A high-intensity pulsed muon beam is becoming available at the at the Japan Proton Accelerator Research Complex (J-PARC). Many experiments to study fundamental physics using this high-intensity muon beam are proposed. An experiment to measure the muon magnetic moment anomaly ($g-2$) and the muon electric dipole moment (EDM) is one of these experiments and it requires a tracking detector for positrons from muon decay. Fine segmentation is required in a detector to tolerate the high rate of positrons. The time resolution is required to be much better than the muon anomalous spin precession period while a buffer depth of a front-end electronics needs to be much longer than the accelerated muon lifetime. Requirements of this detector also meet requirements of a measurement of the muonium hyperfine structure interval at the J-PARC and another experiment to measure the proton charge radius at Tohoku University. We have developed a single-sided silicon strip sensor with a 190 $mu$m pitch, a front-end electronics with a sampling rate of 200 MHz and a buffer memory depth of 8192, and a data acquisition system based on DAQ-Middleware for the J-PARC muon $g-2$/EDM experiment. We have fabricated detector modules consisting of this sensor and the front-end electronics. Performance of fabricated detector modules was evaluated at a laboratory and a beam test using the positron beam at Tohoku University. The detector is confirmed to satisfy all requirements of the experiments except for the time walk, which will be solved by the next version of a front-end electronics.
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