Abstract:Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to regularization by dimensional reduction.

This paper describes the Mathematica package FeynArts used for the generation and visualization of Feynman diagrams and amplitudes. The main features of version 3 are: generation of diagrams in three levels, user-definable model files, support for supersymmetric models, and publication-quality Feynman diagrams in PostScript or L A T E X.

New results for the complete one-loop contributions to the masses and mixing effects in the Higgs sector are obtained for the MSSM with complex parameters using the Feynman-diagrammatic approach. The full dependence on all relevant complex phases is taken into account, and all the imaginary parts appearing in the calculation are treated in a consistent way. The renormalization is discussed in detail, and a hybrid on-shell/DR scheme is adopted. We also derive the wave function normalization factors needed in processes with external Higgs bosons and discuss effective couplings incorporating leading higher-order effects. The complete one-loop corrections, supplemented by the available two-loop corrections in the Feynman-diagrammatic approach for the MSSM with real parameters and a resummation of the leading (s)bottom corrections for complex parameters, are implemented into the public Fortran code FeynHiggs 2.5. In our numerical analysis the full results for the Higgs-boson masses and couplings are compared with various approximations, and CP-violating effects in the mixing of the heavy Higgs bosons are analyzed in detail. We find sizable deviations in comparison with the approximations often made in the literature. *

The Cuba library provides new implementations of four general-purpose multidimensional integration algorithms: Vegas, Suave, Divonne, and Cuhre. Suave is a new algorithm, Divonne is a known algorithm to which important details have been added, and Vegas and Cuhre are new implementations of existing algorithms with only few improvements over the original versions. All four algorithms can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces.

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