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
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
1/2,1/1 and 1/0 as complex numbers for
an arbitrary tadpole, bubble, triangle or box integral.
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