Leptonic contributions to muon-electron scattering at NNLO

Confirmation of the long-standing muon g-2 discrepancy requires both experimental and theoretical progress. On the theory side, the hadronic corrections are under close scrutiny, as they induce the leading uncertainty of the Standard Model prediction. In this context, the MUonE experiment has been proposed at CERN to provide a new direct determination of the leading hadronic contribution to the muon g-2, measuring the differential cross section of muon-electron scattering. As the shape of this differential cross section must be measured with a systematic uncertainty of 10 ppm or better, an analogous precision is required in its theoretical prediction. In this thesis we calculated the leptonic QED corrections to muon-electron scattering at next-to-next-to-leading order (NNLO). They arise from two-loop diagrams with leptonic vacuum polarization insertions in the photon propagator. Non-factorizable two-loop diagrams were computed using the dispersive approach. These results will play a crucial role in the analysis of MUonE's data.