Large scale analytic calculations in quantum field theories

Abstract

We present a survey on the mathematical structure of zero-and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.

New 2- and 3-loop heavy flavor corrections to unpolarized and polarized deep-inelastic scattering

“…A survey on the calculation methods for the 3-loop massive OMEs has been given in Ref. [75]. Massive OMEs contain, beyond the usual Feynman rules, those for the twist-2 local operators, cf.…”

New 2- and 3-loop heavy flavor corrections to unpolarized and polarized deep-inelastic scattering

“…A survey on the calculation methods for the 3-loop massive OMEs has been given in Ref. [54]. Massive OMEs contain, beyond the usual Feynman rules, those for the twist-2 local operators, cf.…”

TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses

“…This observation prompted the investigation of new classes of special functions, such as harmonic polylogarithms [2], generalized harmonic polylogarithms [3], and elliptic polylogarithms [4], see e. g. Ref. [5] for a recent review. However, it is not clear if any multi-loop integral can be represented by these classes of functions, in particular beyond the two-loop level.…”