Relics of Supersymmetry in Ordinary 1-flavor QCD: Hairpin Diagrams and Scalar-Pseudoscalar Degeneracy

TL;DR

This paper investigates how supersymmetry-related features manifest in ordinary 1-flavor QCD, focusing on scalar-pseudoscalar meson degeneracy and the effects of quark-antiquark annihilation, supported by lattice QCD and NJL model analyses.

Contribution

It demonstrates that hairpin diagrams induce scalar-pseudoscalar degeneracy in 1-flavor QCD, linking lattice results and NJL model insights to supersymmetry relics.

Findings

Lattice QCD results support approximate degeneracy of scalar and pseudoscalar mesons.

Hairpin diagrams cause opposite mass shifts in scalar and pseudoscalar channels.

Degeneracy constraints relate to the size of anomalous and non-anomalous couplings in NJL model.

Abstract

The large-$N_c$ orientifold planar equivalence between $\mathcal{N}=1$ SUSY Yang-Mills theory and ordinary 1-flavor QCD suggests that low-energy quark-gluon dynamics in QCD should be constrained by the supersymmetry of the parent theory. One SUSY relic expected from orientifold equivalence is the approximate degeneracy of the scalar and pseudoscalar mesons in 1-flavor QCD. Here we study the role of the $q\bar{q}$ annihilation (hairpin) contributions to the meson correlators. These annihilation terms induce mass shifts of opposite sign in the scalar and pseudoscalar channels, making degeneracy plausible. Calculations of valence and hairpin correlators in quenched lattice QCD are consistent with approximate degeneracy, although the errors on the scalar hairpin are large. We also study the role of $q\bar{q}$ annihilation in the 1- and 2-flavor Nambu-Jona Lasinio model, where annihilation terms arise from the chiral field determinant representing the axial U(1) anomaly. Scalar-pseudoscalar degeneracy for the 1-flavor case reduces to a constraint on the relative size of the anomalous and non-anomalous 4-fermion couplings.