ODSL Forum: Ramon Winterhalder, Targeting Multi-Loop Integrals with Neural Networks


Presenter: Ramon Winterhalder, UC Louvain
Title: Targeting Multi-Loop Integrals with Neural Networks


Achieving high-precision in high-energy physics (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 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 [1], 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, which has also been used successfully for phase-space integrals [2,3]. These methods can lead to a significant gain in precision [4]. 






As usual, the format will be a short presentation followed by plenty of discussion.

Please let all interested know about the Journal Club (get them to send their Email address).  We are looking forward to lively discussions.