Signals of $CP$ violation in Higgs decay

We consider an extension of the Standard Model where some Higgs particle is not an eigenstate of $CP$, and discuss the possibility of extracting signals of the resulting $CP$ violation. In the case of Higgs decay to four fermions we study correlations among momenta of the final-state fermions. We discuss 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. In addition to these angular correlations, we consider correlations between energy differences. The former correlations include some recently reported results, whereas the latter ones appear to provide a much better probe for revealing $CP$ violation.