Upper Bound on the Hadronic Light-By-Light Contribution to the Muong−2

There are indications that hadronic loops in some electroweak observables are almost saturated by parton level effects. Taking this as the hypothesis for this work, we propose a genuine parton level estimate of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, $a_{\mu }^{\mathrm{LBL}}(\mathrm{had})$. Our quark mass definitions and values are motivated in detail, and the simplicity of our approach allows for a transparent error estimate. For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses $a_{\mu }^{\mathrm{LBL}}(\mathrm{had})$ is overestimated. Interpolating, this suggests quoting an upper bound. We obtain $a_{\mu }^{\mathrm{LBL}}(\mathrm{had})<1.59\times {10}^{-9}$ (95% C.L.).