Beam Asymmetry in $\gamma$ p $\rightarrow$ $\eta$ $\Delta^+$ at GlueX

The photoproduction mechanism studied in the GlueX experiment by impinging an 8.2-8.8 GeV linearly polarized photon beam on a liquid hydrogen target allows for the mapping of light mesons in unprecedented detail with particular interest in exotic meson candidates. Polarization observable such as beam asymmetry $\Sigma$ is extracted from azimuthal ($\phi$) angular distribution between the meson production plane and the polarized photon beam. Beam asymmetry $\Sigma$ will help understand and constraint quasi-particle t-channel exchange processes using Regge theory. We report preliminary results on the beam asymmetry measurements for $\eta$ in $\gamma$ p $\rightarrow$ $\eta$ $\Delta^+$. This reaction with a recoiling $\Delta^+$ will allow for comparison and validation of theoretical calculations and provide additional validation of the $\eta$ asymmetry with a recoiling proton. The differing isospin of the $\Delta^+$ imposes added restrictions that further constrain allowed Regge exchanges. Understanding the exchange mechanisms is a crucial ingredient in establishing new photoproduced light meson states.