High energy leptonic collisions and electroweak parton distribution functions

In high-energy leptonic collisions well above the electroweak scale, the collinear splitting mechanism of the electroweak gauge bosons becomes the dominant phenomena via the initial state radiation and the final state showering. We point out that at future high-energy lepton colliders, such as a multi-TeV muon collider, the electroweak parton distribution functions (EW PDFs) should be adopted as the proper description for partonic collisions of the initial states. The leptons and electroweak gauge bosons are the EW partons, that evolve according to the unbroken Standard Model (SM) gauge group and that effectively resum potentially large collinear logarithms. We present a formalism for the EW PDFs at the leading-log (LL) accuracy. We calculate semi-inclusive cross sections for some important SM processes at a future multi-TeV muon collider. We conclude that it is appropriate to adopt the EW PDF formalism for future high-energy lepton colliders.