{
  "abstract": "Chiral perturbation theory is a power tool for studying the low-energy strong interactions. In the conventional chiral expansion, according to the power counting rule, the higher-order corrections for physical observables are expected to decrease order by order as the chiral dimension increases. However, most previous study of $πK$ scattering lengths by different references showed that the $\\mathcal{O}(p^6)$ correction to the scattering lengths is anomalously large and even exceeds the $\\mathcal{O}(p^4)$ one. It poses a serious challenge to the convergence of chiral expansion. In order to explore the underlying origin of this phenomenon, the contributions of two-loop diagrams, one-loop diagrams and tree diagrams for the $πK$ scattering amplitude are detailed analyzed. The reducible two-loop integrals, sunset integrals and vertex integrals from the $\\mathcal{O}(p^6)$ order all violate the power counting rule. The sunset and vertex integrals can be largely canceled numerically, but not enough. Furthermore, $πK$ scattering is compared with $ππ$ scattering, which seems not violate the power counting rule. The analysis indicates that $ππ$ scattering contains a higher symmetry, although each $\\mathcal{O}(p^6)$-order part also violates the power counting rule, but the violation is much smaller than the one from $πK$ scattering. Large kaon mass also makes a contribution to the power-counting breaking, but it is not a major origin. Hence, it needs to pay more attention to the many-loop low-symmetry diagrams in future work. These diagrams may give large contribution and cannot be ignored.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17721",
  "author_total": 2,
  "authors": [
    {
      "name": "Ming-Ze Ma"
    },
    {
      "name": "Shao-Zhou Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7t1w45hp3a1p9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17721",
  "fulltext_url": null,
  "id": "7t1w45hp3a1p9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17721",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7221789813",
  "pdf_url": "https://arxiv.org/pdf/2610.17721",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7t1w45hp3a1p9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17721",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17721"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "A mechanism of the power-counting breaking in chiral perturbation theory",
  "title_text": "A mechanism of the power-counting breaking in chiral perturbation theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/7t1w45hp3a1p9",
  "venue": "arXiv",
  "versions": []
}