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 = 4-2epsilon 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/epsilon2,1/epsilon1 and 1/epsilon0 as complex numbers for an arbitrary tadpole, bubble, triangle or box integral.
Journal of High Energy Physics
- Pub Date:
- February 2008
- High Energy Physics - Phenomenology
- 27 pages, 5 figures, associated fortran code available at http://qcdloop.fnal.gov/. New version corrects typographical error in Eq. 5.2