The Dichotomous Nature of the $\sigma$ Meson and the Nucleon D-Term

TL;DR

This paper uses a symmetry-preserving approach in QCD to explore the dual nature of the sigma meson, linking it to mass generation and predicting the nucleon D-term consistent with lattice and continuum studies.

Contribution

It introduces a unified framework recognizing the sigma meson as both a quark-antiquark state and a dilaton, connecting it to the nucleon D-term prediction.

Findings

D-terms of quark, pion, and sigma saturate at fixed values above a critical coupling

Sigma meson exhibits dual nature as a quark-antiquark state and a dilaton

Predicted nucleon D-term is approximately -3, aligning with existing studies

Abstract

Employing a symmetry-preserving contact-interaction formulation of the Dyson-Schwinger equations in quantum chromodynamics (QCD), we examine the identity of the $\sigma$ 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 $\sigma$ saturate at fixed values $D_{q,\pi,\sigma}=-1/3,-1,-7/3$. By examining the coupling strength evolution of the D-terms, this pattern follows naturally once a dual nature for the $\sigma$ 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.