Hadronic light-by-light scattering contribution to the muon g-2

TL;DR

This paper reviews recent advances in calculating the hadronic light-by-light scattering contribution to the muon g-2, emphasizing the importance of off-shell form factors and providing a new estimate with updated constraints.

Contribution

It introduces a reevaluation of the pion-exchange contribution using an off-shell form factor satisfying QCD constraints, leading to a revised estimate of the hadronic light-by-light contribution.

Findings

New estimate for muon g-2 hadronic light-by-light contribution: (116 ± 40) x 10^{-11}

Reevaluation of pion-exchange contribution with QCD short-distance constraints

Potential for further improvements in theoretical calculations

Abstract

We review recent developments concerning the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. We first discuss why fully off-shell hadronic form factors should be used for the evaluation of this contribution to the g-2. We then reevaluate the numerically dominant pion-exchange contribution in the framework of large-N_C QCD, using an off-shell pion-photon-photon form factor which fulfills all QCD short-distance constraints, in particular, a new short-distance constraint on the off-shell form factor at the external vertex in g-2, which relates the form factor to the quark condensate magnetic susceptibility in QCD. Combined with available evaluations of the other contributions to hadronic light-by-light scattering this leads to the new result a_{\mu}(LbyL; had) = (116 \pm 40) x 10^{-11}, with a conservative error estimate in view of the many still unsolved problems. Some potential ways for further improvements are briefly discussed as well. For the electron we obtain the new estimate a_{e}(LbyL; had) = (3.9 \pm 1.3) x 10^{-14}.