Laurent series expansion of a class of massive scalar one-loop integrals up to O(ε2) in terms of multiple polylogarithms

DOI10.1063/1.2190336zbMATH Open1112.81080arXivhep-ph/0512159OpenAlexW2001325081MaRDI QIDQ3441948

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Publication date: 16 May 2007

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Abstract: In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one--loop integrals were evaluated in $n=4-2ep$ dimension and the results were presented in terms of a Laurent series expansion up to $calO(e{p}^2)$. We found that some of the $e{p}^2$ coefficients contain a new class of functions which we termed the $L$ functions. The $L$ functions are defined in terms of one--dimensional integrals involving products of logarithm and dilogarithm functions. In this paper we derive a complete set of algebraic relations that allow one to convert the $L$ functions of our previous approach to a sum of classical and multiple polylogarithms. Using these results we are now able to present the $e{p}^2$ coefficients of the one-loop master integrals in terms of classical and multiple polylogarithms.

Full work available at URL: https://arxiv.org/abs/hep-ph/0512159

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