{
  "abstract": "The second sine harmonic $\\Pz$ of longitudinal $Λ$ polarization is sensitive to the balance between the kinematic-vorticity contribution $\\Pz^ω$ and the kinematic-shear contribution $\\Pz^Ξ$ at decoupling. We quantify this competition in a scan of 48 Pb-Pb initial states evolved with the (3+1)-dimensional Particle-In-Cell Relativistic (PICR) ideal-hydrodynamic code. With the isothermal local-equilibrium (ILE) prescription, the total harmonic follows $\\Pz\\simeq a\\,\\efo-b\\,v_2$, with $a\\simeq0.010$ and $b\\simeq0.014$, where $\\efo$ is the freeze-out eccentricity and $v_2$ the elliptic flow of $Λ$ hyperons. With coefficients fixed on these 48 states, the relation describes 86\\% of the variation of $\\Pz$ in 12 states outside the fit. To identify the origin of the two terms, we decompose the ILE integrand exactly into an emission-gradient term and a curl term. On the PICR decoupling surfaces, the tangential emission gradient is positive on average, correlates most strongly with $\\efo$, and admits a surface-curvature representation, whereas the normal emission gradient and the curl term are negative on average and correlate most strongly with $v_2$. A blast-wave calculation with the same integrand gives coefficients of comparable magnitude and shows how the cancellation point $\\efo/v_2=b/a$ changes with the flow and the surface geometry; both PICR and blast-wave calculations predict that $b/a$ rises with hadron mass from the proton to the $Ω$ when the decoupling surface is held fixed. Although the geometry inferred from ALICE data depends on the background, the measured polarization constrains the displacement of $\\efo$ from the cancellation boundary $\\efo=(b/a)v_2$. For the central ALICE measurement values at $5.36\\,\\mathrm{TeV}$, the backgrounds examined give $\\efo\\simeq0.2$--$0.4$ in 30--50\\% Pb-Pb collisions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26740",
  "author_total": 3,
  "authors": [
    {
      "name": "Yilong Xie"
    },
    {
      "name": "Simin Wu"
    },
    {
      "name": "Laszlo P. Csernai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6dc4y4xert9sb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26740",
  "fulltext_url": null,
  "id": "6dc4y4xert9sb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26740",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|High-Energy Particle Collisions Research"
    ]
  ],
  "openalex": "W7222931471",
  "pdf_url": "https://arxiv.org/pdf/2609.26740",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6dc4y4xert9sb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2609.26740",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26740"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Longitudinal $Λ$ polarization as a competition between freeze-out geometry and elliptic flow in Pb-Pb collisions at $\\sqrt{s_{\\mathrm{NN}}}=5.36\\,\\mathrm{TeV}$",
  "title_text": "Longitudinal Λ polarization as a competition between freeze-out geometry and elliptic flow in Pb-Pb collisions at √(s_NN)=5.36 TeV",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/6dc4y4xert9sb",
  "venue": "arXiv",
  "versions": []
}