graviton. Its high-energy limit yields the massive scalar--graviton impact factor and, through the KMOC formalism, a representation of the leading high-energy collinear waveform. Finally, by sewing the relevant vertices across unitarity cuts, we construct the elastic H kernel, its radiative extension and a classical next-to-multi-Regge kernel. The latter reproduces the standard H kernel in the multi-Regge limit and the universal Weinberg current in the soft limit.
ER -