Planar rooted line arrangements and an operad for factorized scattering

TL;DR

This paper introduces operad structures on planar line arrangements to model particle scattering in 1+1 dimensions, linking geometric orderings with algebraic operad concepts.

Contribution

It presents novel topological operad structures on line arrangements and interprets them in the context of factorized scattering theories.

Findings

Defined two operad structures on planar line arrangements

Connected geometric ordering with particle scattering diagrams

Proposed an operadic framework for factorized scattering

Abstract

We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in terms of scattering diagrams in purely elastic (1+1)-dimensional theories. We discuss a possible approach to factorized scattering in operadic terms.