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~(LBL)_μ(had). For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses a~(LBL)_μ(had) is overestimated. Interpolating, this suggests to quote an upper bound. We obtain a(had) < 1.59 × 10~(-9) (95% CL).
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