Spontaneous Generation of Pseudoscalar Mass in the U(3)xU(3) Linear Sigma Model

Abstract

A novel, nonperturbative, way to generate chiral symmetry breaking within the linear sigma model for 3 flavours is discussed. After spontaneous chiral symmetry breaking in the vacuum at the tree level the scalar nonet obtains mass, while the pseudoscalars are massless. Then, including quantum loops in a nonperturbative, self-consistent way chiral symmetry is broken by nonplanar graphs in a second step, and also the pseudoscalars become massive. By interpreting the basic symmetry to be a discrete permutation symmetry, in accord with superselection rules, no additional Goldstone bosons are expected.