Analytic Results for Massless Three-Loop Form Factors
R.N. Lee, A.V. Smirnov, V.A. Smirnov
TL;DR
This paper provides exact analytical evaluations of master integrals for massless three-loop QCD form factors, combining advanced techniques to complete the analytic form of the form factors.
Contribution
It introduces a novel combination of methods to evaluate master integrals exactly in d and derives the full analytic form of the three-loop form factors.
Findings
Exact expressions for master integrals in d-dimensional space.
Complete analytic form of the three-loop QCD form factors.
Determination of previously unknown constants in the expansion.
Abstract
We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.
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