Eur. Phys. J. C (2017) 77: 274
https://doi.org/10.1140/epjc/s10052-017-4833-6

Regular Article - Theoretical Physics

Numerical implementation of the loop–tree duality method

¹ Instituto de Física Corpuscular, Universitat de València-Consejo Superior de Investigaciones Científicas, Parc Científic, 46980, Paterna, Valencia, Spain
² Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, C/ Nicolás Cabrera 15, 28049, Madrid, Spain
³ Institute of Nuclear and Particle Physics, NCSR “Demokritos”, 15310, Agia Paraskevi, Greece

^* e-mail: chachamis@gmail.com

Received: 19 January 2017
Accepted: 13 April 2017
Published online: 2 May 2017

Abstract

We present a first numerical implementation of the loop–tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs.