How Valuable is Polarization at a Muon Collider? A Test Case: Determining the CP Nature of a Higgs Boson

We study the use of polarization asymmetries at a muon collider to determine the CP-even and CP-odd couplings of a Higgs boson to $\mu^+mu^-$. We determine achievable accuracy as a function of beam polarization and luminosity. The appropriate techniques for dealing with the polarization precession are outlined. Strategies especially appropriate for a two-Higgs-doublet model (including the MSSM) are given. Our general conclusion is that polarization will be very useful, especially if the proton source is such that full luminosity in the storage ring can be retained even after imposing cuts on the originally accepted muons necessary for $P\gsim 0.4$ for each beam.