High-Precision evaluation of Master Integrals with LINE

by Prof. Francesco Tramontano

Wednesday 5 Nov 2025, 16:00 → 17:00 Europe/Rome

0M04

The calculation of higher-order scattering amplitudes in perturbative Quantum Field Theory relies critically on the precise evaluation of a finite set of irreducible loop integrals, known as Master Integrals (MIs). Developing robust and computationally efficient methods for this task is a central challenge in modern high-precision particle physics. In this talk I'll present the methodology implemented in the open-source program LINE (Loop Integrals Numerical Evaluation), which is designed for the numerical evaluation of MIs. Our strategy focuses on solving the systems of first-order ordinary differential equations satisfied by the integrals, employing a generalized series expansion approach. This method allows for the treatment of complex topologies with high accuracy and numerical stability. A key feature of LINE is the streamlined management of boundary conditions which can be supplied by the user or computed internally and automatically using the method of expansion by regions. I will present ongoing and future developments of the LINE program.