Measurement of the $t$-dependence for the Beam Asymmetry of Photoproduced $\eta$ Mesons at GlueX

We report on the photoproduction of $\eta$ mesons studied at the GlueX experiment at Thomas Jefferson National Laboratory in Newport News, VA. A linearly polarized photon beam at energies between 8.2 and 8.8 GeV, incident on a liquid hydrogen target, produces $\eta$ dominantly through $t$-channel exchanges. Azimuthal angular distributions of the $\eta$, with respect to the direction of the polarized photon facilitate the extraction of the beam asymmetry $\Sigma$ for the reaction $\vec\gamma p \rightarrow \eta p$. We can understand the production mechanisms of the $\eta$ by analyzing $\Sigma_\eta$, which is sensitive to the particles exchanged. Compared to previous GlueX results [1,2], we have access to six times the statistics, thereby allowing us to extend these measurements to values beyond the previous limitation of $-t \leq$ 1.1 (GeV/$c$)$^2$. Preliminary results will be shown for events reconstructed from the decay of $\eta \rightarrow \gamma \gamma$. [1] S.~Adhikari {\it et al.} [GlueX Collaboration],Phys.\ Rev.\ C {\bf 100}, no. 5, 052201 (2019) [2] H.~Al Ghoul \textit{et al.} [GlueX Collaboration], Phys. Rev. C \textbf{95}, no. 4, 042201 (2017)