Reduction schemes for oneloop tensor integrals
Abstract
We present new methods for the evaluation of oneloop tensor integrals which have been used in the calculation of the complete electroweak oneloop corrections to e^{+}e^{} → 4 fermions. The described methods for 3point and 4point integrals are, in particular, applicable in the case where the conventional PassarinoVeltman 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 5point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4point integrals with tensor rank reduced by one. Similar formulas are provided for 6point 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.
 Publication:

Nuclear Physics B
 Pub Date:
 January 2006
 DOI:
 10.1016/j.nuclphysb.2005.11.007
 arXiv:
 arXiv:hepph/0509141
 Bibcode:
 2006NuPhB.734...62D
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 55 pages, latex, some references updated and few comments added, version to appear in Nucl. Phys. B