Hadronic contribution to the muong−2factor: A theoretical determination

Abstract

The leading order hadronic contribution to the muon g-2, a HAD µ , is determined entirely from theory using an approach based on Cauchy's theorem in the complex squared energy s-plane. This is possible after fitting the integration kernel in a HAD µ with a simpler function of s. The integral determining a HAD µ in the light-quark region is then split into a low energy and a high energy part, the latter given by perturbative QCD (PQCD). The low energy integral involving the fit function to the integration kernel is determined by derivatives of the vector correlator at the origin, plus a contour integral around a circle calculable in PQCD. These derivatives are calculated using hadronic models in the light-quark sector. A similar procedure is used in the heavy-quark sector, except that now everything is calculable in PQCD, thus becoming the first entirely theoretical calculation of this contribution. Using the dual resonance model realization of Large Nc QCD to compute the derivatives of the correlator leads to agreement with the experimental value of aµ. Accuracy, though, is currently limited by the model dependent calculation of derivatives of the vector correlator at the origin. Future improvements should come from more accurate chiral perturbation theory and/or lattice QCD information on these derivatives, allowing for this method to be used to determine a HAD µ accurately entirely from theory, independently of any hadronic model.The value of the muon g-2 is well known as a test of the standard model (SM) of particle physics.[1]. The SM result for the anomalous magnetic moment of the muon is conveniently separated into the contributions due to QED, the hadronic sector, and the electroweak sector. A sizable theoretical uncertainty arises from the (leading order) hadronic vacuum polarization term, the second largest contribution after that of QED. A substantial effort has been made to determine this contribution from experimental data on e + e − → hadrons and τ → hadrons [2]- [3]. Currently, there is some yet unresolved discrepancy between both results. Writing the muon anomaly in the SM asthe leading contribution is that from QED, followed by the hadronic and the electroweak terms. In this paper we concentrate on the leading order hadronic contribution and discuss a new approach to its calculation entirely from theory. The method relies on Cauchy's theorem in the complex squared energy s-plane, after fitting the integration kernel entering a HAD µwith a simple function of s . In the region of the light-quark sector the method requires knowledge of some of the derivatives of the (electromagnetic) vector correlator at zero momentum, as well as its perturbative QCD (PQCD) behavior. Currently, these derivatives will be obtained here from hadronic models, thus being affected by systematic uncertainties. Hence, at this stage the method cannot rival in accuracy with the standard approach of using experimental data on the vector correlator at low/intermediate energies. However, future precision determinations of these ...

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