Semi-analytical evaluation of electroweak two-loop Feynman diagrams based on the Bernstein-Tkachov technique

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The impressive precision reached by experiments at LEP, SLAC and FNAL, as well as the even greater accuracy to be attained in the next generation of colliders (such as LHC at CERN and possibly TESLA at DESY), demand very precise theoretical predictions of the electroweak observables, based on the study of quantum corrections in the Standard Model. This need is particularly acute, since the detection of deviations from the predictions of the current theoretical paradigm may well constitute an experimental proof of the existence of new physics beyond the Standard Model. In this framework, two different aspects assume a special relevance: 1) the precise determination of the input parameters for the calculation of the electroweak observables; 2) the control over the theoretical errors of the electroweak radiative corrections. Both of the above-mentioned goals require the evaluation of multi-loop and multi-leg Feynman diagrams; from the technical point of view, such calculations are particularly complex because of the presence of a large number of different mass scales that are involved in each diagram. Recently, a new semi-numerical technique, based on the Bernstein-Tkachov theorem, has been proposed and applied to specific sets of Feynman graphs. The purpose of the present research project is to further investigate and extend the applications of this technique to new classes of diagrams. The final goal is to calculate the relevant electroweak observables, such as the pole masses of the gauge bosons and the weak effective mixing angle, taking into account the full set of two-loop electroweak corrections. This kind of accuracy is required by the experimental precision that will be reached by the next generation of colliders.