Scalar one-loop integrals for QCD

Dec, 2007
27 pages
Published in:
  • JHEP 02 (2008) 002
e-Print:
Report number:
  • FERMILAB-PUB-07-633-T,
  • OUTP-07-16P

Citations per year

20072012201720222025010203040
Abstract: (arXiv)
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.
  • NLO Computations
  • QCD
  • loop integral: 4
  • loop integral: 3
  • loop integral: 1
  • quantum chromodynamics
  • regularization
  • formula