Abstract
The theoretical uncertainty of (g-2)_{μ} 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 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-2)_{μ}. From the sum rule, we rederive the Schwinger α/2π 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.
Highlights
Introduction.—The anomalous magnetic moment (AMM) of the muon, κμ ≡ 1/2ðg − 2Þμ, serves as a stringent precision test of the Standard Model (SM)
The data-driven approach is fairly well founded and routinely used for the hadronic vacuum polarization (HVP) contribution [Fig. 1(a)], since it can be written exactly as a dispersion integral of the decay rate of a virtual timelike photon into hadrons, which to a good approximation is expressed in terms of the observed ratio μþμ−/eþe− → hadrons; see, e.g., Refs. [9,10]
In what follows we focus on a sum rule which is linear in the AMM and involves an observable crosssection quantity
Summary
Introduction.—The anomalous magnetic moment (AMM) of the muon, κμ ≡ 1/2ðg − 2Þμ, serves as a stringent precision test of the Standard Model (SM). The hadronic contribution to κμ starts at Oðα2Þ; the lhs of the GDH sum rule is Oðα5Þ, whereas the cross sections of hadronic photoproduction starts at Oðα3Þ. We “only” need to know how (a moment of) the muon spin-structure function combination g1 þ g2 is affected by hadronic contributions.
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