Non-perturbative Test of the Witten-Veneziano Formula from Lattice QCD

TL;DR

This study tests the Witten-Veneziano formula non-perturbatively using lattice QCD, comparing topological susceptibility and decay constants, and finds good agreement within uncertainties after continuum and chiral limits.

Contribution

First lattice QCD computation of both sides of the Witten-Veneziano formula including the flavor singlet decay constant with dynamical fermions.

Findings

Good agreement between both sides after continuum and chiral limits.

First use of spectral projector method for topological susceptibility in quenched simulations.

Inclusion of flavor singlet decay constant in lattice QCD calculations.

Abstract

We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with $N_f=2+1+1$ dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU$(2)$ chiral limits we compare both sides and find good agreement within uncertainties.