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arXiv · 2110.12885

Direct numerical evaluation of multi-loop integrals without contour deformation

Roberto Pittau·Bryan Webber
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Abstract

We propose a method for computing numerically integrals defined via $i \epsilon$ 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.

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Roberto Pittau, Bryan Webber. 2021-10-25. Direct numerical evaluation of multi-loop integrals without contour deformation. https://doi.org/10.1140/epjc%2Fs10052-022-10008-6

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