Precise Measurement of $\Gamma(K^+\rightarrow e^+\nu)/\Gamma(K^+\rightarrow \mu^+\nu)$ and Search for New Physics by the TREK-E36 Experiment

The J-PARC TREK-E36 experiment will provide a precise measurement of the ratio of decay widths $R_K=\Gamma(K^+\rightarrow e^+\nu)/\Gamma(K^+\rightarrow \mu^+\nu)$ to test lepton universality. $R_K$ is very precisely predicted by the Standard Model (SM) with the uncertainty of $4\times10^{-4}$ and a deviation from the prediction would very clearly indicate the existence of New Physics beyond the SM. Additionally, the experiment intends to search for visible decay modes of $A^{'}\rightarrow e^+e^-$ in $K^+$ decays. The existence of an $A^{'}$ is well motivated by dark matter observations and $g_{\mu}$-2 anomaly, as well as the proton radius puzzle. In the E36 experiment, a $K^+$ beam was stopped by a scintillating fiber target, and charged decay products were momentum analyzed and tracked by a 12-sector superconducting toroidal magnet spectrometer and multi-wire proportional chambers combined with a photon calorimeter with a large solid angle (75\% of $4\pi$) and 3 different particle identification systems. In this talk, the status of the data analysis is presented. This work has been supported by the U.S. DOE Award DE-SC0013941.