One-loop tensor Feynman integral reduction with signed minors
Publikation: Bidrag til tidsskrift › Konferenceartikel › Forskning › fagfællebedømt
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One-loop tensor Feynman integral reduction with signed minors. / Fleischer, Jochem; Riemann, Tord; Yundin, Valery.
I: Journal of Physics: Conference Series (Online), Bind 368, Nr. 1, 012057, 2012.Publikation: Bidrag til tidsskrift › Konferenceartikel › Forskning › fagfællebedømt
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TY - GEN
T1 - One-loop tensor Feynman integral reduction with signed minors
AU - Fleischer, Jochem
AU - Riemann, Tord
AU - Yundin, Valery
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
M3 - Conference article
VL - 368
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012057
ER -
ID: 49746139