The Dichotomous Nature of the $σ$ Meson and the Nucleon D-Term
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| Format: | Preprint |
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2025
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| _version_ | 1866912763881717760 |
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| author | Xing, Zanbin Raya, Khépani Liu, Yu-xin Chang, Lei |
| author_facet | Xing, Zanbin Raya, Khépani Liu, Yu-xin Chang, Lei |
| contents | Employing a symmetry-preserving contact-interaction formulation of the Dyson-Schwinger equations in quantum chromodynamics (QCD), we examine the identity of the $σ$ meson and its implications for the gravitational structure of hadrons. In this framework, the scalar meson emerges as the chiral partner of the pion, with both states' properties tightly connected to the mechanisms of mass generation in QCD. We find that, above a critical coupling that triggers dynamical chiral symmetry breaking, the D-terms of the constituent quark, the pion, and $σ$ saturate at fixed values $D_{q,π,σ}=-1/3,-1,-7/3$. By examining the coupling strength evolution of the D-terms, this pattern follows naturally once a dual nature for the $σ$ meson is recognized: it behaves both as a quark-antiquark composite and as a dilaton arising from spontaneous scale symmetry breaking. This unified picture yields the prediction $D_N\sim -3$ for the nucleon D-term, consistent with contemporary lattice-QCD, continuum, and dispersive studies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Dichotomous Nature of the $σ$ Meson and the Nucleon D-Term Xing, Zanbin Raya, Khépani Liu, Yu-xin Chang, Lei High Energy Physics - Phenomenology Employing a symmetry-preserving contact-interaction formulation of the Dyson-Schwinger equations in quantum chromodynamics (QCD), we examine the identity of the $σ$ meson and its implications for the gravitational structure of hadrons. In this framework, the scalar meson emerges as the chiral partner of the pion, with both states' properties tightly connected to the mechanisms of mass generation in QCD. We find that, above a critical coupling that triggers dynamical chiral symmetry breaking, the D-terms of the constituent quark, the pion, and $σ$ saturate at fixed values $D_{q,π,σ}=-1/3,-1,-7/3$. By examining the coupling strength evolution of the D-terms, this pattern follows naturally once a dual nature for the $σ$ meson is recognized: it behaves both as a quark-antiquark composite and as a dilaton arising from spontaneous scale symmetry breaking. This unified picture yields the prediction $D_N\sim -3$ for the nucleon D-term, consistent with contemporary lattice-QCD, continuum, and dispersive studies. |
| title | The Dichotomous Nature of the $σ$ Meson and the Nucleon D-Term |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.05583 |