Spin-Spin Interactions in High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>⊥</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Elastic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mi>p</mml:mi></mml:math>Scattering

We measured $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ for $p+p\ensuremath{\rightarrow}p+p$ at 11.75 GeV/c using the zero-gradient synchrotron 70% polarized-proton beam and a 65% polarized-proton target. We obtained the spin-orbit asymmetry parameter $A$ and the spin-spin correlation parameter ${C}_{m}$ out to ${{P}_{\ensuremath{\perp}}}^{2}=4.2$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. We found that $A$ drops smoothly towards zero, but that ${C}_{\mathrm{nn}}$ increases abruptly near ${{P}_{\ensuremath{\perp}}}^{2}=3.6$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, where the $\mathrm{exp}(\ensuremath{-}1.4{{P}_{\ensuremath{\perp}}}^{2})$ component of elastic scattering becomes dominant. This suggests that large-${{P}_{\ensuremath{\perp}}}^{2}$ "hard" elastic scattering may occur mostly when the two proton spins are parallel.