Dissecting the hadronic contributions to $(g-2{)}_{\mu }$ by Schwinger's sum rule

Abstract

The theoretical uncertainty of $(g-2{)}_{\mu }$ is currently dominated by hadronic contributions. In order to express those in terms of directly measurable quantities, we consider a sum rule relating $g-2$ to an integral of a photo-absorption cross section. The sum rule, attributed to Schwinger, can be viewed as a combination of two older sum rules: Gerasimov-Drell-Hearn and Burkhardt-Cottingham. The Schwinger sum rule has an important feature, distinguishing it from the other two: the relation between the anomalous magnetic moment and the integral of a photo-absorption cross section is linear, rather than quadratic. The linear property makes it suitable for a straightforward assessment of the hadronic contributions to $(g-2{)}_{\mu }$. From the sum rule we rederive the Schwinger $\alpha /2\pi$ correction, as well as the formula for the hadronic vacuum-polarization contribution. As an example of the light-by-light contribution we consider the single-meson exchange.

6 pages, 10 figures, published version extended by a few clarifying remarks and an Appendix

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• Pseudoscalar pole light-by-light contributions to the muon $(g-2)$ in Resonance Chiral Theory
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• Hadronic light-by-light scattering contribution to the muon g-2 on the lattice
• Vacuum polarization contribution to muon $g-2$ as an inverse problem
• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
• Lattice calculation of the hadronic leading order contribution to the muon $g-2$
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