Testing the Neutrino Content of the Muon at Muon Colliders

Collinear emission of $W$ bosons off a high-energy muon induces a large muon-neutrino component among the Parton Distribution Functions (PDFs) of a muon. In this paper we study the phenomenology related to the $\nu_\mu$ PDF at future high-energy muon colliders. We examine total rates and differential distributions of the $e \bar{\nu}_e$ and $W \gamma$ production processes, which receive a large, and often dominant, contribution from this PDF, allowing for a detailed experimental study. As a demonstration of the impact the $\nu_\mu$ PDF could have for searches of new physics, we study the charged-current pair production of a couple of heavy states, components of a ${\rm SU}(2)_L$ doublet. In both $e\bar{\nu}_e$ production and charged-current pair production of heavy states, we compare results obtained using PDFs with those of a fixed-order simulation.