Polarization effects in the Higgs boson decay to γZ and test of CP and CPT symmetries

Polarization characteristics of gamma gamma and gamma Z states in the Higgs boson decays h h -> gamma gamma and h -> gamma Z are discussed. Based on effective Lagrangian, describing h gamma gamma and h gamma Z interactions with CP-even and CP-odd parts, we calculate polarization parameters xi(1), xi(2), xi(3). A nonzero value of the photon circular polarization, defined by parameter xi(2), arises due to presence of both parts in effective Lagrangian and its non-Hermiticity. The circular polarization is proportional to the forward-backward asymmetry of fermions in the decay h -> gamma Z -> gamma f (f) over bar. Measurement of this observable would allow one to search for deviation from the standard model and possible violation of CPT symmetry. We discuss also a possibility to measure parameters xi(1), xi(3), describing correlation of linear polarizations of photon and Z boson, in the decay h -> gamma*Z -> l(+)l(-)Z via distribution over the azimuthal angle between the decay planes of gamma* -> l(+)l(-) and Z -> (f) over barf. Deviation of the measured value of xi(1) from zero will indicate CP violation in the Higgs sector.