Sigma Mass in the Large N Limit of QCD

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.