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Setting Limits on Supersymmetry Using Simplified Models

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Published on: November 15, 2013

Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals.

Claudia Fevola¹, Sebastian Mizera², Simon Telen³

¹Université Paris-Saclay, Inria, 91120 Palaiseau, France.

Physical Review Letters

|March 22, 2024

Summary

This summary is machine-generated.

This study presents a new method for analyzing Feynman integral singularities, crucial for standard model calculations. The approach uses computational algebraic geometry to classify and compute these singularities, even with complex conditions like massless particles.

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Area of Science:

Theoretical Particle Physics
Computational Physics
Quantum Field Theory

Background:

Traditional analysis of Landau singularities in Feynman integrals presents challenges for practical perturbative computations.
Existing methods struggle with complexities such as massless particles and ultraviolet/infrared divergences.

Purpose of the Study:

To reformulate the analysis of Feynman integral singularities for practical application in the standard model.
To develop a robust algorithm for classifying and computing Landau singularities.

Main Methods:

Application of computational algebraic geometry techniques.
Introduction of the principal Landau determinant algebraic variety.
Testing with 114 example Feynman diagrams.

Main Results:

A novel, practical algorithm for classifying and computing Landau singularities.
The principal Landau determinant effectively captures singularities under various conditions, including massless particles and divergences.
Successful illustration on complex processes like a 2-loop 5-point nonplanar QCD process.

Conclusions:

The reformulated analysis provides a powerful tool for perturbative computations in quantum field theory.
The developed algorithm and algebraic variety offer a significant advancement in understanding Feynman integral singularities.