We study the potential of lepton collisions with about 10\text{ TeV} center of mass energy to probe Electroweak, Higgs and Top short-distance physics at the 100\text{ TeV} scale, pointing out the interplay with the long-distance (100\text{ GeV}) phenomenon of Electroweak radiation. On one hand, we find that sufficiently accurate theoretical predictions require the resummed inclusion of radiation effects, which we perform at the double logarithmic order. On the other hand, we notice that short-distance physics does influence the emission of Electroweak radiation. Therefore the investigation of the radiation pattern can enhance the sensitivity to new short-distance physical laws. We illustrate these aspects by studying Effective Field Theory contact interactions in di-fermion and di-boson production, and comparing cross-section measurements that require or that exclude the emission of massive Electroweak bosons. The combination of the two types of measurements is found to enhance the sensitivity to the new interactions. Based on these results, we perform sensitivity projections to Higgs and Top Compositeness and to minimal Z' new physics scenarios at future muon colliders.
