$\epsilon$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^{+}{e}^{-}\to 2(Q\bar{Q})$

Abstract

We argue that in many physical calculations where the "eliptic" sectors are involved, one can express the results via iterated integrals with almost all weights being rational. Our method is based on the existence of $\epsilon$-regular basis, which is akin to the $\epsilon$-finite basis defined in Ref. [hep-ph/0601165]. As a demonstration of our technique, we calculate the photon contribution to the total cross section of the production of two $Q\bar{Q}$ pairs in the electron-positron collisions.

17 pages

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• Master integrals for bipartite cuts of three-loop photon self energy
• Learning Feynman integrals from differential equations with neural networks
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Two-loop corrections to Lamb shift and hyperfine splitting in hydrogen via multi-loop methods
• Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions
• Massive Two-Loop Heavy Particle Diagrams
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