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arXiv · 1906.06138

Loop Tree Duality for multi-loop numerical integration

Zeno Capatti·Valentin Hirschi·Dario Kermanschah·Ben Ruijl
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Abstract

Loop Tree Duality (LTD) offers a promising avenue to numerically integrate multi-loop integrals directly in momentum space. It is well-established at one loop, but there have been only sparse numerical results at two loops. We provide a formal derivation for a novel multi-loop LTD expression and study its threshold singularity structure. We apply our findings numerically to a diverse set of up to four-loop finite topologies with kinematics for which no contour deformation is needed. We also lay down the ground work for constructing such a deformation. Our results serve as an important stepping stone towards a generalised and efficient numerical implementation of LTD, applicable to the computation of virtual corrections.

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Zeno Capatti, Valentin Hirschi, Dario Kermanschah, Ben Ruijl. 2019-06-14. Loop Tree Duality for multi-loop numerical integration. https://doi.org/10.1103/physrevlett.123.151602

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