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 propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this method leads to the desired hadronic vacuum polarization function in Minkowski spacetime. We show with the example of the leadingorder QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.

We calculate perturbative contributions of Wilson loops of various sizes up to order 20 in SU (3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high orders of perturbation theory. We observe differences in the behavior of those series as function of the loop order n. Up to n = 20 we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. For Wilson loops of moderate sizes the summed series in boosted perturbation theory reach stable plateaus already for moderate orders in perturbation theory. The coefficients in the boosted series become much more stable in the result of smoothing the coefficients of the original series effected by the hypergeometric model. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their non-perturbative parts.

Abstract:The vacuum polarization tensor and the corresponding vacuum polarization function are the basis for calculations of numerous observables in lattice QCD. Examples are the hadronic contributions to lepton anomalous magnetic moments, the running of the electroweak and strong couplings and quark masses. Quantities which are derived from the vacuum polarization tensor often involve a summation of current correlators over all distances in position space leading thus to the appearance of short-distance terms. The mechanism of O(a) improvement in the presence of such short-distance terms is not directly covered by the usual arguments of on-shell improvement of the action and the operators for a given quantity. If such short-distance contributions appear, the property of O(a) improvement needs to be reconsidered. We discuss the effects of these short-distance terms on the vacuum polarization function for twisted mass lattice QCD and find that even in the presence of such terms automatic O(a) improvement is retained if the theory is tuned to maximal twist.

We present preliminary results achieved within a recently started project dealing with QCD thermodynamics in the presence of a fully dynamical second quark family. We are employing the Wilson twisted mass discretization. To reduce the amount of zero temperature simulations and the cost of analysis we have chosen the fixed-scale approach. We show a variety of basic thermodynamic observables for temperatures ranging from 158 to 633 MeV. Simulations were performed for three lattice spacings below 0.1 fm each and at a single value of the pion mass which allows a comparison with previously obtained N f = 2 results. We determine the chiral crossover temperature from the bare chiral susceptibility and show results for the gauge part of the trace anomaly.