{
  "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 $v^μ$. 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40263",
  "author_total": 3,
  "authors": [
    {
      "name": "Yong-Kang Li"
    },
    {
      "name": "Yi-Ning Wang"
    },
    {
      "name": "Jiang-Hao Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/by3rkcp3z9ynz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40263",
  "fulltext_url": null,
  "id": "by3rkcp3z9ynz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40263",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/by3rkcp3z9ynz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40263"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Heavy-Particle Effective Theory: from On-Shell Formalism to Gravitational Compton Amplitudes",
  "title_text": "Heavy-Particle Effective Theory: from On-Shell Formalism to Gravitational Compton Amplitudes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/by3rkcp3z9ynz",
  "venue": "arXiv",
  "versions": []
}