Open AccessSeminumerical evaluation of one-loop corrections
Author(s) -
R. Keith Ellis,
Walter T. Giele,
Giulia Zanderighi
Publication year - 2006
Publication title -
physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology
Language(s) - English
Resource type - Journals
eISSN - 1550-7998
pISSN - 1550-2368
DOI - 10.1103/physrevd.73.014027
Subject(s) - scalar (mathematics) , dimensional regularization , regularization (linguistics) , amplitude , loop (graph theory) , scattering amplitude , physics , massless particle , recursion (computer science) , higgs boson , mathematics , quantum electrodynamics , mathematical physics , particle physics , algorithm , computer science , quantum mechanics , geometry , renormalization , combinatorics , artificial intelligence
We present a semi-numerical algorithm to calculate one-loop virtualcorrections to scattering amplitudes. The divergences of the loop amplitudesare regulated using dimensional regularization. We treat in detail the case ofamplitudes with up to five external legs and massless internal lines, althoughthe method is more generally applicable. Tensor integrals are reduced togeneralized scalar integrals, which in turn are reduced to a set of known basisintegrals using recursion relations. The reduction algorithm is modified nearexceptional configurations to ensure numerical stability. To test the procedurewe apply these techniques to one-loop corrections to the Higgs to four quarkprocess for which analytic results have recently become available.Comment: 33 pages, 10 figures, some typos fixed and references added, to appear in Phys. Rev. D. v3 corrects a typo in eq. A2
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