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RESEARCH PRODUCT

Dissecting the Hadronic Contributions to (g−2)μ by Schwinger’s Sum Rule

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The theoretical uncertainty of $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ is currently dominated by hadronic contributions. In order to express those in terms of directly measurable quantities, we consider a sum rule relating $g\ensuremath{-}2$ to an integral of a photoabsorption 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 photoabsorption cross section is linear, rather than quadratic. The linear property makes it suitable for a straightforward assessment of the hadronic contributions to $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$. From the sum rule, we rederive the Schwinger $\ensuremath{\alpha}/2\ensuremath{\pi}$ 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.