Direct numerical evaluation of multi-loop integrals without contour deformation

We propose a method for computing numerically integrals defined via $i \epsilon$ deformations acting on single-pole singularities. achieve this without an explicit analytic contour deformation. Our solution is then used to produce precise Monte Carlo estimates of multi-scale multi-loop directly in Minkowski space. corroborate the validity our strategy by presenting several examples ranging from one three loops. When connection with four-dimensional regularization techniques, treatment can be extended ultraviolet and infrared divergent integrals.