Testing the Witten-Veneziano Formula on the Lattice

TL;DR

This paper tests the Witten-Veneziano formula using lattice QCD simulations, employing spectral projector methods and dynamical fermions, and finds good agreement within uncertainties.

Contribution

It provides a lattice-based verification of the Witten-Veneziano formula with improved techniques and dynamical fermions.

Findings

Good agreement with the Witten-Veneziano formula within uncertainties

Effective use of spectral projector method for topological susceptibility

First lattice test with $N_f=2+1+1$ dynamical Wilson twisted mass fermions

Abstract

In this proceeding contribution we report on a test of the famous Witten-Veneziano formula using lattice techniques. We perform dedicated quenched simulations and apply the spectral projector method to determine the topological susceptibility in pure Yang-Mills theory. In order to compute the relevant meson masses and the flavor singlet decay constant we employ lattice QCD with $N_f=2+1+1$ dynamical Wilson twisted mass fermions. Taking the continuum and the $SU(2)$ chiral limits we find good agreement within uncertainties for both sides of the formula.