Chirality violating condensates in QCD and their connection with zero mode solutions of quark Dirac equations

TL;DR

This paper demonstrates that chirality violating condensates in massless QCD originate from zero mode solutions of the Dirac equation, with instantons playing a key role, and discusses their temperature dependence and phase transition nature.

Contribution

It introduces a model linking zero mode solutions in instanton fields to chirality violating condensates and calculates related susceptibilities consistent with hadronic spectrum data.

Findings

Zero mode solutions are the sole source of chirality violating condensates in QCD.

Calculated susceptibilities align with values from hadronic spectrum.

The QCD phase transition related to the quark condensate is a crossover.

Abstract

It is demonstrated, that chirality violating condensates in massless QCD arise entirely from zero mode solutions of Dirac equations in arbitrary gluon fields. The model is suggested, where the zero mode solutions are the ones for quarks, moving in the instanton field. Basing on this model were calculated the quark condensate magnetic susceptibilities of dimensions $3(\chi)$ and 5 ($\kappa$ and $\xi$). The good considence of the values $\chi,\kappa$ and $\xi$, obtained in this approach with ones, found from the hadronic spectrum ia a serious argument in favour, that instantons are the only source of chirality violating condensates in QCD. The temperature dependence of the quark condensate is discussed. It is shown that the phase transition, corresponding to the $T$-dependence of the quark condensate $\alpha(T)$ as an order parameter, is of the type of crossover.