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In many extensions of the standard model, there exist a few extra Higgsbosons. Suppose a heavy neutral Higgs boson H is discovered at the LHC, onecould then investigate CP and CPT~ properties of its couplings to a pair of $Z$bosons through $H \to ZZ \to 4\ell$. We use the helicity-amplitude method towrite down the most general form for the angular distributions of the fourfinal-state leptons, which can cover the case of CP-even, -odd, and -mixedstate for the Higgs boson. We figure out there are 9 types of angularobservables and all the $H$ couplings to $Z$ bosons can be fully determined byexploiting them. A Higgs-boson mass of 260 GeV below the $t\bar t$ threshold isillustrated with full details. With a total of $10^3$ events of $H \to ZZ \to4\ell$, one can determine the couplings up to 12-20\% uncertainties.

Measuring properties of a Heavy Higgs boson in the $H\to ZZ \to 4\ell$ decay