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Electroweak fragmentation at high energies: A Snowmass White Paper

In particle collisions at energies higher than the mass scale involved, the collinear splitting becomes the dominant phenomena. Suitable descriptions of the physics in this regime include the parton distribution functions, the initial state radiations, the final state radiations and the fragmentation functions. It is of fundamental importance to formulate those functions with consistent theoretical treatments, and to provide the adequate formalism for applications, as motivated by the recent discussions of partonic scatterings at the multi-TeV energy regime. In this report, we briefly present the resummation of the final-state logarithms as fragmentation functions for the electroweak processes. As an explicit example, we study an electroweak gauge boson splitting in the process $pp\to WZj$ and demonstrate the important effects from the fragmentation.