English

Resummation methods for Master Integrals

High Energy Physics - Phenomenology 2021-02-24 v3 High Energy Physics - Theory

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 x1x \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}\{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.

Keywords

Cite

@article{arxiv.2010.06947,
  title  = {Resummation methods for Master Integrals},
  author = {Dhimiter D. Canko and Nikolaos Syrrakos},
  journal= {arXiv preprint arXiv:2010.06947},
  year   = {2021}
}

Comments

20 pages, 3 figures and 2 tables, section 3.3 rewritten, version accepted for publication to JHEP

R2 v1 2026-06-23T19:20:11.099Z