Прямая численная оценка многопетлевых интегралов без деформации контура
Direct numerical evaluation of multi-loop integrals without contour deformation: https://arxiv.org/abs/2110.12885
Roberto Pittau, Bryan Webber
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.
Comments: 21 pages, 18 figures
Roberto Pittau, Bryan Webber
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.
Comments: 21 pages, 18 figures