Sigma Mass in the Large N Limit of QCD

TL;DR

This paper investigates the relationship between scalar and pseudoscalar mesons in large N QCD, revealing mass degeneracies and implications for hadron phenomenology using worldline techniques.

Contribution

It demonstrates a mass degeneracy between scalar and pseudoscalar mesons in the large N limit of QCD, even with chiral symmetry breaking, using novel worldline methods.

Findings

Scalar and pseudoscalar mesons have identical masses in the large N limit.

The sigma and eta mesons are predicted to have the same mass in the planar limit.

Results are relevant for quenched lattice QCD and hadron phenomenology.

Abstract

We study the leading contribution to the scalar and the pseudoscalar two-point function in the large N expansion of QCD using the worldline techniques. We find that in this limit there exists a relationship between these two Green's functions which implies that for every massive pseudoscalar meson there exists a scalar meson of identical mass. This is true even when chiral symmetry is spontaneously broken. The relationship between the Green's function further suggests that in the planar limit the sigma mass must be identical to the eta mass. We also discuss the relevance of these results for the quenched lattice QCD simulations and for hadron phenomenology.