Abstract
The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The theoretical formulation for the fixed-order NNLO photonic radiative corrections is described and the impact of the numerical results obtained with the corresponding Monte Carlo code is discussed for typical event selections of the MUonE experiment. In particular, the gauge-invariant subsets of corrections due to electron radiation as well as to muon radiation are treated exactly. The two-loop contribution due to diagrams where at least two virtual photons connect the electron and muon lines is approximated taking inspiration from the classical Yennie-Frautschi-Suura approach. The calculation and its Monte Carlo implementation pave the way towards the realization of a simulation code incorporating the full set of NNLO corrections matched to multiple photon radiation, that will be ultimately needed for data analysis.
Highlights
Following ideas first put forward in Refs. [21, 22] for the evaluation of aμ as an integral over the photon vacuum-polarization function at negative q2, a novel approach has been recently proposed to derive aHμ LO from a measurement of the effective electromagnetic coupling constant in the space-like region via scattering data [23]
The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer
The calculation and its Monte Carlo implementation pave the way towards the realization of a simulation code incorporating the full set of NNLO corrections matched to multiple photon radiation, that will be needed for data analysis
Summary
We discuss how the full two-loop virtual QED corrections can be approximated to catch its complete IR structure. We are approximating only the diagrams obtained by inserting a virtual photon into a QED one-loop box diagram, all the rest of the corrections being exact. We stress that Ya with a = e, μ, eμ are the factors which factorize the IR divergence of the diagrams obtained by dressing the underlying amplitude with an extra virtual photon attached to the electron (a = e) or muon (a = μ) line or connecting them (a = eμ). Muon lines, which are not known yet for the process under consideration This is made possibly more explicit in the equivalent form of Eq (3.6), where each term in the second row, approximately accounting for the missing contributions, has a factor with an “eμ”.
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