The microscopic Twisted Mass Dirac spectrum and the spectral determination of the LECs of Wilson $\chi$-PT

TL;DR

This paper compares analytical and lattice spectral densities of twisted mass fermions in lattice QCD to extract low-energy constants, providing a novel spectral analysis method for Wilson chiral perturbation theory.

Contribution

It introduces a spectral comparison approach to determine low-energy constants in Wilson chiral perturbation theory using twisted mass fermions.

Findings

Estimated the chiral condensate from spectral data.

Determined the low-energy constant W_8.

Validated the spectral method against lattice data.

Abstract

We present the comparison of the analytical microscopic spectral density for lattice QCD with $N_{\rm f}=2$ twisted mass fermions with the one obtained on the lattice utilizing configurations produced by the ETM collaboration. We extract estimates for the chiral condensate as well as the low-energy constant $W_8$ of Wilson $\chi$-PT by employing spectral information of the Wilson Dirac operator with fixed index at finite volume.