Source-linked AI summary
Scattering Amplitudes with Open Loops
Fabio Cascioli, Philipp Maierhöfer, Stefano Pozzorini
TL;DR
High-multiplicity one-loop calculations face a trade-off between CPU efficiency and automation. The paper promotes recursive tree algorithms to loop-momentum polynomial generators called open loops, which interface with tensor-integral and OPP reduction and produce fast, stable results across collider processes.
Problem
One-loop calculations for high-multiplicity collider processes face a trade-off between CPU efficiency and automation, while large particle multiplicities can make amplitudes unmanageable.
Method
The method recursively constructs Feynman diagrams while treating building blocks as functions of loop momentum, encoding the result as polynomial open loops that interface with tensor-integral and OPP reduction.
Results
The approach yields compact codes, fast code generation, nearly linear CPU scaling with diagram count, and robust double-precision tensor-reduction results across 12 non-trivial processes.
Takeaways & Limitations
Open loops provide a flexible one-loop generation technique applicable from 2 →2 scattering to multi-particle processes with up to O(105) diagrams.
Abstract
from arXiv · showhide
We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and OPP reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with non-trivial applications, the open-loop approach will permit to obtain precise predictions for a very wide range of collider processes.