Cluster adjacency beyond MHV

TL;DR

This paper investigates the concept of cluster adjacency in non-MHV scattering amplitudes, linking pole structures, symbol singularities, and the $ar{Q}$-equation to deepen understanding of amplitude singularity patterns.

Contribution

It extends cluster adjacency to BCFW decompositions and connects it to symbol adjacency and the $ar{Q}$-equation, providing new insights into amplitude singularity structures.

Findings

Cluster adjacency controls pole appearance in BCFW terms.

Adjacency relates to symbol branch cut singularities.

Intertwining of poles and symbols via cluster adjacency.

Abstract

We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $\bar{Q}$-equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.