Precision, Precisely: From Theory to Computation in High-Order Calculations

by Bakar Chargeishvili (Institute for Theoretical Physics, Karlsruhe Institute of Technology)

Friday 25 Sept 2026, 14:00 → 15:00 Europe/Budapest

We spend years pushing theoretical precision - higher loop orders, careful scheme choices, refined PDFs - yet the question of whether we can actually evaluate the result reliably is often overlooked. Using pp -> ttH at two loops as a case study, I discuss what happens when carefully derived amplitudes meet computational reality.

I will begin with a pedagogical overview of High-Performance Computing concepts essential for modern physics calculations, including vectorization and GPU offloading. Following this, I will discuss the specific pitfalls of floating-point arithmetic in amplitude evaluation. Finally, I will describe a systematic effort - combining exhaustive worst-case search with modern verification and optimization techniques from computer science - to determine and minimize the actual error of the special functions underlying essentially any high-precision calculation. The measured worst cases of standard building blocks saturate the bounds proven in the literature, and re-engineered implementations achieve smaller errors at the same speed, outperforming standard mathematical libraries by up to an order of magnitude. The aim of the talk is to offer practical guidance for any high-precision calculation where reliability cannot be left to chance or to generic "arbitrary precision" libraries.

slides_precision_chargeishvili.pdf