The Leading Hadronic Vacuum Polarization Contribution To The Muon Anomalous Magnetic Moment Using Nf

The theory of the muon anomalous magnetic is "particle physics in a nutshell" and as such is interesting, exciting and difficult. The current precision of the experimental value for this quantity, improved significantly in the past several years due to experiment E821 at Brookhaven National Laboratory, is so high that a large number of subtle effects not relevant previously, become important for the interpretation of the experimental result. The theory of the muon anomalous magnetic moment is at the cutting edge of current research in particle physics and includes multiloop calculati.

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, 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. Including the complete first two generations of quarks allows for a direct comparison with phenomenological determinations of a?hvp. Our final result involving an estimate of the systematic uncertainty a?hvp=6.74 (21)(18) 10-8 shows a good overall agreement with these computations.

This book reviews the present state of knowledge of the anomalous magnetic moment a=(g-2)/2 of the muon. The muon anomalous magnetic moment is one of the most precisely measured quantities in elementary particle physics and provides one of the most stringent tests of relativistic quantum field theory as a fundamental theoretical framework. It allows for an extremely precise check of the standard model of elementary particles and of its limitations.

The contribution of strong isospin-breaking (SIB) effects to the value of the anomalous magnetic moment of the muon is studied using the leading-order SIB component of the photon vacuum polarisation function, calculated in Chiral Perturbation Theory (ChPT) in the low Euclidean momentum-squared regime. At two-loop order in ChPT the result is found to be aSIB= 0.82(12)1010, approximately 1 order of magnitude less than recent determinations using Lattice Quantum Chromodynamics (QCD) and also phenomenology. It is shown that the inclusion of a tree-level term from next-to-next-to-next-to leading order (NNNLO) raises the ChPT prediction to aSIB= 3.61(98)1010. This result is consistent with the most precise result from Lattice QCD. The dominant NNNLO contribution is interpreted as parameterising the SIB physics of the lightest resonances which are predicted to be the most significant processes at low momentum.