A fresh look at hadronic light-by-light scattering in the muon g - 2 with the Dyson-Schwinger approach

C.S. Fischer; T. Goecke; R. Williams

doi:10.1140/epja/i2011-11028-1

EPJ

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2023 Impact factor 2.6

Hadrons and Nuclei

Open Access

Eur. Phys. J. A (2011) 47: 28
https://doi.org/10.1140/epja/i2011-11028-1

Letter

A fresh look at hadronic light-by-light scattering in the muon g - 2 with the Dyson-Schwinger approach

C.S. Fischer¹^,2^,3, T. Goecke³ and R. Williams³

¹ Institut für Theoretische Physik, Universität Giessen, 35392, Giessen, Germany
² Gesellschaft für Schwerionenforschung mbH, Planckstr. 1, D-64291, Darmstadt, Germany
³ Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289, Darmstadt, Germany

Received: 11 January 2011
Accepted: 4 February 2011
Published online: 24 February 2011

Abstract

Using the Dyson-Schwinger and Bethe-Salpeter equations, we calculate the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon $\ensuremath a_\mu$ , using a phenomenological model for the gluon and quark-gluon interaction. We find $\ensuremath a_\mu=(84 \pm 13)\times 10^{-11}$ for meson exchange, and $\ensuremath a_\mu = (107 \pm 2 \pm 46)\times 10^{-11}$ for the quark loop. The former is commensurate with past calculations; the latter much larger due to dressing effects. This leads to a revised estimate of $\ensuremath a_\mu=116 591 865.0(96.6)\times 10^{-11}$ , reducing the difference between theory and experiment to ≃ 1.9 $\sigma$ .