Twisted Loops and Models for Form-factors and the Muon g-2

Abstract: In this thesis we use effective field thory methods and models for low energy QCD in two different contexts. One is direct calculation of contributions to the anomalous magnetic moment of the muon, muon g-2. The other is estimates of systematic sources of uncertainty in lattice QCD simulations. The work is presented in five papers. Papers II, IV and V describe calculations for muon g-2 and papers I, III and V contain estimates of various systematic effects in lattice QCD simulations.Paper I deals with the use of twisted boundary conditions. Using chpt we calculate one loop effects of twisted boundary conditions for a number of different observables. Furthermore, we show how the direction dependence of masses, which shows up when using twisted boundary conditions, should be taken into account in order to fulfill Ward identities.Twisted boundary conditions together with other effects are considered in papers III and V as well. In paper V we use partially twisted partially quenched chpt at two loops to estimate the systematic uncertainties in hadronic vacuum polarization which is relevant for muon g-2. In paper III we estimate systematic uncertainties for Kl3 decays, which are relevant for the CKM matrix element Vus, using partially twisted partially quenched rooted staggered chpt at one loop. In paper II we use several different models to compute the pion loop contribution to hadronic light-by-light scattering. Most models are inspired by vector meson dominance but we try to go beyond that and include also the lightest axial vector meson, a1. We also present an estimate of the ratio of disconnected to connected contributions to hadronic light-by-light scattering relevant for lattice QCD. In paper IV we use chpt to estimate the ratio between disconnected and connected contributions to hadronic vacuum polarization. This was studied in earlier work at one loop. We give an underlying reason for their result and show that the ratio holds for a large part of the higher loop corrections. We also discuss corrections to the ratio.