The spin dependence of high energy proton scattering

TL;DR

This paper investigates the spin dependence of high-energy proton-proton elastic scattering amplitudes, focusing on the helicity-flip amplitude, to improve the understanding of polarization measurements at RHIC.

Contribution

It provides a comprehensive analysis of the asymptotic behavior of the helicity-flip amplitude and demonstrates that proton-proton elastic scattering can be self-analysing for polarization measurements.

Findings

r_5 is likely less than 10% at high energies

Experimental bounds on |r_5| are below 15% from Fermilab E704

Proton-proton elastic scattering can determine all helicity amplitudes without polarization knowledge

Abstract

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.