Mass and structure of the nucleon: Gluon trace anomaly versus spontaneous symmetry breaking

TL;DR

This paper compares two approaches to understanding the nucleon's mass and structure: lattice QCD focusing on gluon contributions and spontaneous symmetry breaking involving quark-antiquark pairs, highlighting their complementary roles.

Contribution

It clarifies how gluon trace anomaly and spontaneous symmetry breaking provide different but related insights into nucleon mass and stability.

Findings

Lattice QCD approach relates to unstable nucleon configurations.

Spontaneous symmetry breaking approach relates to stable nucleon configurations.

The $\sigma$ field emerges from quark-antiquark condensates.

Abstract

Two different approaches to mass and structure of the nucleon are discussed in recent works, ${\it viz.}$ (case 1) the QCD lagrangian evaluated via lattice calculations and (case ii) spontaneous symmetry breaking mediated by the $\sigma$ field. These approaches are complementary in the sense that the QCD lagrangian makes use of the gluon content of the nucleon entering in terms of the gluon trace-anomaly and ignores the effects of $q{\bar q}$ vacuum polarization, whereas in spontaneous symmetry breaking masses are formed by attaching $q{\bar q}$ pairs to the valence quarks, thus giving them a definite mass which is named the constituent mass. By the same process the $q{\bar q}$ pairs of the vacuum polarization acquire mass and in this form are the elements of the quark condensate, having an up-quark and a down-quark component. A linear combination of these two components in the form $\sigma=1/\sqrt{2}(u{\bar u} + d{\bar d})$ shows up as the $\sigma$ field. It is shown that (case i) corresponds to an unstable nucleon configuration whereas (case ii) corresponds to a stable nucleon configuration as observed in low-energy photo-nuclear and pion-nuclear reactions.