Search for light neutral bosons in the TREK/E36 experiment

The TREK/E36 (E36) experiment conducted at J-PARC in Japan aims to test lepton universality in the ratio of decay widths, $R_{K} = \Gamma(K_{e2})/\Gamma(K_{\mu2})$, by utilizing a scintillating fiber target to stop a beam of up to 1.2 million $K^+$ per spill. In addition, the E36 detector system allows us to search for light $U(1)$ gauge bosons below 300 MeV/$c^2$, which could be associated with dark matter or explain the established muon-related anomalies such as the muon $g-2$ value, and the proton radius puzzle. Particle identification systems in combination with a highly segmented CsI(Tl) photon calorimeter covering $75\%$ of $4\pi$ are being used to search for these exotic particles in rare $K^+$ decay modes. The status of the particle search as well as simulation based exclusion limits will be presented.