Scalar one-loop integrals for QCD

Abstract

We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in $D=4-2\epsilon$ dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integrals we give results for our basis set containing 16 divergent integrals. We provide analytic results for the 5 divergent box integrals in the basis set which are missing in the literature. Building on the work of van Oldenborgh, a general, publicly available code has been constructed, which calculates both finite and divergent one-loop integrals. The code returns the coefficients of $1/{\epsilon }^2,1/{\epsilon }^1$ and $1/{\epsilon }^0$ as complex numbers for an arbitrary tadpole, bubble, triangle or box integral.

27 pages, 5 figures, associated fortran code available at http://qcdloop.fnal.gov/. New version corrects typographical error in Eq. 5.2

References in corpus (1)

• Loop induced interference effects in Higgs Boson plus two jet production at the LHC

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