Evidence for a new $SU(4)$ symmetry with $J=2$ mesons

TL;DR

This paper provides evidence that an emergent $SU(4)$ symmetry, previously observed in $J=1$ mesons after quasi-zero mode removal, also applies to $J=2$ mesons, indicating a higher symmetry structure in QCD.

Contribution

The study extends the observation of $SU(4)$ symmetry to $J=2$ mesons using lattice simulations with the Overlap Dirac operator, revealing a broader symmetry pattern in mesons.

Findings

Degeneracy observed in $J=2$ isovector mesons after quasi-zero mode removal.

Supports the existence of $SU(4)$ symmetry for mesons with spin $J \\geq 1$.

Further evidence of higher symmetry in QCD beyond the Lagrangian.

Abstract

Recently, a new symmetry of mesons has been found upon truncation of the quasi-zero modes of the Overlap Dirac operator in lattice simulations. Namely, the $\rho,\rho',\omega,\omega',a_1, b_1,h_1$ and possibly $f_1$ $J=1$ mesons get degenerate after removal of the quasi-zero modes. This emergent symmetry has been established to be $SU(4)\supset SU(2)_L \times SU(2)_R \times U(1)_A$. It is higher than the symmetry of the QCD Lagrangian and provides not only a mixing of quarks of given chirality in the isospin space, but also the mixing of left-handed and right-handed components. Here we study, with the Overlap Dirac operator, the isovector $J=2$ mesons upon the quasi-zero mode reduction and observe a similar degeneracy. This result further supports the $SU(4)$ symmetry in mesons of given spin $J \geq 1$.