Higgs Production and $H^0\to c\bar{c}$ at a Future Muon-Ion Collider

We investigate the production of Higgs bosons in neutral- and charged-current interactions at a future Muon-Ion Collider (MuIC) with emphasis on $H^0\to c\bar{c}$ decay. In particular, we focus on the leading production mechanisms and explore the impact of a range of Parton Distribution Function (PDF) scenarios, with emphasis on the role of heavy intrinsic quark flavor. We emphasize estimates of non-resonant di-charm background production and explore the impact of this background on a possible future measurement of $H^0\to c\bar{c}$ at a future Muon-Ion Collider facility.