Single Charged Higgs production as a probe of CP violation at a Muon Collider

We consider single charged Higgs ($H^{\pm}$) production in association with a $W^{\pm}$ boson at $\mu^+\mu^-$ colliders, in the context of the general CP violating Two Higgs Doublet Model (2HDM). We find that large cross-sections for the processes $\mu^+\mu^-\to H^+W^-,H^-W^+$ are possible, and offer an attractive way of producing $H^{\pm}$ at $\mu^+\mu^-$ colliders. The difference in the cross-sections for $H^+W^-$ and $H^-W^+$ may exceed 1000 fb, and this represents a novel way of probing CP violation in the Higgs sector.