Pions in Lattice QCD with the Overlap Fermions at Strong Gauge Coupling

TL;DR

This paper derives a low-energy effective theory for lattice QCD with overlap fermions at strong coupling, demonstrating the emergence of massless pions as Nambu-Goldstone bosons due to spontaneous chiral symmetry breaking.

Contribution

It provides a novel derivation of the effective pion action in lattice QCD with overlap fermions, highlighting the nonlocal nature of pions at strong coupling.

Findings

Existence of quasi-Nambu-Goldstone bosons identified as pions.

Pions are massless in the zero bare-quark mass limit.

Pions are nonlocal composite fields of quark-antiquark pairs.

Abstract

In the previous paper we developed a strong-coupling expansion for the lattice QCD with the overlap fermions and showed that L\"usher's "extended" chiral symmetry is spontaneously broken in some parameter region of the overlap fermions. In this paper, we obtain a low-energy effective action and show that there exist quasi-Nambu-Goldsone bosons which are identified as the pions. The pion field is a {\em nonlocal} composite field of quark and anti-quark even at the strong-coupling limit because of the nonlocality of the overlap fermion formalism and L\"usher's chiral symmetry. The pions become massless in the limit of the vanishing bare-quark mass as it is desired.