# Muon-electron scattering at NNLO: the hadronic corrections

## TL;DR

This paper evaluates hadronic QCD corrections to muon-electron scattering at NNLO using dispersive methods, highlighting their importance for precise future experiments like MUonE.

## Contribution

It provides the first detailed calculation of hadronic corrections at NNLO for muon-electron scattering using dispersive techniques with experimental data.

## Key findings

- Hadronic corrections are significant at NNLO for muon-electron scattering.
- Uncertainty estimates for the hadronic contributions are provided.
- Results are essential for high-precision measurements in upcoming experiments.

## Abstract

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.