Hadronic light-by-light scattering in the muon g-2: a new short-distance constraint on pion exchange

TL;DR

This paper presents a new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2, deriving a short-distance constraint and providing an updated estimate that refines previous calculations.

Contribution

We derive a new short-distance constraint on the pion-photon-photon form factor and evaluate the pion-exchange contribution using large-N_C QCD with all constraints satisfied.

Findings

New estimate for pion-exchange contribution: (72 ± 12) x 10^{-11}

Updated total light pseudoscalar contribution: (99 ± 16) x 10^{-11}

Overall hadronic light-by-light contribution: (116 ± 40) x 10^{-11}

Abstract

We summarize our recent new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in a_\mu which relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a_{\mu}(LbyL;\pi^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for the contributions from the exchanges of the eta and eta-prime using simple vector-meson dominance form factors, we get a_{\mu}(LbyL; PS) = (99 \pm 16) x 10^{-11} for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic light-by-light scattering this leads to the estimate a_{\mu}(LbyL; had) = (116 \pm 40) x 10^{-11}. The corresponding contributions to the anomalous magnetic moment of the electron are also given.