The reconstruction of the Higgs potential in the Standard Model or supersymmetric theories demands the measurement of the trilinear Higgs couplings. These couplings affect the multiple production of Higgs bosons at high energy colliders. We present a systematic overview of the cross sections for the production of pairs of (light) neutral Higgs bosons at the LHC. The analysis is carried out for the Standard Model and its minimal supersymmetric extension.

Higgs decays to Z boson pairs may be exploited to determine spin and parity of the Higgs boson, a method complementary to spin-parity measurements in Higgsstrahlung. For a Higgs mass above the on-shell ZZ decay threshold, a modelindependent analysis can be performed, but only by making use of additional angular correlation effects in gluon-gluon fusion at the LHC and γγ fusion at linear colliders. In the intermediate mass range, in which the Higgs boson decays into pairs of real and virtual Z bosons, threshold effects and angular correlations, parallel to Higgs-strahlung, may be adopted to determine spin and parity, though high event rates will be required for the analysis in practice.

High-precision analyses of supersymmetry parameters aim at reconstructing the fundamental supersymmetric theory and its breaking mechanism. A well defined theoretical framework is needed when higher-order corrections are included. We propose such a scheme, Supersymmetry Parameter Analysis SPA, based on a consistent set of conventions and input parameters. A repository for computer programs is provided which connect parameters in different schemes and relate the Lagrangian parameters to physical observables at LHC and high energy e + e − linear collider experiments, i.e., masses, mixings, decay widths and production cross sections for supersymmetric particles. In addition, programs for calculating high-precision low energy observables, the density of cold dark matter (CDM) in the universe as well as the cross sections for CDM search experiments are included. The SPA scheme still requires extended efforts on both the theoretical and experimental side before data can be evaluated in the future at the level of the desired precision. We take here an initial step of testing the SPA scheme by applying the techniques involved to a specific supersymmetry reference point.

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