Measurements of single and double spin asymmetry in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mi>p</mml:mi></mml:math>elastic scattering in the CNI region with a polarized atomic hydrogen gas jet target

Precise measurements of the single spin asymmetry ${A}_{N}$, and the double spin asymmetry ${A}_{NN}$, in proton-proton ($pp$) elastic scattering in the region of four-momentum transfer squared $0.001&lt;\ensuremath{-}t&lt;0.032\text{ }\text{ }(\mathrm{GeV}/c{)}^{2}$ have been performed using a polarized atomic hydrogen gas jet target and the Relativistic Heavy Ion Collider (RHIC) polarized proton beam. We present measurements of ${A}_{N}$ and ${A}_{NN}$ at center-of-mass energies $\sqrt{s}=6.8$ and 13.7 GeV. These spin-dependent observables are sensitive to the poorly known hadronic spin-dependent amplitudes. Comparing ${A}_{N}$ at different energies, a $\sqrt{s}$ dependence of the hadronic single spin-flip amplitude is suggested. A hadronic double spin-flip amplitude from the ${A}_{NN}$ data is consistent with zero within a 2-$\ensuremath{\sigma}$ level. We also present $\ensuremath{\Delta}{\ensuremath{\sigma}}_{T}$, estimated from the measured ${A}_{NN}$ data. The results for $\ensuremath{\Delta}{\ensuremath{\sigma}}_{T}$ are consistent with zero. Our results provide significant constraints toward a comprehensive understanding of the reaction mechanism for $pp$ elastic scattering.