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. These particles are produced by a linearly polarized photon beam at energies between 8.2 and 8.8 GeV incident on protons in a liquid hydrogen target. Azimuthal ($\phi$) angular distributions 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 $. $\Sigma$ is derived as a function of four-momentum transfer $-t$. Compared with previous GlueX results [1,2,3], the 2018 run period produced approximately 3-4 times more 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 decays of $\eta \rightarrow \pi^{+} \pi^{-} \pi^{0} $ and $\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],Phys. Rev. C \textbf{95}, no.4, 042201 (2017) [3] P.~Collins {\it et al.} [CLAS Collaboration],Phys.\ Lett.\ B {\bf 771}, 213 (2017)