Spontaneous chiral symmetry breaking on the lattice

TL;DR

This paper uses lattice QCD with overlap fermions to analyze low-lying eigenmodes, confirming spontaneous chiral symmetry breaking and extracting low energy constants through comparison with chiral perturbation theory.

Contribution

It provides a detailed lattice QCD study of low-lying fermion eigenmodes with exact chiral symmetry, confirming spontaneous symmetry breaking and determining low energy constants.

Findings

Confirmed spontaneous chiral symmetry breaking on the lattice

Determined low energy constants from eigenmode distributions

Validated chiral perturbation theory beyond leading order

Abstract

Using lattice QCD we study the spectrum of low-lying fermion eigenmodes. According to the Banks-Casher relation, accumulation of the low-mode is responsible for the spontaneous breaking of chiral symmetry in the QCD vacuum. On the lattice we use the overlap fermion formulation that preserves exact chiral symmetry. This is essential for the study of low-lying eigenmode distributions. Through a detailed comparison with the expectations from chiral perturbation theory beyond the leading order, we confirm the senario of the spontaneous symmetry breaking and determine some of the low energy constants. We also discuss on other related physical quantities, which can be studied on the lattice with exact chiral symmetry.