Impact of NNLO QED corrections on lepton-proton scattering at MUSE

TL;DR

This paper calculates the complete NNLO QED corrections to lepton-proton scattering, including three-photon exchange, and assesses their significance for the MUSE experiment's low-momentum-transfer measurements.

Contribution

It provides the first full NNLO QED correction calculation for lepton-proton scattering, including three-photon exchange and lepton-mass effects, with no photon energy approximation.

Findings

NNLO QED corrections are comparable to or smaller than TPE corrections in the MUSE kinematic range.

Including NNLO corrections is essential for precise proton structure extraction from scattering data.

NNLO corrections are smaller for muon-proton scattering than for electron-proton scattering.

Abstract

We present the complete next-to-next-to-leading order (NNLO) pure pointlike QED corrections to lepton-proton scattering, including three-photon-exchange contributions, and investigate their impact in the case of the MUSE experiment. These corrections are computed with no approximation regarding the energy of the emitted photons and taking into account lepton-mass effects. We contrast the NNLO QED corrections to known next-to-leading order corrections, where we include the elastic two-photon exchange (TPE) through a simple hadronic model calculation with a dipole ansatz for the proton electromagnetic form factors. We show that, in the low-momentum-transfer region accessed by the MUSE experiment, the improvement due to more sophisticated treatments of the TPE, including inelastic TPE, is of similar if not smaller size than some of the NNLO QED corrections. Hence, the latter have to be included in a precision determination of the low-energy proton structure from scattering data, in particular for electron-proton scattering. For muon-proton scattering, the NNLO QED corrections are considerably smaller.