{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9f28798b5b397b6a01ccc78c6e9a739b623d0b4f6d90b9c15923a4e8a0a3aeb8","created":"2026-10-03T07:18:07Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","7b02a893f4e0dc176f20bf2e98bddec1d9ba7e622edd96f63dd87fb2bae9bbc9"],"salt":"dc22971b693f1958545f0025fd682db89abb8b43229edec7c169deaa2eca8162","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"nuc.proton-structure.pion-nucleon-sigma-term","kind":"well-posed","literature_status":"contested","n":"1","parents":[{"note":"","parent_revision":"7b02a893f4e0dc176f20bf2e98bddec1d9ba7e622edd96f63dd87fb2bae9bbc9","relation":"special_case"}],"plain":"The $\\sigma$ term measures how much of the proton mass comes from the small masses of the up and down quarks. Extractions from pion-proton scattering give about 59 MeV, while several lattice QCD calculations (QCD solved numerically on a space-time grid) give about 40 to 45 MeV.","posed_since":"","precise":"sigma_piN = m_hat <N| u-bar u + d-bar d |N> with $m_{\\mathrm{hat}} = (m_{u} + m_{d})/2$. Roy-Steiner analysis of $\\pi N$ scattering gives $59.1 \\pm 3.5\\,\\mathrm{MeV}$ (Hoferichter et al., PRL 115, 092301, 2015); lattice QCD with standard excited-state treatment gives about $40 \\text{ to } 45\\,\\mathrm{MeV}$ (for example $43.7 \\pm 3.6\\,\\mathrm{MeV}$, Agadjanov et al., arXiv 2303.08741), while including $N\\pi$ and $N\\pi\\pi$ excited states raises it to $59.6 \\pm 7.4\\,\\mathrm{MeV}$ (Gupta et al., PRL 127, 242002, 2021). Answer: sigma_piN with uncertainty below $3\\,\\mathrm{MeV}$ agreed between physical-point lattice QCD and the dispersive value, with the cause of the discrepancy identified.","problem_ref":null,"references":"","settled_by":"Lattice QCD at physical quark masses with variational nucleon, N pi and N pi pi operator bases and continuum extrapolation, compared with the Roy-Steiner value.","status_note":"A two-loop chiral analysis of lattice data gave $55.9(2.5)\\,\\mathrm{MeV}$ (Liang et al., arXiv 2508.11435, 2025), and a variational lattice study at $m_{\\pi} = 429\\,\\mathrm{MeV}$ showed reduced excited-state contamination with multi-hadron operators (Barca, Bali, Collins, arXiv 2412.13138, 2024); no physical-point lattice consensus existed as of 2026.","title":"Pion-nucleon $\\sigma$ term: lattice QCD versus pion-nucleon 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