Low-lying mode contribution to the quenched meson correlators in the epsilon-regime

TL;DR

This study investigates meson correlators in the epsilon-regime using quenched lattice QCD with overlap fermions, highlighting the dominant role of low-lying eigenmodes in scalar and pseudo-scalar channels and extracting key chiral parameters.

Contribution

It demonstrates that low-lying eigenmodes suffice to approximate certain meson correlators in the epsilon-regime and extracts physical parameters from lattice data.

Findings

Scalar and pseudo-scalar correlators are dominated by low-lying modes.

Axial-vector correlator requires higher eigenmodes for accurate description.

Chiral parameters F_pi, Sigma, m_0, and alpha are successfully extracted.

Abstract

We present a quenched calculation of meson correlators with the overlap fermion at very small masses 2.6--13 MeV. In this region the pion Compton wavelength is larger than our lattice size L\simeq 1.23fm and the system is in the so-called epsilon-regime of chiral perturbation theory. We found that the scalar and pseudo-scalar correlators are precisely approximated by a few hundred low-lying fermion eigenmodes in this regime, whereas axial-vector correlator receives significant contributions from higher eigenmodes. We also measure the disconnected pseudo-scalar correlator, which is well saturated with the low-lying modes. Matching these lattice data with the one-loop expressions for the correlators in quenched chiral perturbation theory, we evaluate the decay constant F_pi and the chiral condensate Sigma as well as the parameters m_0 and alpha, which describe the artifacts of the quenched approximation.