English

Scalar one-loop integrals for QCD

High Energy Physics - Phenomenology 2011-06-30 v4

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=42ϵD=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/ϵ2,1/ϵ11/\epsilon^2,1/\epsilon^1 and 1/ϵ01/\epsilon^0 as complex numbers for an arbitrary tadpole, bubble, triangle or box integral.

Keywords

Cite

@article{arxiv.0712.1851,
  title  = {Scalar one-loop integrals for QCD},
  author = {R. Keith Ellis and Giulia Zanderighi},
  journal= {arXiv preprint arXiv:0712.1851},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T09:53:07.808Z