Numerical implementation of the loop–tree duality method

• Main Authors: Sebastian Buchta, Grigorios Chachamis, Petros Draggiotis, Germán Rodrigo
• Format: Article
• Language: English
• Published: SpringerOpen 2017-05-01
• Series: European Physical Journal C: Particles and Fields
• Subjects: External Momentum; Internal Mass; Loop Momentum; Loop Integral; Contour Deformation
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-017-4833-6

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.