We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, a hvp µ , arising from quark-connected Feynman graphs. It is based on ensembles featuring N f = 2+1+1 dynamical twisted mass fermions generated by the European Twisted Mass Collaboration (ETMC). Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass. We employ three lattice spacings to examine lattice artefacts and several different volumes to check for finite-size effects. Incorporating the complete first two generations of quarks allows for a direct comparison with phenomenological determinations of a hvp µ . Our final result including an estimate of the systematic uncertainty a hvp µ = 6.74(21)(18) · 10 −8 shows a good overall agreement with these computations.

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.

We present physics results from simulations of QCD using N f = 2 dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations were enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, a ≈ 0.09 fm. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the ∆ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.

We investigate the thermal QCD transition with two flavors of maximally twisted mass fermions for a set of pion masses, 300 MeV

We investigate the temperature dependence of the Landau gauge gluon and ghost propagators in lattice QCD with two flavors of maximally twisted mass fermions. For these propagators we provide and analyze data which corresponds to pion mass values between 300 and 500 MeV. For the gluon propagator we find that both the longitudinal and transversal component change smoothly in the crossover region, while the ghost propagator exhibits only a very weak temperature dependence. For momenta between 0.4 and 3.0 GeV we give a parametrization for our lattice data. It may serve as input to studies which employ continuum functional methods.

Abstract:The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, α QED , and the weak mixing angle, θ W , are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.

We report on lattice QCD results for the thermodynamic equation of state of quark-gluon matter obtained with N f = 2 degenerate quark flavors. For the fermion field discretization we are using the Wilson twisted mass prescription. Simulations have been carried out at three values of the bare quark masses corresponding to pion masses of ∼ 360, ∼ 430 and ∼ 640 MeV. We highlight the importance of a good control of the lattice cutoff dependence of the trace anomaly which we have studied at several values of the inverse temperature T −1 = aNτ with a time-like lattice extent up to Nτ = 12. We contrast our results with those of other groups obtained for N f = 0 and N f = 2 + 1. At low temperature we also confront them with hadron resonance gas model predictions for the trace anomaly.

The leading hadronic contributions to the anomalous magnetic moments of the electron and the τ -lepton are determined by a four-flavour lattice QCD computation with twisted mass fermions. The results presented are based on the quark-connected contribution to the hadronic vacuum polarisation function. The continuum limit is taken and systematic uncertainties are quantified. Full agreement with results obtained by phenomenological analyses is found.