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

We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $ a_{\mu}^{\mathrm{hvp}} $ , 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_{\mu}^{\mathrm{hvp}} $ . Our final result including an estimate of the systematic uncertainty $ a_{\mu}^{\mathrm{hvp}} $ = 6 . 74(21)(18) · 10 −8 shows a good overall agreement with these computations