On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams

Abstract

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $\epsilon =(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.

3 pages, 1 figure, results unchanged, discussion improved, to appear in European Physical Journal C

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• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Feynman integrals and hyperlogarithms
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method
• On the analytic computation of massless propagators in dimensional regularization
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• DRA method: Powerful tool for the calculation of the loop integrals
• The four-propagator three-loop vacuum integral by the hypergeometry
• Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals