The spectrum of Feynman integral geometries at two loops

by Dr Piotr Bargiela

Thursday 18 Jun 2026, 14:00 → 15:00 Europe/London

In this talk, I present my recent results on constraining the analytic structure of 2-loop Feynman integrals for Standard Model scattering amplitudes dimensionally regulated in the 't Hooft-Veltman scheme. I show an explicit reduction resulting from partial fractioning the high-multiplicity integrands into subsectors of the 12 distinct topologies with 11 generalized propagators (arXiv:2408.06325). It improves the performance of the IBP reduction and numerical evaluation of integrals beyond 5-point scattering. I also provide a functionally distinct basis of 347 Master Integrals arising from 84 distinct Feynman graphs which spans the whole corresponding 2-loop transcendental function space (arXiv:2503.16299). In addition, I indicate that all the 2-loop Master Integrals with more than 8 denominators, in an appropriate basis, do not contribute to the finite part of any 2-loop scattering amplitude. Moreover, I present a complete classification of Feynman-integral geometries at 2-loop order in any 4-dimensional Quantum Field Theory with standard quadratic propagators (arXiv:2512.13794). Finally, I show which geometries appear in example Standard Model processes from the Les Houches wishlist.