One-loop tensor Feynman integral reduction with signed minors

Fleischer J, Riemann T, Yundin V (2012)
In: Journal of Physics Conference Series. 368. IOP Publishing.

Conference Paper | Published | English

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Abstract
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one-to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions.
Publishing Year
Conference
14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT)
Location
Uxbridge, ENGLAND
Conference Date
SEP 05-09, 2011
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Cite this

Fleischer J, Riemann T, Yundin V. One-loop tensor Feynman integral reduction with signed minors. In: Journal of Physics Conference Series. Vol 368. IOP Publishing; 2012.
Fleischer, J., Riemann, T., & Yundin, V. (2012). One-loop tensor Feynman integral reduction with signed minors. Journal of Physics Conference Series, 368.
Fleischer, J., Riemann, T., and Yundin, V. (2012). “One-loop tensor Feynman integral reduction with signed minors” in Journal of Physics Conference Series, vol. 368, (IOP Publishing).
Fleischer, J., Riemann, T., & Yundin, V., 2012. One-loop tensor Feynman integral reduction with signed minors. In Journal of Physics Conference Series. no.368 IOP Publishing.
J. Fleischer, T. Riemann, and V. Yundin, “One-loop tensor Feynman integral reduction with signed minors”, Journal of Physics Conference Series, vol. 368, IOP Publishing, 2012.
Fleischer, J., Riemann, T., Yundin, V.: One-loop tensor Feynman integral reduction with signed minors. Journal of Physics Conference Series. 368, IOP Publishing (2012).
Fleischer, Jochem, Riemann, Tord, and Yundin, Valery. “One-loop tensor Feynman integral reduction with signed minors”. Journal of Physics Conference Series. IOP Publishing, 2012.Vol. 368.
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