Planar binary trees in scattering amplitudes

TL;DR

This paper explores the role of planar binary trees in the computation of tree-level scattering amplitudes, highlighting their combinatorial properties and identities that emerge in this physical context.

Contribution

It introduces the application of planar binary trees to scattering amplitudes and presents new identities, bridging combinatorics and theoretical physics.

Findings

Planar binary trees appear naturally in scattering amplitude calculations.

Certain identities involving these trees are observed, some previously known only through examples.

The work suggests combinatorial structures underpinning physical amplitude computations.

Abstract

These notes are a written version of my talk given at the CARMA workshop in June 2017, with some additional material. I presented a few concepts that have recently been used in the computation of tree-level scattering amplitudes (mostly using pure spinor methods but not restricted to it) in a context that could be of interest to the combinatorics community. In particular, I focused on the appearance of {\it planar binary trees} in scattering amplitudes and presented some curious identities obeyed by related objects, some of which are known to be true only via explicit examples.