Chebyshev Approximations of Feynman Integrals for Collider Physics

by Ben Page (Ghent University)

Tuesday 20 Oct 2026, 11:00 → 12:00 Europe/Berlin

TUM, Physics Department, Garching

Precision measurements at the LHC need theory predictions at the same level of precision. In practice this means computing multi-loop scattering amplitudes involving multiple scattering particles. A central bottleneck is evaluating the underlying Feynman integrals quickly and reliably across the physical phase space. In this talk I will argue that, for this purpose, we benefit from working with approximations of Feynman integrals, and that Chebyshev approximations are particularly well suited to the task. Feynman integrals have well-understood regions of analyticity, through unitarity and Landau analysis, and Chebyshev approximations converge exponentially for analytic functions. Approximating the integrals along a line in physical phase space discards their intricate multi-sheeted structure, so a hard analytic problem becomes a simple numerical one. I will show how such approximations can be constructed efficiently by solving canonical differential equations. Applied to two-loop five-point integrals, the approach is competitive with state-of-the-art one-fold integral methods, without case-by-case handling of spurious singularities.

MPP2026.pdf