The condensate for two dynamical chirally improved quarks in QCD

TL;DR

This paper compares the eigenvalue spectra of the Dirac operator in lattice QCD with two dynamical chirally improved quarks to Random Matrix Theory predictions, enabling a direct determination of the quark condensate.

Contribution

It provides the first detailed comparison of Dirac eigenvalues from chirally improved fermions with RMT, extracting the quark condensate in the chiral limit.

Findings

Eigenvalue distributions match RMT predictions well.

Quark condensate in the MS-bar scheme is approximately -(276(11)(16) MeV)^3.

Finite size and renormalization effects are properly accounted for.

Abstract

We compare the eigenvalue spectra of the Dirac operator from a simulation with two mass degenerate dynamical chirally improved fermions with Random Matrix Theory. Comparisons with distribution of k-th eigenvalues (k=1,2) in fixed topological sectors (nu=0,1) are carried out using the Kolmogorov-Smirnov test. The eigenvalue distributions are well described by the RMT predictions. The match allows us to read off the quark condensate in the chiral limit directly. Correcting for finite size and renormalization we obtain a mean value of -(276 (11)(16) MeV)**3 in the MS-bar scheme.