Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals

By Erik Panzer. Computer Physics Communications, 2014

422 citations recorded by the source corpus.

We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we discuss in particular their application to the computation of Feynman integrals.

Subfields: Algebra and Number Theory, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/bdf1236d9157769ba2f9c0741498f08da2270eda

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In Algebra and Number Theory

In Theoretical Computer Science

Citations in the corpus

Feynman integrals and hyperlogarithms (2015, methodology): “Our results show that one can go much further and compute such integrals, to arbitrary loop order, also with two off-shell legs, with HyperInt.”
Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016, methodology): “…of the approach are illustrated by discussing the simple cases of the 1-loop self-mass and of a particular vertex amplitude, and then used for the evaluation of the two-loop massive sunrise and the QED kite graph (the problem studied by Sabry in 1962), up to first order in the (d − 4) expansion.”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “The HyperInt [57] and mpl [58] packages have focused mainly on zero and one scale integrals with a high number of loops, but the algorithms employed have potential applications to a wider class of integrals.”
Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report (2016, background): “Panzer’s HyperInt [14] and Bogner’s MPL [15] packages have focused mainly on zero and one scale integrals with a high number of loops (see for example [16]) but the algorithms employed have potential applications to a wider class of two-loop integrals with more scales.”
Minimally subtracted six loop renormalization of $O(n)$-symmetric $\phi^4$ theory and critical exponents (2017, methodology): “These were obtained in a Feynman diagram computation, that became feasible through the automatization of new techniques [30, 32, 130] to calculate Feynman integrals, very briefly summarized in section III.”
Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism (2017, background): “k ;x), N = 3;4, may diverge logarithmically whenever x approaches c 1. In the following we show how we can extract the logarithmic singularities. We rst apply some results on shue algebras from ref. [54] (in particular Denition 2.1 and Lemma 2.2), which allow us to rewrite E N( n 1 :::n k c 1 :::c k”
Collider physics at the precision frontier (2020, methodology): “This procedure leads to multiple polylogarithmic functions, and the program HyperInt [718] automates the iterative integration over the parameters occurring linearly.”
A quasi-finite basis for multi-loop Feynman integrals (2014, methodology): “For example, the well-studied [24–26], nine-line, planar master integral for the three-loop form factor in massless QCD (A9,1 in the notation of reference [25]) will quickly consume more than 30 gigabytes of random-access memory if one attempts a singularity resolution of the integral along the line”
Lectures on differential equations for Feynman integrals (2014, background): “The question whether a given class of Feynman integrals can be evaluated in terms of iterated integrals is crucial to an approach based on direct integration in Feynman parameter space [85, 86], where it is related to the question of linear reducibility.”