Header

UZH-Logo

Maintenance Infos

Magnus and Dyson series for Master Integrals


Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo; Mirabella, Edoardo; Schlenk, Johannes; Schubert, Ulrich; Tancredi, Lorenzo (2014). Magnus and Dyson series for Master Integrals. Journal of High Energy Physics:082.

Abstract

We elaborate on the method of differential equations for evaluating Feynman integrals. We focus on systems of equations for master integrals having a linear dependence on the dimensional parameter. For these systems we identify the criteria to bring them in a canonical form, recently identified by Henn, where the dependence of the dimensional parameter is disentangled from the kinematics. The determination of the transformation and the computation of the solution are obtained by using Magnus and Dyson series expansion. We apply the method to planar and non-planar two-loop QED vertex diagrams for massive fermions, and to non-planar two-loop integrals contributing to 2 → 2 scattering of massless particles. The extension to systems which are polynomial in the dimensional parameter is discussed as well.

Abstract

We elaborate on the method of differential equations for evaluating Feynman integrals. We focus on systems of equations for master integrals having a linear dependence on the dimensional parameter. For these systems we identify the criteria to bring them in a canonical form, recently identified by Henn, where the dependence of the dimensional parameter is disentangled from the kinematics. The determination of the transformation and the computation of the solution are obtained by using Magnus and Dyson series expansion. We apply the method to planar and non-planar two-loop QED vertex diagrams for massive fermions, and to non-planar two-loop integrals contributing to 2 → 2 scattering of massless particles. The extension to systems which are polynomial in the dimensional parameter is discussed as well.

Statistics

Citations

Dimensions.ai Metrics
44 citations in Web of Science®
54 citations in Scopus®
93 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

76 downloads since deposited on 17 Feb 2015
33 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:2014
Deposited On:17 Feb 2015 13:56
Last Modified:23 Sep 2018 05:50
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/JHEP03(2014)082

Download

Download PDF  'Magnus and Dyson series for Master Integrals'.
Preview
Content: Published Version
Filetype: PDF
Size: 600kB
View at publisher
Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)