On $\varepsilon$-factorised bases and pure Feynman integrals

Frellesvig, Hjalte; Weinzierl, Stefan

doi:10.21468/SciPostPhys.16.6.150

SciPost Physics

On $\varepsilon$-factorised bases and pure Feynman integrals

Hjalte Frellesvig, Stefan Weinzierl

SciPost Phys. 16, 150 (2024) · published 6 June 2024

doi: 10.21468/SciPostPhys.16.6.150
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Abstract

We investigate $\varepsilon$-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms. We show that a $\varepsilon$-factorised differential equation does not necessarily lead to Feynman integrals of uniform transcendental weight. We also point out that a proposed definition of purity works locally, but not globally.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.6.150
TI  - On $\varepsilon$-factorised bases and pure Feynman integrals
PY  - 2024/06/06
UR  - https://scipost.org/SciPostPhys.16.6.150
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 6
SP  - 150
A1  - Frellesvig, Hjalte
AU  - Weinzierl, Stefan
AB  - We investigate $\varepsilon$-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms. We show that a $\varepsilon$-factorised differential equation does not necessarily lead to Feynman integrals of uniform transcendental weight. We also point out that a proposed definition of purity works locally, but not globally.
ER  -

@Article{10.21468/SciPostPhys.16.6.150,
	title={{On $\varepsilon$-factorised bases and pure Feynman integrals}},
	author={Hjalte Frellesvig and Stefan Weinzierl},
	journal={SciPost Phys.},
	volume={16},
	pages={150},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.6.150},
	url={https://scipost.org/10.21468/SciPostPhys.16.6.150},
}

Cited by 4

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¹ Hjalte Frellesvig,
² Stefan Weinzierl

Funders for the research work leading to this publication

Carlsbergfondet / Carlsberg Foundation
Horizon 2020 (through Organization: European Commission [EC])