Testing $CP$ in the Bjorken process

In a more general electroweak theory, there could be Higgs particles that are odd under $CP$, and also Higgs-like particles which are not eigenstates of $CP$. We discuss distributions which for the Bjorken process are sensitive to the $CP$ parity. Correlations among momenta of the initial electron and final-state fermions yield this kind of information. We discuss also observables which may demonstrate presence of $CP$ violation and identify a phase shift $\delta$ which is a measure of the strength of $CP$ violation in the Higgs-vector-vector coupling, and which can be measured directly in the decay distribution. We present Monte Carlo data on the expected efficiency, and conclude that it is relatively easy to determine whether the produced particle is even or odd under $CP$. However, observation of any $CP$ violation would require a very large amount of data.