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We introduce a novel construction of a contour deformation within theframework of Loop-Tree Duality for the numerical computation of loop integralsfeaturing threshold singularities in momentum space. The functional form of ourcontour deformation automatically satisfies all constraints without the needfor fine-tuning. We demonstrate that our construction is systematic andefficient by applying it to more than 100 examples of finite scalar integralsfeaturing up to six loops. We also showcase a first step towards handlingnon-integrable singularities by applying our work to one-loop infrareddivergent scalar integrals and to the one-loop amplitude for the orderedproduction of two and three photons. This requires the combination of ourcontour deformation with local counterterms that regulate soft, collinear andultraviolet divergences. This work is an important step towards computinghigher-order corrections to relevant scattering cross-sections in a fullynumerical fashion.

Numerical Loop-Tree Duality: contour deformation and subtraction