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If the Standard Model (SM) Higgs particle is sufficiently heavy, then itscontribution to gamma gamma to Z Z should be largely imaginary, interferingwith the also predominantly imaginary SM "background" generated by the W-loop.For standard model Higgs masses in the region 200 \lsim m_H \lsim 500 GeV, thisinterference is found to be constructive and increasing the Higgs signal. Inthe minimal SUSY case an interference effect should also appear for thecontribution of the heavier CP-even neutral Higgs boson H^0, provided it issufficiently heavy. The effect is somewhat reduced though, by the smallness ofthe H^0 width and the gamma gamma and ZZ branching ratios. The interference isagain found to be constructive for part of the parameter space corresponding tosfermion masses at the TeV scale and maximal stop mixing. For both the SM andSUSY cases, regions of the parameter space exist though, where the interferencemay be destructive. It is therefore essential to take these effects intoaccount when searching for possible scalar Higgs-like candidates. To this aim,we present the complete analytic expressions for both resonance and backgroundamplitudes.Comment: version submitted to EPJC; 34 pages and 6 figures. e-mail:  renard@lpm.univ-montp2.f

The heavy neutral Higgs signature in the $\gamma \gamma \to Z Z $ process