Speaker
Description
Precision predictions for LHC processes at NNLO and beyond rely on the efficient reduction of multi-loop Feynman integrals to a small set of master integrals, a task that becomes increasingly computationally expensive as the number of loops and external legs grows. We present a new strategy that constructs integration-by-parts relations directly from the soft and collinear singularities of the integral family. We show that these singularities give rise to compact determinantal syzygies with controlled propagator powers, thereby translating the singularity structure directly into efficient reduction identities. We demonstrate the method for the planar two-loop five-point integral families relevant to $pp \to t\bar{t}H$, a benchmark multi-scale $2 \to 3$ process of direct relevance to precision phenomenology at the LHC. The construction can be systematically extended to the increasingly complex integral topologies encountered in scattering amplitudes, offering a practical route to the multi-loop, multi-leg calculations required for future precision studies at the LHC.