Precise Predictions for $μ^{\pm}e^-\rightarrowμ^{\pm}e^-$ at the MUonE Experiment

TL;DR

This work delivers precise predictions for $μ^{\pm}e^- \rightarrow μ^{\pm}e^-$ at MUonE by applying all-order soft and soft-collinear resummation via the YFS formalism implemented in SHERPA, and by matching to complete NLO EW corrections and dominant NNLO contributions. The approach resolves infrared instabilities in the signal region (notably at small electron scattering angles) and demonstrates that resummation significantly alters predictions where soft photons dominate, while fixed-order matching reduces perturbative uncertainties. The study introduces three YFS levels—$\mathrm{YFS}_{\mathbf{LO}}$, $\mathrm{YFS}_{\mathbf{NLO}}$, and $\mathrm{YFS}_{\mathbf{nNLO}}$—and shows that, especially with an acoplanarity cut, uncertainties can be driven down to the per‑mille level, approaching the 10 ppm precision target for MUonE. The results underscore the necessity of resummation for high‑precision extraction of $Δα_{\text{Had}}$ and discuss future directions, including partial $N^3LO$ corrections and potential hybrids with collinear approaches or parton showers.

Abstract

The proposed fixed-target experiment, MUonE, at CERN will aim to measure the hadronic contribution to the running of the QED coupling by analysing the scattering of muons on electrons. Here we present state-of-the-art predictions for the process $μ^{\pm}e^-\rightarrowμ^{\pm}e^-$, where for the first time an all-order resummation of soft and soft-collinear logarithms has been performed. Further, we match this resummation with the complete next-to-leading and the dominant next-to-next-to-leading higher-order corrections. We find that the resummation has a dominant effect in the signal region, while the systematic matching significantly reduces the perturbative uncertainty.

Figures (6)

• Figure 1: The impact of ${\Delta \alpha_{\text{had}}}(t)$ on electron observables at the MUonE experiment.
• Figure 2: Top: The number of digits the pole cancellations are achieved to for both the virtual (left) and real-virtual (right) corrections in dimensional regularization. Bottom: The behaviour of the real (left) and double-real (right) corrections in the limit where photon momentum becomes ultra-soft.
• Figure 3: Leading-order, resummed, and truncated predictions for the electron's scattering angle. The truncated expansion includes only the $\mathrm{NLO}$ fixed-order corrections.
• Figure 4: Electron polar angle distribution for different sign scenario for $\mathrm{YFS}_{\mathbf{LO}}$(red), $\mathrm{YFS}_{\mathbf{NLO}}$(blue), and $\mathrm{YFS}_{\mathbf{nNLO}}$(green).
• Figure 5: Electron polar angle distribution for same sign scenario for $\mathrm{YFS}_{\mathbf{LO}}$(red), $\mathrm{YFS}_{\mathbf{NLO}}$(blue), and $\mathrm{YFS}_{\mathbf{nNLO}}$(green).