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# Charged Pion Contribution to the Anomalous Magnetic Moment of the Muon

## Citation

Engel, Kevin Thomas (2013) Charged Pion Contribution to the Anomalous Magnetic Moment of the Muon. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/M463-8Z93. https://resolver.caltech.edu/CaltechTHESIS:05212013-160540441

## Abstract

The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.

Item Type: Thesis (Dissertation (Ph.D.)) magnetic moment; LBL; charged pion; chiral perturbation theory; g-2 California Institute of Technology Physics, Mathematics and Astronomy Physics Public (worldwide access) Wise, Mark B. Caltech Theory Wise, Mark B. (chair)Carroll, Sean M.Cheung, Clifford W.Porter, Frank C. 16 May 2013 kevin.t.engel (AT) gmail.com CaltechTHESIS:05212013-160540441 https://resolver.caltech.edu/CaltechTHESIS:05212013-160540441 10.7907/M463-8Z93 No commercial reproduction, distribution, display or performance rights in this work are provided. 7732 CaltechTHESIS Kevin Engel 29 May 2013 23:47 26 Oct 2021 17:57

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