Measuring the relative CP-even and CP-odd Yukawa couplings of a Higgs boson at a muon-collider Higgs factory

We study a possibility of a measurement of muon Yukawa couplings in s-channel Higgs boson production at a muon collider with transversely polarized beams. We investigate sensitivity to the relative size of the CP-odd and CP-even muon Yukawa couplings. Provided the event rate observed justify the operation of the $\mu^+\mu^-$ Higgs boson factory, we have found that polarization degree 40% is sufficient to resolve the CP nature of a single resonance as well as disentangle it from two overlapping CP conserving resonances