Poincar\'e Constraints on Celestial Amplitudes

TL;DR

This paper explores how Poincaré symmetry constrains celestial amplitudes for massless and massive particles, deriving functional relations and solving specific cases, including a new gluon three-point coefficient.

Contribution

It derives and solves recurrence relations for celestial amplitudes constrained by Poincaré symmetry, providing new explicit coefficients and insights into their structure.

Findings

Recurrence relations for celestial amplitudes are established.

Explicit solutions for three-point functions involving massive scalars are obtained.

A new three-point gluon coefficient in Minkowski signature is derived.

Abstract

The functional structure of celestial amplitudes as constrained by Poincar\'e symmetry is investigated in $2,3,$ and $4$-point cases for massless external particles of various spin, as well as massive external scalars. Functional constraints and recurrence relations are found (akin to the findings in arXiv:1901.01622) that must be obeyed by the respective permissible correlator structures and function coefficients. In specific three-point cases involving massive scalars the resulting recurrence relations can be solved, e.g. reproducing purely from symmetry a three-point function coefficient known in the literature. Additionally, as a byproduct of the analysis, the three-point function coefficient for gluons in Minkowski signature is obtained from an amplitude map to the celestial sphere.