Factorization of standard model cross sections at ultrahigh energy

The factorization theorem for organizing multiple electroweak boson emissions at future colliders with energy far above the electroweak scale is formulated. Taking the inclusive muon-pair production in electron-positron collisions as an example, we argue that the summation over isospins is demanded for constructing the universal distributions of leptons and gauge bosons in an electron. These parton distributions are shown to have the same infrared structure in the phases of broken and unbroken electroweak symmetry, an observation consistent with the Goldstone equivalence theorem. The electroweak factorization of processes involving protons is sketched, with an emphasis on the subtlety of the scalar distributions. This formalism, in which electroweak shower effects are handled from the viewpoint of factorization theorem for the first time, is an adequate framework for collider physics at ultra high energy.