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          Institute: MPI für Physik     Collection: MPI für Physik     Display Documents



ID: 544260.0, MPI für Physik / MPI für Physik
Reduction schemes for one-loop tensor integrals
Authors:Denner, A.; Dittmaier, S.
Date of Publication (YYYY-MM-DD):2006
Title of Journal:Nuclear Physics B
Journal Abbrev.:Nucl.Phys.B
Issue / Number:734
Start Page:62
End Page:115
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e+ e- -> 4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex.
Classification / Thesaurus:Phenomenology of High Energy Physics
Comment of the Author/Creator:55 pages, latex, some references updated and few comments added, version to appear in Nucl. Phys. B
External Publication Status:published
Document Type:Article
Communicated by:N.N.
Affiliations:MPI für Physik
Identifiers:LOCALID:MPP-2005-84
URL:http://www.slac.stanford.edu/spires/find/hep/www?r...
URL:http://arXiv.org/abs/hep-ph/0509141
URL:http://publications.mppmu.mpg.de/?action=search&mp...
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