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Direct numerical evaluation of multi-loop integrals without contour deformation

Published version
Peer-reviewed

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Authors

Pittau, Roberto 
Webber, Bryan 

Abstract

Abstract: We propose a method for computing numerically integrals defined via iϵ deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce precise Monte Carlo estimates of multi-scale multi-loop integrals directly in Minkowski space. We corroborate the validity of our strategy by presenting several examples ranging from one to three loops. When used in connection with four-dimensional regularization techniques, our treatment can be extended to ultraviolet and infrared divergent integrals.

Description

Keywords

Regular Article - Theoretical Physics

Journal Title

The European Physical Journal C

Conference Name

Journal ISSN

1434-6044
1434-6052

Volume Title

82

Publisher

Springer Berlin Heidelberg
Sponsorship
Science and Technology Facilities Council (ST/P000681/1, ST/T000694/1)
Junta de Andalucía (A-FQM-467-UGR18, P18-FR-4314)
Agencia Estatal de Investigación (AEI) (PID2019-106087GB-C21 (10.13039/501100011033))
European Cooperation in Science and Technology (CA16201 PARTICLEFACE)