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This§theses reports on an experimental search for an exotic hadron, _ + (1540)§pentaquark, which is a genuine exotic hadron with a five-quark system of uudds bar . The§results of this book support that the existence of _ + was§strongly constrained.§§The _ + pentaquark was searched for via the _ - p _ K - X§reaction using a beam momentum of 2.01 GeV/c at the J-PARC hadron experimental§facility, taking advantage of high-statistics and high-resolution compared with§previous experiments, some of which claimed the evidence of _ + . In§order to realize a good missing-mass resolution of 2 MeV, the beam spectrometer§and superconducting kaon spectrometer were constructed.§§No clear peak was observed in the missing mass spectrum of the _ - p _ K - X§reaction, and the upper limit of the production cross section was found to be§less than 0.28 _b/sr at the 90% confidence level in a mass region of§1500-1560 MeV/c 2 . This upper limit is an order of magnitude smaller§than that of the previous KEK experiment. Compared with a theoretical§calculation using the effective Lagrangian approach, the decay width of _ + was§evaluated. The upper limits on the decay width were estimated to be 0.36 and§1.9 MeV for the _ + spin-parity of 1/2 + and 1/2 - ,§respectively. These are quite small for a width of ordinary hadron resonances,§and the existence of _ + was strongly constrained and is§doubtful.§§