Probing CP in the Higgs Sector

We discuss how one may determine whether some Higgs particle is an eigenstate of $CP$ or not, and if so, how we may probe whether it is $CP$-odd or $CP$-even. The idea is applied to Higgs decay where correlations among momenta of the decay products may yield the desired information. These are correlations of decay planes defined by the momenta of pairs of particles as well as correlations between energy differences. In the case that the Higgs particle is an eigenstate of $CP$, our study includes finite-width effects. The correlations between energy differences turn out to be a much better probe for investigating $CP$ properties than the previously suggested angular correlations, especially for massive Higgs bosons.