Emergence of a newSU(4)symmetry in the baryon spectrum

Abstract

Recently a large degeneracy of J = 1 mesons, that is larger than the SU (2)L × SU (2)R × 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 turnes 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.

On the nature of an emergent symmetry in QCD with low-lying Dirac modes removed

“…one in which correlation functions of sources connected to each other by chiral transformations are identical. Moreover, for most channels a plateau in the effective mass plot continues to exist after the removal of these modes [1][2][3][4][5][6] which may be interpreted as suggesting that reasonably well defined hadronic resonances survive the truncation. However, what was found when the correlation functions were calculated was totally unexpected: a set of identical correlation functions that was much larger than could be explained by chiral symmetry alone.…”

“…It was not introduced lightly [1,2,[4][5][6]. Rather, it was suggested to explain a totally unexpected phenomenon recently observed in lattice calculations of correlation functions with various sources including those with the quantum numbers of spin zero, spin one and spin two mesons and of baryons.…”

“…In particular, one of the J=1 correlation functions (an SU(4) singlet channel) was observed to be nearly identical to others (in an SU(4) 15-plet) [2] even though this is "accidental" from the perspective of SU(4) [7]. In this paper a natural solution to this puzzle is explored: namely that the emergent symmetry group is larger than SU (4) (and contains SU(4) as a subgroup). However, as will be shown here, the nature of any such emergent symmetry must be rather peculiar: there is no symmetry transformation of the usual kind for a continuous symmetry in a field theory (i.e.…”

“…The emergent symmetry proposed to explain this pattern was SU(4); it was interpreted as a symmetry of the confining part of the QCD [4][5][6][7]. It was suggested that an SU(4) symmetry associated with the color-Coulomb interaction might ultimately be responsible for it [5,7].…”

“…Recent lattice gauge calculations [1][2][3][4][5][6][7] may have shed significant light on this relationship. These calculations are quite remarkable in that they suggest that in a regime where effects of chiral dynamics are turned off by hand (and thus confinement dynamics may be expected to dominate) a new symmetry emerges which is larger than any explicitly in the QCD lagrangian [1,2,[4][5][6][7]. The nature of this putative emergent symmetry is the subject of the present paper.…”