The $U_A(1)$ Problem on the Lattice
L. Giusti, G.C. Rossi, M. Testa, G. Veneziano
TL;DR
This paper demonstrates that using Ginsparg--Wilson fermions on the lattice allows a rigorous proof of the Witten--Veneziano formula for the $ ext{eta'}$ mass, supported by numerical simulations in 2D and 4D.
Contribution
It provides a lattice-based proof of the Witten--Veneziano formula using Ginsparg--Wilson fermions and confirms the theoretical predictions with numerical results.
Findings
Numerical results agree with theoretical expectations.
Overlap fermions yield consistent $ ext{eta'}$ mass measurements.
Lattice formulation validates the Witten--Veneziano formula.
Abstract
If the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg--Wilson relation, is employed, it is possible to prove on the lattice the validity of the Witten--Veneziano formula for the mass. Recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions give values for the mass of the lightest pseudo-scalar flavour-singlet state that agree with theoretical expectations and/or experimental data.
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