Muon-electron scattering at NNLO with McMule

TL;DR

This paper discusses the implementation of a Monte Carlo integrator for muon-electron scattering at NNLO in QED within the McMule framework, crucial for the MUonE experiment's goal to measure the muon g-2 contribution with high precision.

Contribution

It introduces a Monte Carlo integrator for NNLO QED corrections to muon-electron scattering, enabling precise theoretical predictions for the MUonE experiment.

Findings

Infrared-safe differential results at NNLO in QED

Phenomenological insights into MUonE setup

Identification of the need for beyond-NNLO corrections

Abstract

A recently proposed experiment, MUonE, aims to extract the hadronic vacuum polarisation contribution to the muon g-2 from muon-electron scattering at low energy. The extrapolation requires that both experimental and theoretical uncertainties do not exceed 10 ppm. This corresponds, at least, to next-to-next-to-leading-order (NNLO) QED corrections to $e \mu \to e \mu$. I will discuss the implementation of a Monte Carlo integrator for this process in the McMule framework arXiv:2212.06481, which provides infrared-safe differential results at said order in QED. An approximation of the MUonE setup provides some phenomenological results and sheds light on the need for beyond-NNLO corrections, which are currently under study within McMule.