Evaluating Parametric Integrals in the Minkowski Regime without Contour Deformation

We present selected examples demonstrating an alternative approach to contour deformation for
numerically computing loop integrals in the Minkowski regime. This method focuses on identify-
ing singular hypersurfaces (varieties of the F polynomial) and mapping them to known points
which can then be resolved by employing blow-ups/sector decomposition techniques, thereby
avoiding the need for contour deformation. Using this technique, we achieve improved conver-
gence properties without the need for contour deformation, which is known to significantly in-
crease the complexity of the integrand by introducing, for example, derivatives of the F poly-
nomial and complicated Jacobians. We highlight that while we have only tested the approach on
selected one-, two- and three-loop massless and one-loop massive examples, it shows promise for
practical applications, offering potential benefits over the traditional approach. Evaluation times
are compared with existing contour deformation implementations to illustrate the performance of
this alternative method.