Chiral properties of dynamical Wilson fermions

TL;DR

This paper investigates the chiral properties of two-flavor QCD with improved Wilson fermions on the lattice, addressing explicit chiral symmetry breaking, algorithmic challenges, and non-perturbative improvement and renormalization of axial currents.

Contribution

It introduces non-perturbative methods to improve and renormalize axial currents, restoring chiral symmetry up to quadratic order in lattice spacing.

Findings

Algorithmic performance improves with polynomial hybrid Monte Carlo.

Chiral symmetry is restored up to quadratic order in lattice spacing.

Non-perturbative renormalization aligns lattice results with continuum Ward identities.

Abstract

We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite renormalization if they are to satisfy continuum Ward--Takahashi identities up to small lattice corrections of O(a^2). Algorithmic difficulties at coarse lattice spacings, where HMC suffers from a distorted Dirac spectrum, are discussed. This is shown to be a cutoff effect, which disappears rapidly as the lattice spacing is decreased. An alternative algorithm, the polynomial hybrid Monte Carlo algorithm, is found to perform significantly better in the presence of exceptionally small eigenvalues. Extending previously used methods both the improvement and the renormalization of the axial current are implemented non--perturbatively in terms of correlation functions formulated in the framework of the Schroedinger functional. In both cases this is achieved by enforcing continuum Ward identities at finite lattice spacing. Together, this restores the isovector chiral symmetry to quadratic order in the lattice spacing. With little additional effort the normalization factor of the local vector current is also obtained.