ResonantCP−ViolatingScalar-Pseudoscalar Transitions atμ+μ−Colliders

A ${\mu }^{+}{\mu }^{-}$ collider is an appealing machine to probe resonant $\mathrm{CP}-\mathrm{v}\mathrm{i}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}$ transitions of a $\mathrm{CP}-\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}$ Higgs particle into the $Z$ boson or into another $\mathrm{CP}-\mathrm{o}\mathrm{d}\mathrm{d}$ Higgs scalar. These phenomena are studied within a manifestly gauge-invariant approach implemented by the pinch technique. The $\mathrm{CP}$ invariance of an extended Higgs sector motivated by supersymmetric ${\mathrm{E}}_6$ models is assumed to be broken radiatively by the presence of heavy Majorana fermions. $\mathrm{CP}$ violation originating from Higgs- $Z$ mixing is found to be very modest, whereas $\mathrm{CP}$-number-violating transitions involving Higgs scalars only can be resonantly enhanced up to order of unity.