Muon-Electron Scattering at Next-To-Next-To-Leading Order: The Hadronic Corrections.

The standard model prediction for muon-electron scattering beyond leading order requires the inclusion of QCD contributions which cannot be computed perturbatively. At next-to- and next-to-next-to-leading order, they arise from one- and two-loop diagrams with hadronic vacuum polarization insertions in the photon propagator. We present their evaluation using the dispersive approach with hadronic e^{+}e^{-} annihilation data and estimate their uncertainty. We find that these corrections are crucial for the analysis of future high-precision muon-electron scattering data, like those of the recently proposed MUonE experiment at CERN.