Exploring a new SU(4) symmetry of meson interpolators

TL;DR

This paper demonstrates that upon quasi-zero mode truncation in lattice QCD, mesons with spin J ≥ 1 exhibit an emergent SU(4) symmetry that extends beyond the traditional chiral and axial symmetries, revealing new insights into confinement.

Contribution

It establishes that SU(4) symmetry governs J ≥ 1 mesons in lattice QCD after quasi-zero mode removal, expanding understanding of meson symmetries beyond conventional models.

Findings

SU(4) symmetry relates meson interpolators of the same spin

Correlation functions confirm SU(4) symmetry in J ≥ 1 mesons

SU(4) symmetry is linked to confining interactions in QCD

Abstract

In recent lattice calculations it has been discovered that mesons upon truncation of the quasi-zero modes of the Dirac operator obey a symmetry larger than the $SU(2)_L \times SU(2)_R\times U(1)_A$ symmetry of the QCD Lagrangian. This symmetry has been suggested to be $SU(4) \supset SU(2)_L \times SU(2)_R\times U(1)_A$ that mixes not only the u- and d-quarks of a given chirality, but also the left- and right-handed components. Here it is demonstrated that bilinear $\overline{q}q$ interpolating fields of a given spin $J \geq 1$ transform into each other according to irreducible representations of $SU(4)$ or, in general, $SU(2N_F)$. This fact together with the coincidence of the correlation functions establishes $SU(4)$ as a symmetry of the $J \geq 1$ mesons upon quasi-zero mode reduction. It is shown that this symmetry is a symmetry of the confining instantaneous charge-charge interaction in QCD. Different subgroups of $SU(4)$ as well as the $SU(4)$ algebra are explored.