The Higgs Mechanism and Loop-induced Decays of a Scalar into Two Z Bosons

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.