Targeting Multi-Loop Integrals with Neural Networks
Abstract: Achieving high-precision in HEP theory predictions requires the evaluation of scattering amplitudes beyond leading order. These (multi)-loop amplitudes can contain complicated integrals where an analytic solution is often not feasible. In this case, they have to be evaluated numerically, and a careful treatment of possible singularities of the integrand is required. After isolating and factorizing the UV and IR poles of the integrand, using sector decomposition, only threshold singularities remain, which can be avoided by a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the chosen contour. We present methods to optimize this contour using a combination of optimized, global complex shifts and a normalizing flow. These methods can lead to a significant gain in precision.
Zoom Meeting ID: 948 7183 3595