We present results on QCD with four dynamical flavors in the temperature range 150 MeV T 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 /Tc 2, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to Tc 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.

On the basis of perturbative QCD and the relativistic quark model, we calculate relativistic corrections to the process of pair J=c production in proton-proton collisions at LHC energy ffiffiffi S p ¼ 7 TeV. Relativistic terms in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave functions to the reference frame of moving J=c mesons are taken into account. For the gluon and quark propagators entering the amplitude, we use a truncated expansion in relative quark momenta up to the second order. Relativistic corrections to the quark bound state wave functions are considered by means of the Breit-like potential. It turns out that the examined effects decrease initial nonrelativistic cross section more than two times. The final result lies below the experimental value measured by LHCb.

We present results for the topological susceptibility at nonzero temperature obtained from lattice QCD with four dynamical quark flavours. We apply different smoothing methods, including gradient Wilson flow and over-improved cooling, before calculating the susceptibility. It is shown that the considered smoothing techniques basically agree among each other, and that there are simple scaling relations between flow time and the number of cooling/smearing steps. The topological susceptibility exhibits a surprisingly slow decrease at high temperature.

QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the quark–gluon plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.