Grit Hotzel

Four-flavour leading-order hadronic contribution to the muon anomalous magnetic moment

A bstractWe present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon,

Computing the hadronic vacuum polarization function by analytic continuation

a_{\mu}^{\mathrm{hvp}}

The Hadronic Vacuum Polarization and Automatic

, arising from quark-connected Feynman graphs. It is based on ensembles featuring Nf = 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

\mathcal{O}(a)

a_{\mu}^{\mathrm{hvp}}

Improvement for Twisted Mass Fermions

. Our final result including an estimate of the systematic uncertainty

Leading-order hadronic contributions to a_{\mu} and \alpha_{QED} from N_f=2+1+1 twisted mass fermions

a_{\mu}^{\mathrm{hvp}}

Using analytic continuation for the hadronic vacuum polarization computation

= 6.74(21)(18) · 10−8 shows a good overall agreement with these computations.

Leading-order hadronic contribution to the anomalous magnetic moment of the muon from N_f=2+1+1 twisted mass fermions

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 present with the example of the leading-order 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.

Thermodynamics with

A bstractThe 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 Oa