GRACE at ONE-LOOP: Automatic calculation of 1-loop diagrams in the electroweak theory with gauge parameter independence checks

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  • 7 August 2003
Abstract
A general non-linear gauge condition is implemented into GRACE, an automated system for the calculation of physical processes in high-energy physics. These new gauge-fixing conditions are used as a very efficient means to check the results of large scale automated computation in the standard model. We describe in detail the implementation of the general gauge condition and the renormalisation procedure at one-loop in the standard model. Explicit formulae for all two-point functions in a generalised non-linear gauge are given, together with the complete set of counterterms. We also show how infrared divergences are dealt with in the system. A new technique for the reduction of the tensor integrals is described. We give a comprehensive presentation of some systematic test-runs which have been performed at the one-loop level for a wide variety of two-to-two processes to show the validity of the gauge check. These cover fermion-fermion scattering, gauge boson scattering into fermions, gauge bosons and Higgs bosons scattering processes. Comparisons with existing results on some one-loop computations in the standard model show excellent agreement. These include e+ e- --> t \bar t, W^+ W^-, ZH$; \gamma \gamma --> t \bar t, W^+ W^-; e \gamma --> e Z, \nu W$ and W^+ W^- --> W^+ W^-. All these tests confirm the reliability of the system to automatically perform one-loop radiative corrections in the standard model with the added possibility of conducting powerful checks on the result.

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