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CP mixed property of the Higgs-like particle in the decay channel $h\to Z Z^*\to 4l$

Current experiments do not support, as ATLAS and CMS collaborations at the Large Hadron Collider reported, that the Higgs-like resonance discovered in July 2012 is a pure CP-odd state. We examine a general $hZZ$ vertex which contains CP-even and CP-odd couplings, by studying the process $h\to ZZ^*\to l_1^+l_1^-l_2^+l_2^-$ with $l_1,\, l_2= e$ or $μ$, to explore the CP mixed property of the Higgs-like particle. One momentum asymmetry and two angular asymmetries have been analyzed in order to reveal the difference from different CP-couplings. Our study shows that these asymmetries could be interesting observables in the future precise experiments.