Abstract
We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected susceptibility, on lattices with spacings as fine as 0.065 fm. For most observables spacing effects are below statistical errors, which enables us to identify lattice results with continuum estimates. Our estimate of the pseudocritical temperature compares favorably with continuum results from staggered and domain wall fermions, confirming that a dynamical charm does not contribute in the transition region. From the high temperature behaviour of the disconnected chiral susceptibility we infer the topological susceptibility, which encodes relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility thus measured exhibits a power-law decay for $T/T_c \gtrsim 2$, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to $T_c$ the temperature dependent effective exponent seems to approach the DIGA result from above, a behaviour which would support recent analytic calculations based on an Instantons-dyons model. These results constrain the mass of a hypothetic QCD post-inflationary axion, once an assumption concerning the relative contribution of axions to Dark Matter is made.
Highlights
The properties of strong interactions at high temperatures are under active scrutiny both theoretically and experimentally
We have studied chiral and topological properties of Nf 1⁄4 2 þ 1 þ 1 QCD with twisted mass Wilson fermions
We have found that an extrapolation to the pseudocritical temperature for the physical pion is robust with respect to different assumptions for the universality class of the two-flavor massless theory, and agrees well with previous estimates
Summary
The properties of strong interactions at high temperatures are under active scrutiny both theoretically and experimentally. We use the results for the disconnected chiral susceptibility to calculate the topological susceptibility for temperatures as high as 500 MeV, apparently reaching the onset of the dilute instanton gas approximation Since this second aspect is at the moment under active investigation by several groups, we conclude this introduction with a brief review of the current status of topology in hot QCD. Recent methodological progress, together with more adequate computer resources, have to some extent reopened the field, leading to the first results on topology at high temperature with dynamical fermions [9,17,18,19,20] These studies exhibit some common features, which we will review in the following together with our own results, a quantitative agreement has not been reached yet. Some of the results presented here have been presented in a preliminary form at conferences [10,28]
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