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

TL;DR

This thesis analyzes the charged pion loop contribution to the hadronic light-by-light scattering effect on the muon g-2, comparing different models and studying the impact of pion properties and effective theories.

Contribution

It provides a detailed comparison of models like VMD, HLS, and ChPT for the pion loop contribution to muon g-2, including effects of pion polarizability and charge radius.

Findings

Different models yield varying results for the pion loop contribution.

Momentum regions responsible for model differences have been identified.

Effects of pion polarizability and charge radius at order p^4 in ChPT have been studied.

Abstract

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.