Heavy-Particle Effective Theory: from On-Shell Formalism to Gravitational Compton Amplitudes
Abstract
We formulate on-shell heavy-particle effective theory (HPET) amplitudes by projecting the spinor-helicity variables onto the SU(2) little group of a timelike reference velocity vμ. Retaining both large and small components of the velocity-projected spinors gives an intermediate velocity-projected amplitudes in which reparameterization invariance can be imposed before expanding in the inverse heavy-particle mass. Integrating out the small component then yields HPET amplitudes organized by heavy-particle power counting, with a direct correspondence to local operators at fixed order. We determine the three-point velocity-projected amplitudes for two equal-mass particles of arbitrary spin S coupled to a soft massless boson of helicity h. Four-point gravitational Compton amplitudes can be constructively obtained using velocity-projected three-point amplitudes, and expanded into HPET amplitudes which is free of spurious poles up to sub-leading order. As a gravitational application, we show that the projected gravitational minimal coupling reproduces the Kerr spin-induced multipoles up to order 2S, and find the classical limits of the tree-level elastic gravitational scattering and gravitational Compton amplitudes agreed with the literature up to contact terms undetermined by factorization.
Related
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- Three-particle di-light-cone distribution amplitudes of the B-meson in heavy-quark effective theory
- Compton amplitude and contact term(s) in the spinor helicity formalism
- A General Manifestly Covariant Construction of Partial-Wave Amplitudes in the Rarita-Schwinger Formalism
- Gravitational Compton scattering at the fourth post-Minkowskian order
BibTeX
@misc{li2026heavyparticle,
title = {{Heavy-Particle Effective Theory: from On-Shell Formalism to Gravitational Compton Amplitudes}},
author = {Yong-Kang Li and Yi-Ning Wang and Jiang-Hao Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40263},
eprint = {2610.40263},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40263},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Heavy-Particle Effective Theory: from On-Shell Formalism to Gravitational Compton Amplitudes
AU - Yong-Kang Li
AU - Yi-Ning Wang
AU - Jiang-Hao Yu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40263
UR - https://arxiv.org/abs/2610.40263
AB - We formulate on-shell heavy-particle effective theory (HPET) amplitudes by projecting the spinor-helicity variables onto the SU(2) little group of a timelike reference velocity v^μ. Retaining both large and small components of the velocity-projected spinors gives an intermediate velocity-projected amplitudes in which reparameterization invariance can be imposed before expanding in the inverse heavy-particle mass. Integrating out the small component then yields HPET amplitudes organized by heavy-particle power counting, with a direct correspondence to local operators at fixed order. We determine the three-point velocity-projected amplitudes for two equal-mass particles of arbitrary spin S coupled to a soft massless boson of helicity h. Four-point gravitational Compton amplitudes can be constructively obtained using velocity-projected three-point amplitudes, and expanded into HPET amplitudes which is free of spurious poles up to sub-leading order. As a gravitational application, we show that the projected gravitational minimal coupling reproduces the Kerr spin-induced multipoles up to order 2S, and find the classical limits of the tree-level elastic gravitational scattering and gravitational Compton amplitudes agreed with the literature up to contact terms undetermined by factorization.
ER -