Moments of Angular Distributions in Photoproduced η^(')π⁰→4γ at GlueX

Exotic hybrid mesons are postulated within the framework of Quantum Chromodynamics (QCD) as composition of a quark-antiquark pair with explicit gluonic field excitation. The lightest hybrid meson candidate, called π₁(1600), is established primarily through hadron production and its mass aligns with recent lattice QCD predictions. GlueX, a photoproduction experiment utilizing a linearly polarized photon beam impinging on a liquid hydrogen target, is built with primary physics goal to map the spectrum of light exotic hybrid mesons. The research presented here focuses on the study of two-pseudoscalar meson systems, ηπ⁰→4γ and η'π⁰→4γ, as they provide golden channels that are experimentally accessible to observe π₁. Partial Wave Analysis (PWA) is widely used to describe the angular distribution of meson systems by determining partial wave amplitudes, which represent the contributions of spin angular momentum. However, PWA may leads to ambiguous solutions due to under-constrained equations. Moment Analysis, as an alternative approach, ensures unique solutions by decomposing intensity into spherical harmonics. In this talk, we present the preliminary results of the first moments measured in ηπ⁰ and η'π⁰ produced in polarized photon-proton collisions, shedding new light on the angular distributions of these systems and their potential role in identifying the presence of π₁ hybrid meson.