Two-Loop Extraction of the Pion-Nucleon Sigma Term
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| Format: | Preprint |
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2025
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| _version_ | 1866909737886416896 |
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| author | Liang, Ze-Rui Chen, Han-Xue Guo, Feng-Kun Guo, Zhi-Hui Yao, De-Liang |
| author_facet | Liang, Ze-Rui Chen, Han-Xue Guo, Feng-Kun Guo, Zhi-Hui Yao, De-Liang |
| contents | The pion-nucleon sigma term, characterizing the mass component of Higgs origin related to $u$ and $d$ quarks inside the nucleon, is investigated within relativistic baryon chiral perturbation theory at leading two-loop order using the extended-on-mass-shell renormalization scheme. The two-loop representation of the sigma term is derived from the nucleon mass via the Feynman-Hellmann theorem and verified through a direct calculation of the forward isoscalar-scalar nucleon matrix element. We apply the derived chiral expression to extract the physical pion-nucleon sigma term by extrapolating $N_f=2+1$ lattice quantum chromodynamics (QCD) data at unphysical quark masses. We find that, at the two-loop level, the long-standing tension between lattice QCD and dispersive determinations can be naturally resolved, owing to the incorporation of intermediate $ππ$ rescattering effects that begin to contribute at two-loop order. Our final result for the nucleon sigma term based on recent lattice QCD calculations is $σ_{πN}=55.9(2.5)$ MeV. It is compatible with the result of the Roy-Steiner equation analysis and thus provides a satisfactory resolution to the previous debate between lattice QCD and phenomenological determinations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Loop Extraction of the Pion-Nucleon Sigma Term Liang, Ze-Rui Chen, Han-Xue Guo, Feng-Kun Guo, Zhi-Hui Yao, De-Liang High Energy Physics - Phenomenology High Energy Physics - Lattice The pion-nucleon sigma term, characterizing the mass component of Higgs origin related to $u$ and $d$ quarks inside the nucleon, is investigated within relativistic baryon chiral perturbation theory at leading two-loop order using the extended-on-mass-shell renormalization scheme. The two-loop representation of the sigma term is derived from the nucleon mass via the Feynman-Hellmann theorem and verified through a direct calculation of the forward isoscalar-scalar nucleon matrix element. We apply the derived chiral expression to extract the physical pion-nucleon sigma term by extrapolating $N_f=2+1$ lattice quantum chromodynamics (QCD) data at unphysical quark masses. We find that, at the two-loop level, the long-standing tension between lattice QCD and dispersive determinations can be naturally resolved, owing to the incorporation of intermediate $ππ$ rescattering effects that begin to contribute at two-loop order. Our final result for the nucleon sigma term based on recent lattice QCD calculations is $σ_{πN}=55.9(2.5)$ MeV. It is compatible with the result of the Roy-Steiner equation analysis and thus provides a satisfactory resolution to the previous debate between lattice QCD and phenomenological determinations. |
| title | Two-Loop Extraction of the Pion-Nucleon Sigma Term |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2508.11435 |