New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams

Details New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams

2000-12-20

arxiv.org/abs/hep-th/0012189v3

Nucl.Phys. B605 (2001) 266-318

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, LaTeX, two figures (one in eps format), v3 is journal version; in v3 the typos in Egs.(2.17), (4.16), (B.12) correct

Scientific paper

10.1016/S0550-3213(01)00095-5

For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion can be calculated. For more complicated cases, only a few higher terms in epsilon are obtained. Apart from the one-loop two- and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler--Zagier sums are established, and some useful results for the hypergeometric functions of argument 1/4 are presented.

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