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/M4638Z93. https://resolver.caltech.edu/CaltechTHESIS:05212013160540441
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 lightbylight (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.)) 

Subject Keywords:  magnetic moment; LBL; charged pion; chiral perturbation theory; g2 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  Caltech Theory 
Thesis Committee: 

Defense Date:  16 May 2013 
NonCaltech Author Email:  kevin.t.engel (AT) gmail.com 
Record Number:  CaltechTHESIS:05212013160540441 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:05212013160540441 
DOI:  10.7907/M4638Z93 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7732 
Collection:  CaltechTHESIS 
Deposited By:  Kevin Engel 
Deposited On:  29 May 2013 23:47 
Last Modified:  04 Oct 2019 00:01 
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