Spontaneous Chiral Symmetry Breaking as Condensation of Dynamical Chirality

TL;DR

This paper links spontaneous chiral symmetry breaking in QCD to the emergence of locally chiral polarized modes, introducing a scale that acts as an order parameter for the phenomenon.

Contribution

It proposes that chiral polarization of Dirac modes characterizes chiral symmetry breaking and introduces the chiral polarization scale as a new order parameter.

Findings

Chiral polarization scale Lambda_ch is about 150 MeV for N_f=0.

Lambda_ch is approximately 80 MeV at the physical point with N_f=2+1.

Strange quark is too heavy to be affected by chiral symmetry breaking.

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 Lambda_ch (chiral polarization scale) around the surface of otherwise anti--polarized Dirac sea, and condense. Lambda_ch 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 Lambda_ch 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 Lambda_ch~150 MeV (N_f=0), Lambda_ch~80 MeV (N_f=2+1, physical point), and that the strange quark is too heavy to be crucially influenced by broken chiral symmetry.