Laurent series expansion of a class of massive scalar one-loop integrals to ${\cal O}(\ep^2)

Abstract

We use dimensional regularization to calculate the ${\cal O}(\ep^2)$ expansion of all scalar one-loop one-, two-, three- and four-point integrals that are needed in the calculation of hadronic heavy quark production. The Laurent series up to ${\cal O}(\ep^2)$ is needed as input to that part of the NNLO corrections to heavy flavor production at hadron colliders where the one-loop integrals appear in the loop-by-loop contributions. The four-point integrals are the most complicated. The ${\cal O}(\ep^2)$ expansion of the three- and four-point integrals contains in general polylogarithms up to ${\mathrm{Li}}_4$ and functions related to multiple polylogarithms of maximal weight and depth four.

48 pages, 4 figures in the text, slight change in the title, one reference added, matches published version

References in corpus (1)

• Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions

Cited by in corpus (16)

• The total top quark pair production cross-section at hadron colliders through O(alpha_S^4)
• Percent level precision physics at the Tevatron: first genuine NNLO QCD corrections to q qbar -> t tbar + X
• High-precision differential predictions for top-quark pairs at the LHC
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• Resolving the Tevatron Top Quark Forward-Backward Asymmetry Puzzle: Fully Differential Next-to-Next-to-Leading-Order Calculation
• The singular behavior of one-loop massive QCD amplitudes with one external soft gluon
• The one-loop gluon amplitude for heavy-quark production at NNLO
• Heavy quark pair production in gluon fusion at next-to-next-to-leading $\mathcal{O}({\alpha }_s^4)$ order: One-loop squared contributions
• Next-to-next-to-leading order $\mathcal{O}({\alpha }_s^4)$ results for heavy quark pair production in quark--antiquark collisions: The one-loop squared contributions
• First order radiative corrections to Bhabha scattering in $d$ dimensions
• Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
• One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up to O(epsilon^2)
• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• Laurent series expansion of a class of massive scalar one-loop integrals up to ${\cal O}(\ep^2)$ in terms of multiple polylogarithms
• On the Compton scattering vertex for massive scalar QED
• Next-to-next-to-leading order $\mathcal{O}({\alpha }^2{\alpha }_s^2)$ results for top quark pair production in photon--photon collisions: The one-loop squared contributions