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

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.

The talk presented of Gribov-80 Workshop, May 28-30, 2010, Trieste, 8 pages, minor changes

References in corpus (4)

• Determination of the magnetic susceptibility of the quark condensate using radiative heavy meson decays
• Magnetic susceptibility of the QCD vacuum
• The origin of mass and the experiments on future high energy accelerators
• Zero mode solutions of quark Dirac equations in QCD as the sources of chirality violating condensates