CPviolation, Higgs couplings, and supersymmetry

Supersymmetric extensions of the standard model generically contain additional sources of $\mathrm{CP}$ violation. We discuss how at one loop a potentially large $\mathrm{CP}$ violating coupling of the lightest Higgs boson $h^0$ to leptons is induced in the minimal supersymmetric standard model (MSSM). The $\mathrm{CP}$ violating couplings of $h^0$ in extensions of the MSSM, such as the next-to-minimal supersymmetric standard model (NMSSM) are also considered. We indicate how this $\mathrm{CP}$ violation might be observed; in particular a polarization-dependent production asymmetry, in the context of a muon collider, provides a means to access this coupling cleanly. In the MSSM, existing limits on the electric dipole moment of the electron, coupled with standard universality assumptions, severely constrains any such signal. Nevertheless, extensions of the MSSM, such as the NMSSM, allow $\mathrm{CP}$-violating signals as large as 100%.