Abstract
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 $Z_P/Z_S$.
Highlights
Possible to derive an expression for the topological susceptibility which does not have any power divergences [5, 6]
We have computed the topological susceptibility in dynamical Lattice QCD simulations using the method of spectral projectors
This method has two important advantages that we want to emphasize here:. It relies on a theoretically sound definition of the topological susceptibility from density chain correlators that is free of short distance singularities
Summary
The method that we follow in this paper was introduced in refs. [8, 9] and we refer to these papers for a comprehensive description. In chiral symmetry preserving formulations of Lattice QCD (e.g. using overlap fermions), the observable C is just the index Q of the Dirac operator, i.e. the difference in the number of zero modes with positive and negative chirality, since (η, γ5η) = ±1 if η is a zero mode and 0 otherwise. In such theories ZP = ZS and in the limit N → ∞ eq (2.3) becomes just the well-known formula χ = Q2 /V. I.e. it is the mode number ν(M ) — the number of eigenmodes of the operator D†D with eigenvalues below the threshold value M 2
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