Spontaneous chiral symmetry breaking as condensation of dynamical chirality

Abstract

The occurrence of spontaneous chiral symmetry breaking (SChSB) is equivalent to sufficient abundance of Dirac near-zeromodes. However, dynamical mechanism leading to breakdown of chiral symmetry should be naturally reflected in chiral properties of the modes. Here we offer such connection, presenting evidence that SChSB in QCD proceeds via the appearance of modes exhibiting dynamical tendency for local chiral polarization. These modes form a band of finite width Λch (chiral polarization scale) around the surface of otherwise anti-polarized Dirac sea, and condense. Λch characterizes the dynamics of the breaking phenomenon and can be converted to a quark mass scale, thus offering conceptual means to determine which quarks of nature are governed by broken chiral dynamics. It is proposed that, within the context of SU(3) gauge theories with fundamental Dirac quarks, mode condensation is equivalent to chiral polarization. This makes Λch an “order parameter” of SChSB, albeit without local dynamical field representation away from chiral limit. Several uses of these features, both at zero and finite temperature, are discussed. Our initial estimates are Λch≈150 MeV (Nf=0), Λch≈80 MeV (Nf=2+1, physical point), and that the strange quark is too heavy to be crucially influenced by broken chiral symmetry.