  Motivated by the need for an absolute polarimeter to determine the beam
polarization for the forthcoming RHIC spin program, we study the spin
dependence of the proton-proton elastic scattering amplitudes at high energy
and small momentum transfer.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 non-flip amplitude phi_+.
We discuss theoretical estimates of r_5, essentially the ratio of phi_5 to
phi_+, based upon extrapolation of low and medium energy Regge phenomenological
results to high energies, models based on a hybrid of perturbative QCD and
non-relativistic quark models, and models based on eikonalization techniques.
We also apply the model-independent methods of analyticity and unitarity.The
preponderence of evidence at available energy indicates that r_5 is small,
probably less than 10%. The best available experimental limit comes from
Fermilab E704:those data indicate that |r_5|<15%. These bounds are important
because rigorous methods allow much larger values. 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 models 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. As part of this study, we
demonstrate the surprising result that proton-proton elastic scattering is
self-analysing, 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.
