Muon-electron scattering at NNLO

Abstract

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.

31 pages, 6 figures, 3 tables

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• Bhabha scattering at NNLO with next-to-soft stabilisation
• The Infrared Structure of QCD Amplitudes and $H\to gg$ in FDH and DRED
• Single ${\pi }^0$ production in $\mu e$ scattering at MUonE
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• Singlet and non-singlet three-loop massive form factors

Cited by in corpus (11)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• The LBK theorem to all orders
• Complementarity of $\mu$TRISTAN and Belle II in searches for charged-lepton flavour violation
• Lepton pair production in muon-nucleus scattering
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Multiple soft-photon emission at next-to-leading power to all orders
• Two-loop Vertices with Vacuum Polarization Insertion
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Disperon QED
• Theory for the MUonE experiment