Precise Predictions for $\mu^{\pm}e^-\rightarrow\mu^{\pm}e^-$ at the MUonE Experiment

TL;DR

This paper provides highly precise theoretical predictions for muon-electron scattering at the MUonE experiment, incorporating advanced resummation techniques and higher-order corrections to improve measurement accuracy.

Contribution

It introduces an all-order resummation of soft and collinear logarithms matched with next-to-leading and next-to-next-to-leading order corrections for the first time.

Findings

Resummation significantly impacts the predicted scattering cross-section.

Matching reduces theoretical uncertainties.

Predictions enhance the MUonE experiment's potential for precise hadronic contribution measurements.

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 $\mu^{\pm}e^-\rightarrow\mu^{\pm}e^-$, 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.