The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions

TL;DR

This paper demonstrates a precise lattice implementation of the Witten--Veneziano formula for the eta' mass using Ginsparg--Wilson fermions, with numerical results aligning with theoretical and experimental values.

Contribution

It provides a clear lattice formulation of the topological charge density operator with Ginsparg--Wilson fermions and validates it through numerical simulations.

Findings

Lattice implementation matches continuum Witten--Veneziano formula.

Numerical results agree with theoretical eta' mass expectations.

Results are consistent with experimental data in QCD.

Abstract

We show how it is possible to give a precise and unambiguous implementation of the Witten--Veneziano formula for the eta' mass on the lattice, which looks like the formal continuum one, if the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg--Wilson relation, is employed. By using recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions, one obtains values for the mass of the lightest pseudo-scalar flavour-singlet state that agree within errors with theoretical expectations and experimental data, respectively.