Spin dependence of high energy proton scattering

Motivated by the need for an absolute polarimeter to determine the beam polarization for the forthcoming BNL RHIC spin program, we study the spin dependence of the proton-proton elastic scattering amplitudes at high energy and small momentum transfer. In particular, we examine experimental evidence for the existence of an asymptotic part of the helicity-flip amplitude ${\phi }_5$ which is not negligible relative to the largely imaginary average nonflip amplitude ${\phi }_{+}=\frac{1}{2}({\phi }_1+{\phi }_3).\mathrm{}$ We discuss theoretical estimates of $r_5=m{\phi }_5/\sqrt{-t}\mathrm{Im}{\phi }_{+}$ based upon several approaches: extrapolation of low and medium energy Regge phenomenological results to high energies, models based on a hybrid of perturbative QCD and nonrelativistic quark models, and models based on eikonalization techniques. We also apply the rigorous, model-independent methods of analyticity and unitarity. We find the preponderence of evidence at currently available energy indicates that $r_5$ is small, probably less than 10%. The best available experimental limit comes from Fermilab E704: combined with rather weak theoretical assumptions those data indicate that $|r_5|<15\%.\mathrm{}$ These bounds are important because rigorous methods allow much larger values. Furthermore, in contradiction to a widely held prejudice that $r_5$ decreases with energy, general principles allow it to grow as fast as $\ln s$ asymptotically, and some of the models we consider show an even faster growth in the RHIC range. One needs a more precise measurement of $r_5$ or to bound it to be smaller than 5% in order to use the classical Coulomb-nuclear interference technique for RHIC polarimetry. Our results show how important the measurements of spin dependence at RHIC will be to our understanding of proton structure and scattering dynamics. As part of this study, we demonstrate the surprising result that proton-proton elastic scattering is self-analyzing, in the sense that all the helicity amplitudes can, in principle, be determined experimentally at small momentum transfer without a knowledge of the magnitude of the beam and target polarization.