NLO Electroweak Corrections to Multi-Boson Processes at the Muon Collider

We present first results on NLO electroweak (EW) corrections to multiple massive boson production processes at the proposed muon collider. Inclusive cross sections with $\mathcal{O}(\alpha)$ corrections for processes covering up to four bosons in the final state as well as differential distributions for $HZ$ production are computed for $\sqrt{s}=3$, $10$ and $14$ TeV by using FKS subtraction in the NLO EW automated Monte-Carlo framework WHIZARD+RECOLA. Large logarithmic effects due to collinear ISR and EW virtual correction factors as well as the impacts of an energy cut on hard photons are discussed with an emphasis on the differential distributions for Higgsstrahlung. The tremendous potential of the proposed muon collider for studying physics of the EW sector is underlined by the EW corrections significantly affecting observables for processes at high energies and boson multiplicities. Without precision predictions it is not possible to firmly establish potential signals from New Physics