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The Anatomy of the Pion Loop Hadronic Light by Light Scattering Contribution to the Muon Magnetic Anomaly

This thesis investigates the Hadronic Light by Light (HLL) scattering contribution to the muon $g-2$, which is one of the most important low energy hadronic effects and consists mainly of the quark loop, the pion pole and the charged pion and kaon loops. In this work the charged pion loop has been investigated more closely. After reviewing the subject a preliminary introduction to Chiral Perturbation Theory (ChPT), Hidden Local Symmetry (HLS) model and the full Vector Meson Dominance (VMD) model is given, and they are used to calculate the pion loop HLL scattering contribution to the muon anomalous magnetic moment. The momentum regions where the contributions of the bare pion loop, the VMD model, and the HLS come from, have been studied, to understand why different models give very different results. The effects of pion polarizability and charge radius on the HLL scattering, which appear at order $p^4$ in ChPT, from $ L_9$ and $ L_{10}$ Lagrangian terms and their momentum regions have been studied.