A Measurement of the Eta Meson Radiative Decay Width via the Primakoff Effect

The $\eta$ meson is an interesting tool to study fundamental symmetries in Quantum Chromodynamics (QCD). In particular, its radiative decay width, $\Gamma\left(\eta\rightarrow\gamma\gamma\right)$, is an important quantity that can be predicted in the framework of Chiral Perturbation Theory. A precision measurement of this quantity would provide critical inputs to understanding the mixing of the $\eta$ and $\eta'$ mesons and extracting constants with wide-ranging applications in low-energy QCD. This decay width has been measured in the past using two different experimental techniques. The more popular technique utilized $e^{+}e^{-}$ collisions to produce $\eta$ mesons through electromagnetic interactions. Today, the Particle Data Group (PDG) averages the results of five such experiments to obtain their currently-accepted value of the decay width as: 0.515$\pm$0.018~keV. However the first measurement of this quantity was obtained from a fixed-target experiment that measured the cross section for photoproduction of $\eta$ mesons on a nuclear target via the Primakoff effect. Their result of 0.324$\pm$0.046~keV shows strong tension with the average of the collider measurements, motivating a new, high precision measurement using the Primakoff method.

For this purpose, the PrimEx-\textit{eta} experiment was conducted in Hall D of the Thomas Jefferson National Accelerator Facility (Jefferson Lab or JLab). The data is currently being analyzed to measure the differential cross section for the photoproduction of $\eta$ mesons on a liquid, $^{4}$He target. Preliminary results obtained from the analysis of the first phase of the PrimEx-\textit{eta} experiment show reasonable agreement with the currently-accepted PDG value of the radiative decay width. However, as will be discussed, there are many challenges to this precision measurement which must be studied before any results can be finalized and compared with previous measurements.

In parallel to the $\eta$ decay width measurement, the PrimEx-\textit{eta} experiment measured the total cross section for the fundamental, Quantum Electrodynamics (QED) process of Compton scattering from the atomic electrons inside the target. The results obtained from this measurement are in strong agreement with the next-to-leading order QED calculations, and the total combined uncertainties are below 3\% for incident photon energies between 7-10~GeV. In addition to providing the first precision measurement of the total Compton scattering cross section within this beam energy range, this measurement verifies the capability of the PrimEx-\textit{eta} experimental setup to perform absolute cross section measurements at forward angles, and serves as a reference process for the calibration of systematic uncertainties.