The $\eta$-meson photoproduction off a helium nucleus and off quasi-free nucleons at GlueX.

The PrimEx-eta experiment at Jefferson Lab is aiming to measure the radiative decay width of the $\eta$-meson with a 3.2$\%$ precision via the Primakoff effect from the $\eta$-meson photoproduction

  off a helium nucleus. The produced $\eta$-meson can be reconstructed by detecting either $\eta \to 2\gamma$ or $\eta \to 3\pi$ decays. The particularly long distance between the target and the Forward Calorimeter gives rise to an irreducible background produced along the beam-line for the decay $\eta \to 2\gamma$

  which is strongly suppressed or not present for the decays $\eta \to 3\pi$. Therefore, reconstructing $\eta$-meson from these two decay channels will help controlling the experimental systematics of

  the differential cross-section measurement for the coherent $\eta$-meson photoproduction off the He target at very forward polar angles where the Primakoff peak is expected. In addition, a large

  $\eta$-meson data sample from photoproduction off a helium nucleus and off quasi-free nucleons will allow a precision measurement of the $\eta \to 3\pi$ Dalitz distribution, which will improve

  light-quark mass ratio determination and search for new CP violation beyond the standard model. The first run was performed with the GlueX experimental setup in Hall D in 2019 and the second run in

  fall 2021 with the same setup but with the GlueX solenoid turn on. We will discuss the status of experiment and data analysis.