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 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], the 2018 run period produced approximately 3-4 times more statistics, thereby allowing 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 $\eta \rightarrow \pi^{+} \pi^{-} \pi^{0}$. [1] S. Adhikari {\it et al}. [GlueX Collaboration], Phys. Rev. C {\bf 100}, no. 5, 052201 (2019). [2] P.~Collins {\it et al.} [CLAS Collaboration], Phys.\ Lett.\ B {\bf 771}, 213 (2017).