Non-perturbative Renormalisation of Domain Wall Fermions: Quark Bilinears

TL;DR

This paper computes non-perturbative renormalisation coefficients for domain wall fermions in lattice QCD, analyzing chiral symmetry effects and comparing with perturbative predictions.

Contribution

It provides the first non-perturbative determination of renormalisation factors for quark bilinears using domain wall fermions in a quenched lattice simulation.

Findings

Chiral symmetry relations are approximately satisfied in the results.

Residual chiral symmetry breaking effects are controllable.

Comparison shows good agreement with perturbative predictions.

Abstract

We find the renormalisation coefficients of the quark field and the flavour non-singlet fermion bilinear operators for the domain wall fermion action, in the regularisation independent (RI) renormalisation scheme. Our results are from a quenched simulation, on a 16^3x32 lattice, with beta=6.0 and an extent in the fifth dimension of 16. We also discuss the expected effects of the residual chiral symmetry breaking inherent in a domain wall fermion simulation with a finite fifth dimension, and study the evidence for both explicit and spontaneous chiral symmetry breaking effects in our numerical results. We find that the relations between different renormalisation factors predicted by chiral symmetry are, to a good approximation, satisfied by our results and that systematic effects due to the (low energy) spontaneous chiral symmetry breaking and zero-modes can be controlled. Our results are compared against the perturbative predictions for both their absolute value and renormalisation scale dependence.