Testing the $SU(4)$ degeneracy after low-mode removal with $J=2$ mesons

TL;DR

This paper demonstrates the emergence of an $SU(4)$ symmetry in $J=2$ mesons after low-mode removal in lattice QCD, indicating a new form of confinement symmetry that affects quark interactions.

Contribution

It provides the first demonstration of $SU(4)$ degeneracy among all $J=2$ iso-vector states after low-mode removal, revealing a new symmetry of confinement.

Findings

$SU(4)$ symmetry appears in $J=2$ mesons after low-mode removal

Degeneracy observed within $SU(4)$ irreducible representations

Quark interactions with the color-magnetic field vanish under this symmetry

Abstract

Recent lattice results on Dirac low-mode removed $J=1,2$ mesons and $J=\frac{1}{2}$ baryons reveal the appearance of a new $SU(4)$ symmetry of confinement. Here the degeneracy of all $J=2$ iso-vector states within an irreducible representation of $SU(4)$ after low-mode removal is demonstrated. The $SU(4)$ symmetry contains $SU(2)_L \times SU(2)_R$ and $U(1)_A$ symmetries as subgroups and mixes all compontents $u_L,u_R,d_L,d_R$ of the two-flavor Dirac field. It implies the vanishing of the interaction of quarks with the color-magnetic field, which is shown by using the QCD Hamiltonian in Coulomb gauge.