{
  "abstract": "In arXiv:2211.13753 we proposed a novel theoretical approach for non-perturbative QCD, named the inverse problem approach. It extracts non-perturbative quantities by solving a dispersion integral equation as an inverse problem, using perturbative QCD and operator product expansion as inputs. In this work, we apply this approach to the pion and $a_1(1260)$ decay constants, as well as the continuum spectral function. The extracted $f_π= 130.8 \\pm 8.1$ MeV agrees with the experimental value, and the reconstructed spectral function reproduces the ALEPH $τ$-decay data from threshold up to $s \\simeq 3$ GeV$^2$. The advantages of this approach are as follows: (i) the whole non-perturbative range is solved simultaneously, yielding the ground state, excited states, and the continuum spectrum within a single framework; (ii) it is based on rigorous mathematics, with not only statistical but also systematic uncertainties well controlled and quantifiable; (iii) the regularized solutions exhibit convergence, allowing the precision to be systematically improved with better inputs; (iv) quark-hadron duality emerges naturally at high energy scales, avoiding the low-energy duality assumption and the Borel transformation, and eliminating their associated uncertainties. Finally, the successful physical application of the inverse problem approach demonstrates its broad applicability to non-perturbative quantities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40111",
  "author_total": 4,
  "authors": [
    {
      "name": "Yong Zheng"
    },
    {
      "name": "Ao-Sheng Xiong"
    },
    {
      "name": "Fu-Sheng Yu"
    },
    {
      "name": "Ting Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70qhm1r7jmjz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40111",
  "fulltext_url": null,
  "id": "70qhm1r7jmjz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40111",
  "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-lat"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nucl-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70qhm1r7jmjz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40111"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Inverse Problem Approach for Non-Perturbative QCD: Applications",
  "title_text": "Inverse Problem Approach for Non-Perturbative QCD: Applications",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/70qhm1r7jmjz5",
  "venue": "arXiv",
  "versions": []
}