Muon-electron scattering at NLO

Abstract

We consider the process of muon-electron elastic scattering, which has been proposed as an ideal framework to measure the running of the electromagnetic coupling constant at space-like momenta and determine the leading-order hadronic contribution to the muon g−2 (MUonE experiment). We compute the next-to-leading (NLO) contributions due to QED and purely weak corrections and implement them into a fully differential Monte Carlo event generator, which is available for first experimental studies. We show representative phenomenological results of interest for the MUonE experiment and examine in detail the impact of the various sources of radiative corrections under different selection criteria, in order to study the dependence of the NLO contributions on the applied cuts. The study represents the first step towards the realisation of a high-precision Monte Carlo code necessary for data analysis.

Muon-Electron Scattering at Next-To-Next-To-Leading Order: The Hadronic Corrections

“…These contributions to the cross section are equal in size but with opposite sign for µ + and µ − . The same pattern is observed at NLO [17]. Figure 2 shows that, when the muon/antimuon beam has an energy of 150 GeV, for most of the kinematic re- gion scanned by the squared momentum transfer t e the factor K NNLO h (t e ) is of order 10 −4 -10 −5 .…”

“…As a first check, we recalculated these corrections and found agreement with [14] (see also [15,16]). An important step forward was taken very recently by the authors of [17], who calculated the full set of NLO QED corrections without any approximation and developed a fully differential Monte Carlo code. They also computed the full set of NLO electroweak corrections.…”

Hadronic corrections to μ-e scattering at NNLO with space-like data

“…It must contain QED and QCD radiative corrections up to Next-to-Next-to-Leading-Order (NNLO) in α matched to leadinglogarithmic corrections resummed to all orders. A Next-to-Leading-Order (NLO) Monte Carlo generator based on the existing BabaYaga [25][26][27][28][29] framework is currently under development [30]. A first step towards the evaluation of NNLO corrections was presented in [31,32] where the QED two-loop master integrals were calculated for finite muon mass and vanishing electron mass.…”

Muon-electron scattering at next-to-leading order accuracy

“…In turn this requires the inclusion of radiative corrections (RCs), in particular QED RCs, at the highest level of precision. In the last few years a constant effort has been employed for the calculation of RCs at NLO [11] and important progresses have been made towards the calculations of QED RCs at NNLO [12][13][14][15]. In the near future, the ultimate Monte Carlo (MC) tool for data analysis must include all these ingredients together with resummation of higher-order QED corrections and its development is under consideration.…”

“…In the following, largely based on the results of Ref. [11], we sketch an overview of the NLO calculation, which is now implemented into a Monte Carlo event generator (EG) used by the MUonE collaboration, and we show some phenomenological results.…”