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

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.