  We discuss general on-shell couplings of a scalar with two Z bosons using an
operator analysis. In addition to the operator originated from the Higgs
mechanism, two dimension-five operators, one CP-even and one CP-odd, are
generated only at the loop-level. Simple formulas are derived for the
differential decay distributions when the Z pair subsequently decay into four
leptons by computing the helicity amplitudes, from which it is shown the CP-odd
operator merely induces a phase shift in the azimuthal angular distribution
between the two decay planes of the Z bosons. We also investigate new physics
scenarios giving rise to loop-induced decays of a scalar into ZZ pair, and
argue that the total decay width of such a scalar would be order-of-magnitude
smaller than that of a Higgs boson, should such decays be observed in the early
running of the LHC. Therefore, the total decay width alone is a strong
indicator of the Higgs nature, or the lack thereof, of a scalar resonance in ZZ
final states. In addition, we study the possibility of using the azimuthal
angular distribution to disentangle effects among all three operators.
