Studies comparing $\pi^0 \eta$ and $\pi^0 \eta'$ systems in search for exotic hybrid mesons at GlueX

In the search for exotic hybrid mesons at the GlueX experiment, located at Thomas Jefferson National Laboratory, a strong interest has been placed on both the $\pi^0 \eta$ and $\pi^0 \eta'$ systems because of their possibility of containing non quark-antiquark (exotic) quantum numbers due to the systems' odd angular momentum $L$. By comparing both of these channels, the role of flavor symmetry could also be highlighted, allowing for a better understanding of meson production mechanisms. In this talk, preliminary results, including angular distribution analyses and double Regge exchange analyses (i.e. non-resonant Deck processes), for $\gamma p \rightarrow \pi^0 \eta^{(')}p \rightarrow 4\gamma \pi^+ \pi^- p$ will be shown utilizing all of the GlueX Phase-1 data and comparing the observations to previous experimental (COMPASS) and theoretical (JPAC) results of the same channels.