Bounds in proton-proton elastic scattering at low momentum transfer

Abstract

We present a bound on the imaginary part of the single helicity-flip amplitude for spin 1/2-spin 1/2 scattering at small momentum transfer. The variational method of Lagrange multipliers is employed to optimize the single-flip amplitude using the values of the total cross section, the elastic cross section and diffraction slope as equality constraints in addition to the inequality constraints resulting from unitarity. Such bounds provide important information related to the determination of polarization of a proton beam. In the case of elastic proton collisions the analyzing power at small scattering angles inside the Coulomb Nuclear Interference region offers a method of measuring the polarization of a proton beam, the accuracy of the polarization measurement depending on the single helicity-flip amplitude. The bound obtained on the imaginary part of the single helicity-flip amplitude indicates that the analyzing power for proton-proton collisions in the Coulomb nuclear interference region should take positive nonzero values at high energies.