The Muon Anomalous Magnetic Moment and the Pion Polarizability

Abstract

We compute the charged pion loop contribution to the muon anomalous magnetic moment $a_{\mu }$, taking into account the effect of the charged pion polarizability, $({\alpha }_1-{\beta }_1{)}_{{\pi }^{+}}$. We evaluate this contribution using two different models that are consistent with the requirements of chiral symmetry in the low-momentum regime and perturbative quantum chromodynamics in the asymptotic region. The result increases the disagreement between the present experimental value for $a_{\mu }$ and the theoretical, Standard Model prediction by as much as $\sim 60\times 10^{-11}$, depending on the value of $({\alpha }_1-{\beta }_1{)}_{{\pi }^{+}}$ and the choice of the model. The planned determination of $({\alpha }_1-{\beta }_1{)}_{{\pi }^{+}}$ at Jefferson Laboratory will eliminate the dominant parametric error, leaving a theoretical model uncertainty commensurate with the error expected from planned Fermilab measurement of $a_{\mu }$.

5 pages, one figure

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• Towards a data-driven analysis of hadronic light-by-light scattering
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
• On the precision of a data-driven estimate of hadronic light-by-light scattering in the muon g-2: pseudoscalar-pole contribution
• The VV'P form factors in resonance chiral theory and the pi-eta-eta' light-by-light contribution to the muon g-2
• Pion light-by-light contributions to the muon $g-2$
• Dynamical quark loop light-by-light contribution to muon g-2 within the nonlocal chiral quark model
• Hadronic light-by-light contribution to $a_{\mu }$: extended Nambu-Jona-Lasinio, chiral quark models and chiral Lagrangians
• On the Hadronic light-by-light contribution to the muon $g-2$