Implications of nonplanar dual conformal symmetry

TL;DR

This paper explores the implications of nonplanar dual conformal symmetry in five-particle scattering, showing how it simplifies the function space and affects infrared divergence analysis.

Contribution

It extends the understanding of dual conformal symmetry from integrand level to integrated quantities, especially in five-particle scattering, and demonstrates its impact on function space reduction and infrared divergences.

Findings

Symmetry reduces the function space to a known three-variable space.

The Ward identity is verified for leading and subleading poles.

Examples of integrals with both ordinary and dual conformal symmetry are provided.

Abstract

Recently, Bern et al observed that a certain class of next-to-planar Feynman integrals possess a bonus symmetry that is closely related to dual conformal symmetry. It corresponds to a projection of the latter along a certain lightlike direction. Previous studies were performed at the level of the loop integrand, and a Ward identity for the integral was formulated. We investigate the implications of the symmetry at the level of the integrated quantities. In particular, we focus on the phenomenologically important case of five-particle scattering. The symmetry simplifies the four-variable problem to a three-variable one. In the context of the recently proposed space of pentagon functions, the symmetry is much stronger. We find that it drastically reduces the allowed function space, leading to a well-known space of three-variable functions. Furthermore, we show how to use the symmetry in the presence of infrared divergences, where one obtains an anomalous Ward identity. We verify that the Ward identity is satisfied by the leading and subleading poles of several nontrivial five-particle integrals. Finally, we present examples of integrals that possess both ordinary and dual conformal symmetry.