Automatic calculations in high energy physics and GRACE at one-loop

We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file. the graph generation, the symbolic calculation at an intermediate level of the Dirac and tensor algebra, implementation of the loop integrals, the generation of the matrix elements or helicity amplitudes, methods for the phase space integrations and eventually the event generation. The report focuses on the fully automated systems for the calculation of physical processes based on the experience in developing GRACE-loop which is a general purpose code applicable to one-loop corrections in the Standard Model. As such, a detailed description of the renornialisation procedure in the Standard Model is given emphasizing the central role played by the non-linear gauge fixing conditions for the construction of such automated codes. These new gauge-fixing conditions are used as a very efficient means to check the results of large scale automated computations in the Standard Model. Their need is better appreciated when it comes to devising efficient and powerful algorithms for the reduction of the tensorial structures of the loop integrals and the reduction of the N > 4 point-function to lower rank integrals. A new technique for these reduction algorithms is described. 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. 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 computation in the Standard Model show excellent agreement. These include e(+)e- -> tt. W+W-, ZH; yy -> tt, W+W-; e gamma -> eZ, vW and W+W- -> W+W-. We also briefly recount some recent development concerning the calculation of one-loop corrections to 3 body final states cross sections in e(+)e(-) with the help of an automated system. (c) 2006 Elsevier B.V. All rights reserved.