New results for algebraic tensor reduction of Feynman integrals
Abstract
We report on some recent developments in algebraic tensor reduction of oneloop Feynman integrals. For 5point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5point Gram determinants, and inverse small 4point Gram determinants are treated by expansions in higherdimensional 3point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7point functions is discussed. In the present approach one needs for the reductions a $(d+2)$dimensional scalar 5point function in addition to the usual scalar basis of 1 to 4point functions in the generic dimension $d=42 \epsilon$. When exploiting the fourdimensionality of the kinematics, this basis is sufficient. We indicate how the $(d+2)$dimensional 5point function can be evaluated.
 Publication:

arXiv eprints
 Pub Date:
 February 2012
 arXiv:
 arXiv:1202.0730
 Bibcode:
 2012arXiv1202.0730F
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 8 pages, 1 figure. Contribution to Proceedings of "10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)"  Radcor2011, September 2630, 2011, Mamallapuram, India