Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement

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The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories, in particular. We give an explicit construction reducing integrals with massless propagators to a finite basis for planar integrals at two loops, both to all orders in the dimensional regulator , and also when all integrals are truncated to OðÞ. We show how to reorganize integration-by-parts equations to obtain elements of the first basis efficiently, and how to use Gram determinants to obtain additional linear relations reducing this all-orders basis to the second one. The techniques we present should apply to nonplanar integrals, to integrals with massive propagators, and beyond two loops as well.

Quantization and renormalization of the left right symmetric model is the main purpose of the paper. First the model at tree level with a Higgs sector containing one bidoublet and two triplets is precisely discussed. Then the canonical quantization and Faddeev Popov Lagrangian are carried out ('t Hooft gauge). The BRST symmetry is discussed. Subsequently the on-mass-shell renormalization is performed and, as a test of consistency, the renormalization of the ZN i N j vertex is analyzed.