Loop-Tree Duality for Multiloop Numerical Integration
Zeno Capatti1, Valentin Hirschi1, Dario Kermanschah1
1ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland.
Physical Review Letters
|November 9, 2019
Summary
Loop-tree duality (LTD) now extends to multiloop integrals, enabling direct numerical integration in momentum space. This study presents a novel LTD expression and its successful numerical application to four-loop calculations.
Area of Science:
- High Energy Physics
- Computational Physics
- Quantum Field Theory
Background:
- Loop-tree duality (LTD) is established for one-loop integrals but sparse for multiloop.
- Numerical integration of multiloop integrals in momentum space is computationally challenging.
Purpose of the Study:
- To provide a formal derivation of a novel multiloop LTD expression.
- To investigate the threshold singularity structure of the new LTD expression.
- To numerically apply the findings to multiloop finite topologies.
Main Methods:
- Formal derivation of a novel multiloop LTD expression.
- Analysis of threshold singularity structure.
- Numerical integration of up to four-loop finite topologies using the derived LTD expression.
Main Results:
- A novel multiloop LTD expression is derived.
- The threshold singularity structure of the new expression is analyzed.
- Numerical applications to diverse four-loop topologies demonstrate the method's viability.
Conclusions:
- The derived multiloop LTD expression is a significant advancement for numerical integration.
- This work lays groundwork for generalized numerical LTD implementations.
- The method is applicable to computing virtual corrections in particle physics.
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