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arXiv · 2010.06947

Resummation methods for Master Integrals

Dhimiter D. Canko·Nikolaos Syrrakos
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Abstract

We present in detail two resummation methods emerging from the application of the Simplified Differential Equations approach to a canonical basis of master integrals. The first one is a method which allows for an easy determination of the boundary conditions, since it finds relations between the boundaries of the basis elements and the second one indicates how using the $x \rightarrow 1$ limit to the solutions of a canonical basis, one can obtain the solutions to a canonical basis for the same problem with one mass less. Both methods utilise the residue matrices for the letters $\{0,1\}$ of the canonical differential equation. As proof of concept, we apply these methods to a canonical basis for the three-loop ladder-box with one external mass off-shell, obtaining subsequently a canonical basis for the massless three-loop ladder-box as well as its solution.

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Dhimiter D. Canko, Nikolaos Syrrakos. 2020-10-14. Resummation methods for Master Integrals. https://doi.org/10.1007/jhep02(2021)080

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