  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.
