LINE: Loop Integrals Numerical Evaluation

• Published in: The journal of high energy physics Vol. 2025; no. 7; pp. 219 - 47
• Main Authors: Prisco, Renato Maria, Ronca, Jonathan, Tramontano, Francesco
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 22.07.2025; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Automation; Boundary conditions; Classical and Quantum Gravitation; Differential equations; Elementary Particles; Higher-Order Perturbative Calculations; Integrals; Methods; Ordinary differential equations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Series expansion; Spacetime; String Theory; Scattering Amplitudes; Automation; Higher-Order Perturbative Calculations
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP07(2025)219

A bstract We present methods for the numerical evaluation of the master integrals that arise in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order ordinary differential equations through series expansion. We have collected these procedures in an open source computer program called LINE. Boundary conditions can be provided by the user or computed internally using the method of expansion by regions. Illustrative examples are also given.