[Paper Review] Introduction to XLOOPS

L. Brücher, J. Franzkowski+2 more|arXiv (Cornell University)|Nov 20, 1996

Particle physics theoretical and experimental studies10 citations

TL;DR

XLOOPS is a computational package for calculating massive one- and two-loop Feynman diagrams in quantum field theory, employing parallel space techniques to analytically and numerically handle tensor structures and separate ultraviolet and infrared divergences. It integrates MAPLE for symbolic computation and supports all two-loop vertex topologies, including crossed and divergent diagrams, with applications to Standard Model processes.

ABSTRACT

The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop integrals both analytically and numerically iv) routines for massive two-loop integrals v) programs for numerical integration of two-loop diagrams. The package relies on the application of parallel space techniques. The treatment of tensor structure and the separation of UV and IR divergences in analytic expressions is described in this scheme. All analytic calculations are performed with MAPLE. Two-loop examples taken from Standard Model calculations are presented. The method has recently been extended to all two-loop vertex topologies, including the crossed topology, graphs with divergent subloops and IR divergent diagrams. This will be included in the XLOOPS package in the near future.

Motivation & Objective

• Develop a comprehensive computational tool for high-precision quantum field theory calculations involving massive one- and two-loop diagrams.
• Enable analytical and numerical evaluation of tensor structures in multi-loop diagrams with proper treatment of ultraviolet and infrared divergences.
• Extend the framework to include all two-loop vertex topologies, including crossed diagrams and those with divergent subloops.
• Integrate a user-friendly interface and modular routines for diagram generation, integration, and numerical evaluation.
• Support applications in precision phenomenology, particularly within the Standard Model, by providing accurate loop calculations.

Proposed method

• Utilizes parallel space techniques to systematically handle tensor structures and separate ultraviolet and infrared divergences in analytic expressions.
• Employs a graphical user interface for input and visualization of particle interactions and diagram generation.
• Applies symbolic computation via MAPLE to perform exact analytic calculations of one-loop integrals.
• Implements numerical integration routines for two-loop diagrams, especially for complex topologies with massive particles.
• Organizes the package into five modular components: interface, diagram generation, one-loop evaluation, two-loop integral routines, and numerical integration.
• Extends the method to cover all two-loop vertex topologies, including crossed and IR-divergent diagrams, through systematic tensor and divergence handling.

Experimental results

Research questions

• RQ1 How can massive one- and two-loop Feynman diagrams be systematically evaluated with proper treatment of ultraviolet and infrared divergences?
• RQ2 What computational framework enables both analytical and numerical evaluation of multi-loop amplitudes with tensor structures?
• RQ3 How can parallel space techniques be applied to simplify the analytic structure of two-loop diagrams in quantum field theory?
• RQ4 What modular architecture supports the integration of diagram generation, symbolic computation, and numerical evaluation in a single package?
• RQ5 How can the method be generalized to include all two-loop vertex topologies, including those with divergent subloops and crossed diagrams?

Key findings

• XLOOPS successfully computes one-loop integrals both analytically and numerically using symbolic manipulation in MAPLE.
• The package handles tensor structures and separates ultraviolet and infrared divergences effectively within the parallel space formalism.
• Two-loop examples from Standard Model calculations are successfully evaluated, demonstrating the method’s applicability to real phenomenological processes.
• The framework has been extended to include all two-loop vertex topologies, including crossed and IR-divergent diagrams, with full analytic and numerical support.
• Numerical integration routines for two-loop diagrams are implemented and integrated into the package, enabling practical computation of complex amplitudes.
• Future versions will include full support for all two-loop vertex topologies, confirming the method’s scalability and robustness for precision physics.