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We calculate the three loop gauge β-function for an abelian N = 1 supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ β-function, and by generalising this redefinition to the non-abelian case we derive the DRED three loop gauge β-function for the non-abelian case.

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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We calculate the standard model effective potential to two loops using minimal subtraction, and use the result to deduce the two-loop beta-functions for the scalar m 2 and quartic self-interaction.