Emergence of a new $SU(4)$ symmetry in the baryon spectrum

TL;DR

This paper demonstrates that removing near-zero modes from quark propagators reveals an emergent $SU(4)$ symmetry in the baryon spectrum, indicating a deeper symmetry structure related to confinement in QCD.

Contribution

The study extends the observation of $SU(4)$ symmetry from mesons to baryons under near-zero mode removal, revealing a larger symmetry group in the baryon spectrum.

Findings

$SU(4)$ symmetry observed in baryons after mode removal

Degeneracy of states from different $SU(4)$ irreducible representations

Larger symmetry group encompassing $SU(4)$ identified

Abstract

Recently a large degeneracy of $J=1$ mesons, that is larger than the $SU(2)_L \times SU(2)_R \times U(1)_A$ symmetry of the QCD Lagrangian, has been discovered upon truncation of the near-zero modes from the valence quark propagators. It has been found that this degeneracy represents the $SU(4)$ group that includes the chiral rotations as well as the mixing of left- and right-handed quarks. This symmetry group turns out to be a symmetry of confinement in QCD. Consequently, one expects that the same symmetry should persist upon the near-zero mode removal in other hadron sectors as well. It has been shown that indeed the $J=2$ mesons follow the same symmetry pattern upon the low-lying mode elimination. Here we demonstrate the $SU(4)$ symmetry of baryons once the near-zero modes are removed from the quark propagators. We also show a degeneracy of states belonging to different irreducible representations of $SU(4)$. This implies a larger symmetry, that includes $SU(4)$ as a subgroup.