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Scalar one-loop integrals for QCD

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arxiv 0712.1851 v4 pith:JVRL75NS submitted 2007-12-12 hep-ph

classification hep-ph
keywords integralsdivergentbasisepsilonscalargiveone-loopresults
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 7 Pith papers

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