The dichotomous nature of the σ meson and the nucleon D-term

A dual identity of the σ meson is proposed and its implications for the gravitational structure of hadrons is examined. Staring from a q q ¯ bound state view for the σ meson, which emerges naturally as the chiral partner of the pion in the Dyson-Schwinger Equation formalism, 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 ∼ − 3 for the nucleon D-term, consistent with lattice QCD, dispersive analyses, and diverse continuum studies.