pierrevanhove / PicardFuchs

Picard-Fuchs equations for Feynman integrals

Algorithms for minimal Picard-Fuchs operators of Feynman integrals

by Pierre Lairez and Pierre Vanhove

This repository contains the additional files for the article arXiv:2209.10962.

• The identity in eq. (3.5)
• The differential operators for the sunset graph at 2 loops, 3 loops, 4 loops, 5 loops analysed in section 4
• The differential operator for the multiloop ice-cream graph at the triangle graph 1 loop, 2 loops, 3 loops analysed in section~5
• The differential operator for the kite graph of section 6.1
• The differential operator for the tardigrade graph of section 6.2
• The differential operator for the double-box graph of section 6.3
• The differential operator for the pentabox graph of section 6.4

The results given here have been derived using the Magma code Period described in the article Computing periods of rational integrals and the ORE algebra programs Ore Algebra in Sage, arXiv 1306.4263 and the Symbolic-Numeric Factorization of Differential Operators