Analysis of the Axial Anomaly on the Lattice with O(a)-improved Wilson Action

TL;DR

This paper investigates axial Ward identities in lattice QCD with O(a)-improved Wilson action, addressing renormalization, operator mixing, and defining the topological charge operator non-perturbatively.

Contribution

It provides a one-loop matching of renormalization constants, proposes a lattice definition of the gluon operator G~G outside the chiral limit, and develops a non-perturbative method to evaluate operator mixing.

Findings

Calculated renormalization constants matching continuum schemes.

Proposed a lattice definition of G~G considering chiral symmetry breaking.

Developed a non-perturbative approach for mixing constant evaluation.

Abstract

Flavor singlet and non-singlet axial Ward identities are investigated using the Wilson formulation of lattice QCD with Clover O(a)-improvement, which breaks explicitly chiral symmetry. The matching at one-loop order of all the relevant renormalization constants with the continuum \bar{MS} scheme is presented. Our calculations include: 1) the contributions arising from the Clover term of the action; 2) the complete mixing of the gluon operator G \tilde{G} with the divergence of the singlet axial current; 3) the use of both local and extended definitions of the fermionic bilinear operators. A definition of the gluon operator G \tilde{G} on the lattice outside the chiral limit is proposed. Our definition takes into account the possible power-divergent mixing with the pseudoscalar density, generated by the breaking of chiral symmetry. A non-perturbative procedure for the evaluation of such mixing constant is worked out. Finally, the renormalization properties of the composite insertion of the topological charge operator relevant for the lattice calculation of the neutron electric dipole moment, induced by the strong CP-violating term of the QCD Lagrangian, are discussed.