  We performed a novel $\Sigma^+ p$ scattering experiment at the J-PARC Hadron
Experimental Facility. Approximately 2400 $\Sigma^+ p$ elastic scattering
events were identified from $4.9 \times 10^7$ tagged $\Sigma^+$ particles in
the $\Sigma^+$ momentum range 0.44 -- 0.80 GeV/$c$. The differential cross
sections of the $\Sigma^+ p$ 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 $20^\circ<|\delta_{^3S_1}|<35^\circ$.
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.
