Precise measurement of the $K_{e2}/K_{{\mu}2}$ branching ratio and   search for new physics beyond the Standard Model
  The E36 experiment recently conducted at J-PARC by the TREK Collaboration will provide a precise mesurement of the decay ratio $ R_K = \Gamma(K^+ \rightarrow e^+\nu_e) / \Gamma(K^+ \rightarrow \mu^+\nu_{\mu}) $ with the aim of testing lepton universality, a basic assumption of the Standard Model (SM). The SM prediction for the decay ratio $R_K$ is highly precise ($\delta R_K / R_K = 4 \times 10^{-4}$) and any observed deviation from this prediction would clearly indicate the existence of new physics. The E36 experimental apparatus, designed to offer small systematic errors, was installed at the J-PARC K1.1BR kaon beam line in the fall of 2014, fully commissioned in the spring of 2015, and the production data were collected in the fall of 2015. A scintillating fiber target was used to stop a beam of $1.2 \times 10^6 K^+$ per spill. The $K^+$ decay products were then momentum analyzed by a 12-sector superconducting toroidal spectrometer and charged particles were tracked with high precision by Multi-Wire Proportional Chambers (MWPC) combined with a photon calorimeter with a large solid angle ($75\%$ of $4\pi$) and 3 different particle identification systems. Details of the E36 experimental apparatus, as well as the status of the data analysis will be presented. 
S\'ebastien Bianchin (on behalf of the TREK/E36 Collaboration)
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