Muon-electron scattering at NNLO

We present the first calculation of the complete set of NNLO QED corrections for muon-electron scattering. This includes leptonic, non-perturbative hadronic, and photonic contributions. All fermionic corrections as well as the photonic subset that only corrects the electron or the muon line are included with full mass dependence. The genuine four-point two-loop topologies are computed as an expansion in the small electron mass, taking into account both, logarithmically enhanced as well as constant mass effects using massification. A fast and stable implementation of the numerically delicate real-virtual contribution is achieved by combining OpenLoops with next-to-soft stabilisation. All matrix elements are implemented in the McMule framework, which allows for the fully-differential calculation of any infrared-safe observable. This calculation is to be viewed in the context of the MUonE experiment requiring a background prediction at the level of 10 ppm. Our results thus represent a major milestone towards this ambitious precision goal.

Automated summary

We have calculated the complete set of NNLO QED corrections for muon-electron scattering, including leptonic, non-perturbative hadronic, and photonic contributions. Our calculation takes into account all fermionic corrections as well as the photonic subset that only corrects the electron or the muon line with full mass dependence. By expanding the genuine four-point two-loop topologies in the small electron mass, considering logarithmically enhanced as well as constant mass effects using massification, we were able to achieve a fast and stable implementation of the real-virtual contribution. All matrix elements are implemented in the McMule framework, allowing for the fully-differential calculation of any infrared-safe observable. Our results are a significant milestone towards the ambitious precision goal required by the MUonE experiment, which demands a background prediction at the level of 10 ppm.