Gas Electron Multiplier Detectors for TREK at J-PARC

Lepton flavor universality is a basic assumption of the Standard Model (SM). The proposed experiment E36 at J-PARC in Japan measures decay widths of stopped $K^{+}$ using the TREK (Time Reversal Experiment with Kaons) detector system to conduct precision measurements of $R_{K}=\Gamma(K^{+}\rightarrow e^{+}\nu)/\Gamma(K^{+}\rightarrow\mu^{+}\nu)$ in search of lepton flavor universality violation. The SM prediction for the ratio of leptonic $K^{+}$ decays is highly precise with an uncertainty of $\bigtriangleup R_{K} /R_{K} = 4\cdot10^{-4}$. Any observed deviation from the SM prediction would yield clear indication of New Physics beyond the Standard Model. To test lepton flavor universality violation a total uncertainty for the decay ratio of $K_{e2}/K_{\mu2}$ is aimed to be $0.25\%$ ($0.20\%$ stat$+ 0.15\%$ sys). The second portion of the experiment searches for heavy sterile neutrinos (N) in the $K^{+}\rightarrow\mu^{+}N$ decay and allows for further stringent searches for light new particles as a byproduct. Gas Electron Multiplier (GEM) detectors will be constructed for this experiment in order to measure charged tracks of $\mu^{+}$ and $e^{+}$ from charged $K^{+}$ decay. I will present Geant4 simulations of the TREK setup augmented with the GEM detectors.