Planar rooted line arrangements and an operad for factorized scattering

We introduce two topological non-$\mathrm{\Sigma }$ 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.