Topological susceptibility from the twisted mass Dirac operator spectrum

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 .

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

“…As we will show in this paper for the setup of maximally twisted mass fermions used in refs. [1,2], even in the presence of these short distance singularities automatic O(a)-improvement is preserved at maximal twist, thus justifying the strategy to perform an O(a 2 ) scaling, as done in refs. [1,2].…”

“…(3.1) relates the chiral condensate Σ to the spectral density ρ(λ, µ s ). The method based on spectral projectors introduced in [3] offers a new strategy to compute spectral JHEP04 (2015)048 observables, such as the chiral condensate, in an affordable way [1,2,19]. Moreover it allows us, via the connection to density chains, to compute this quantity using a representation which is free of short distance singularities and therefore leads to the correct continuum limit.…”

“…[15], since we are interested in a formula that can be evaluated with the spectral projector method and thus one that can be expressed using the Hermitian Dirac operator D † D. 2 Note that this does not affect the discussion for the chiral condensate, since there are already more than 2 densities to guarantee the absence of short-distance singularities.…”

“…In two recent papers [1,2] we carried out a calculation for the chiral condensate and the topological susceptibility in the chiral and the continuum limit. In these works, we performed an O(a 2 ) scaling towards the continuum limit.…”

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

“…For standard discretizations, such properties are recovered only for small enough lattice spacings, so that a careful investigation of the continuum limit becomes essential. Indeed only recently it was possible to measure the dependence of the topological susceptibility on the quark masses to a sufficient accuracy to be compared with the prediction of chiral perturbation theory [23][24][25][26][27].…”