  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.
