Decays of a neutral particle with zero spin and arbitrary CP parity into two off-mass-shell Z bosons

Effects are investigated of CP symmetry violation in the decay of a scalar particle X (the Higgs boson) into two off-mass-shell Z bosons both decaying into a fermion-antifermion pair, $X \to Z_1^* \, Z_2^* \to f_1 \bar{f_1} \, f_2 \bar{f_2}$. The most general form of the amplitude of the transition $X \to Z_1^* Z_2^*$, wherein the boson X may not have definite CP parity, is considered. Limits of applicability of the narrow-Z-width approximation used when obtaining differential widths of the decay under consideration are determined. Various observables connected with the structure of the amplitude of the decay $X \to Z_1^* Z_2^*$ are studied. These observables are analyzed in the Standard Model, as well as in models conceding indefinite CP parity of the Higgs boson. An experimental measurement at the LHC of angular and invariant mass distributions of the decay $X \to Z_1^* Z_2^* \to f_1 \bar{f_1} f_2 \bar{f_2}$ can give information about the CP properties of the Higgs boson and its interaction with the Z boson.