Positive Integrands and Avoiding Contour Deformation

In this talk, we present an alternative approach to evaluating loop integrals in the Minkowski regime without contour deformation. The method identifies singular hypersurfaces defined by the variety of the Symanzik F polynomial and maps them to the integration boundary where they can be resolved via sector decomposition. This avoids the need for contour deformation - which typically increases integrand complexity through derivatives of the F polynomial and complicated Jacobians - while improving numerical convergence. Although tested so far on selected 1-, 2- and 3-loop examples (including both massless and massive integrals), the approach shows strong potential for broader applications. We will conclude by discussing recent advances in systematising the avoidance of contour deformation using the method of generic (or open) cylindrical algebraic decomposition (GCAD) and compare evaluation times with existing contour-deformation-based implementations.