Correlation between decay planes in Higgs-boson decays into a W pair (into a Z pair)

For a conventional Higgs boson the decay correlation function for the azimuthal angle between the two W decay planes is F(φ)=1+αcosφ+βcos2φ, where α=(3π/8${)}^2$γ/(1+${\gamma }^2$/2), β=1/41/(1+${\gamma }^2$/2), with γ=(${\mathit{M}}_{\mathit{H}}^2$-2${\mathit{m}}_{\mathit{W}}^2$). While β is negligible, there will be a decay correlation fom α if ${\mathit{M}}_{\mathit{H}}$ is not too large (α≥1/4 if ${\mathit{M}}_{\mathit{H}}$≤400 GeV). By α≠0, the standard ${\mathit{g}}_{\to \mathit{v}}$ coupling is distinguished from the complete decoupling of a Higgs boson from transverse W bosons. For a technipion α=0, but uniquely β=-(1/4. For the Z pair decay mode, α contains an extra factor of 2r/(1+$r^2$) from each Z→f¯f, where r is the ratio of the axial-vector- to the vector-coupling coefficients. This suppresses α since 2r/(1+${\mathit{r}}^2$)≃1/√2¯ for d¯d,≃-1/3 for u¯u, and ≃1/4 for ${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$.