Testing the Witten-Veneziano Formula on the Lattice

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.Comment: 7 pages, 4 figures, presented at the 33rd International Symposium on Lattice Field Theory, 14 -18 July 2015, Kobe International Conference Center, Kobe, Japa