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

2000/12/20 by Davydychev, A. I., Kalmykov, M. Yu. · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Numerical Analysis (math.NA) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.hep-th/0012189

Abstract

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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• Closed-form evaluations of log-sine integrals and Apéry-like sums in terms of polylogarithms

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