How large are hadronic contributions to $h \to \gamma \gamma$?

The decay of the Higgs boson into two photons, $h \to \gamma \gamma$, is a loop-induced process within the Standard Model, predominantly mediated by loops of $W$ bosons and top quarks. While these leading contributions are well understood, the role of hadronic effects, which arise from non-perturbative QCD dynamics, has received less attention, with recent studies reporting puzzling and contradictory results. In this work, we present a systematic evaluation of the hadronic contributions to the $h \to \gamma \gamma$ decay width using dispersion relations. Our analysis shows that these contributions are exceedingly small, as expected, altering the decay width by about $0.004\%$ under conservative assumptions. Therefore, hadronic effects can be safely neglected even in the context of future high-precision Higgs measurements at current and next-generation colliders. As an aside, we also estimate the possible size of hadronic contributions to Higgs production in gluon-gluon fusion.