Studies of Cherenkov Photon Production in PbF$_2$ Crystals using Proton Beams at Fermilab
Future lepton colliders such as the FCC-ee, CEPC, ILC, or a muon collider will collect large data samples that allow precision physics studies with unprecedented accuracy, especially when the data is collected by innovative state-of-the-art detectors. An electromagnetic calorimeter based on scintillating crystals, designed to separately record Cherenkov and scintillation light, can achieve precision measurements of electrons and photons without sacrificing jet energy resolution, given adequate light collection efficiency and separation. This paper presents initial measurements from a program aimed at developing such a calorimeter system for future colliders. We focus on using PbF2 crystals to enhance the understanding of Cherenkov light collection, marking the first step in this endeavor.