Towards muon-electron scattering at NNLO

TL;DR

This paper develops high-precision theoretical predictions for muon-electron scattering at NNLO, crucial for the MUonE experiment's goal to accurately determine the muon anomalous magnetic moment.

Contribution

It provides the first complete formulation and Monte Carlo implementation of NNLO radiative corrections for muon-electron scattering, including electron and muon radiation effects.

Findings

Exact treatment of electron and muon radiation corrections.

Approximation of two-loop diagrams using Yennie-Frautschi-Suura approach.

Preparation of a simulation code for full NNLO corrections.

Abstract

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The theoretical formulation for the fixed-order NNLO photonic radiative corrections is described and the impact of the numerical results obtained with the corresponding Monte Carlo code is discussed for typical event selections of the MUonE experiment. In particular, the gauge-invariant subsets of corrections due to electron radiation as well as to muon radiation are treated exactly. The two-loop contribution due to diagrams where at least two virtual photons connect the electron and muon lines is approximated taking inspiration from the classical Yennie-Frautschi-Suura approach. The calculation and its Monte Carlo implementation pave the way towards the realization of a simulation code incorporating the full set of NNLO corrections matched to multiple photon radiation, that will be ultimately needed for data analysis.