# Moments of angular distribution and beam asymmetries in $\eta\pi^0$ photoproduction at GlueX

## TL;DR

This paper develops a formalism and model for analyzing angular distribution moments and beam asymmetries in eta-pi0 photoproduction with linearly polarized photons, aiming to detect exotic mesons.

## Contribution

It generalizes moment extraction and beam asymmetry definitions for two-meson photoproduction, enhancing sensitivity to exotic P-wave resonances.

## Key findings

- Moments of odd angular momentum are sensitive to P-wave interference.
- Beam asymmetry with perpendicular meson momenta enhances P-wave detection.
- Model includes resonant S-, P-, D-waves produced by natural exchanges.

## Abstract

In the search for exotic mesons, the GlueX collaboration will soon extract moments of the $\eta\pi^0$ angular distribution. In the perspective of these results, we generalize the formalism of moment extraction to the case in which the two mesons are produced with a linearly polarized beam, and build a model for the reaction $\vec \gamma p \to \eta \pi^0 p$. The model includes resonant $S$-, $P$-, $D$-waves in $\eta\pi^0$, produced by natural exchanges. Moments of the $\eta\pi^0$ angular distribution are computed with and without the $P$-wave, to illustrate the sensitivity to exotic resonances. Although little sensitivity to the $P$-wave is found in moments of even angular momentum, moments of odd angular momentum are proportional to the interference between the $P$-wave and the dominant $S$- and $D$-waves. We also generalize the definition of the beam asymmetry for two mesons photoproduction and show that, when the meson momenta are perpendicular to the reaction plane, the beam asymmetry enhances the sensitivity to the exotic $P$-wave.