Reduction of general two-loop self-energies to standard scalar integrals

Abstract

We present a method for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model. It includes the tensor integral reduction for all two-loop integrals appearing in self-energy calculations. The results are valid for arbitrary values of the invariant momentum $p^2$, all particle masses, the space-time dimension $D$ and the gauge parameters ${\xi }_i(i=\gamma ,Z,W)$. The algebraic structure of the results clearly displays the gauge dependence of the considered quantities and allows to perform very stringent checks. We explicitly verify Slavnov-Taylor identities by calculating several thousand Feynman-diagrams and adding them up algebraically. As an application we calculate the light fermion contributions to the two-loop gauge boson self-energies of the electroweak SM. We study their gauge dependence and discuss the occurring standard integrals.

arXiv commentLaTex, 32 pages, (+ 7 figures available from the authors as ps-files), to appear in Nuclear Physics B

References in corpus (2)

• Radiative Correction Effects of a Very Heavy Top
• Large momentum expansion of two-loop self-energy diagrams with arbitrary masses

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