  If the Standard Model (SM) Higgs particle is sufficiently heavy, then its
contribution to gamma gamma to Z Z should be largely imaginary, interfering
with 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, this
interference is found to be constructive and increasing the Higgs signal. In
the minimal SUSY case an interference effect should also appear for the
contribution of the heavier CP-even neutral Higgs boson H^0, provided it is
sufficiently heavy. The effect is somewhat reduced though, by the smallness of
the H^0 width and the gamma gamma and ZZ branching ratios. The interference is
again found to be constructive for part of the parameter space corresponding to
sfermion masses at the TeV scale and maximal stop mixing. For both the SM and
SUSY cases, regions of the parameter space exist though, where the interference
may be destructive. It is therefore essential to take these effects into
account when searching for possible scalar Higgs-like candidates. To this aim,
we present the complete analytic expressions for both resonance and background
amplitudes.
