Topological susceptibility from the twisted mass Dirac operator spectrum

We present results of our computation of the topological susceptibility with N f = 2 and N f = 2 + 1 + 1 flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants Z P / Z S

Short distance singularities and automatic O(a) improvement: the cases of the chiral condensate and the topological susceptibility

Short-distance singularities in lattice correlators can modify their Symanzik expansion by leading to additional O( a ) lattice artifacts. At the example of the chiral condensate and the topological susceptibility, we show how to account for these lattice artifacts for Wilson twisted mass fermions and show that the property of automatic O( a ) improvement is preserved at maximal twist

Non-perturbative test of the Witten-Veneziano formula from lattice QCD

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