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We performed a novel Σ+ p scattering experiment at the J-PARC Hadron Experimental Facility. Approximately 2400 Σ+ p elastic scattering events were identified from 4.9 × 107 tagged Σ+ particles in the Σ+ momentum range 0.44–0.80 GeV/ c. The differential cross sections of the Σ+ p elastic scattering were derived with much better precision than in previous experiments. The obtained differential cross sections were approximately 2 mb/sr or less, which were not as large as those predicted by the fss2 and FSS models based on the quark cluster model in the short-range region. By performing phase-shift analyses for the obtained differential cross sections, we experimentally derived the phase shifts of the 3 S 1 and 1 P 1 channels for the first time. The phase shift of the 3 S 1 channel, where a large repulsive core was predicted owing to the Pauli effect between quarks, was evaluated as |$20^\circ \lt |\delta _{^3S_1}|\lt 35^\circ$|⁠. If the sign of |$\delta _{^3S_1}$| is assumed to be negative, the interaction in this channel is moderately repulsive, as the Nijmegen extended-sort-core models predicted. [ABSTRACT FROM AUTHOR]