Abstract
We present a calculation of the full set of next-to-next-to-leading-order QED corrections to unpolarised M{\o}ller scattering. This encompasses photonic, leptonic, and non-perturbative hadronic corrections and includes electron mass effects as well as hard photon radiation. The corresponding matrix elements are implemented in the Monte Carlo framework McMule allowing for the computation of fully-differential observables. As a first application we show results tailored to the kinematics and detector design of the PRad II experiment where a high-precision theory prediction for M{\o}ller scattering is required to achieve the targeted precision. We observe that the corrections become essential to reliably calculate the corresponding differential distributions especially in regions where the leading-order contribution is absent.
Highlights
Recent developments at the low-energy precision frontier have renewed interest in high-precision calculations in QED
With the contributions discussed in the previous section implemented in MCMULE we can compute any infrared safe observable of Møller scattering at NNLO in QED
We have calculated the full set of NNLO QED corrections to Møller scattering including photonic, leptonic, and nonperturbative hadronic corrections
Summary
Recent developments at the low-energy precision frontier have renewed interest in high-precision calculations in QED. Electron-electron or Møller scattering is a prime example where a high-precision theory prediction has become important As it is a ubiquitous process at electron beam lines, it has been investigated in connection with luminosity measurements [1,2] and background studies [3], including a recent dedicated measurement at very low energies to study electron mass effects [4]. The main motivation, is given by PRad [6,7] to which we turn below All of these experiments rely on Standard Model theory predictions for Møller scattering. While for most experiments this level of precision is sufficient, the situation is different for the planned PRad II experiment [7], the upgraded version of its predecessor PRad [6] Both experiments measure the elastic scattering of electrons and protons to extract the proton charge radius.
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