We use contracted spin-flavor symmetry which emerges in the large $N_c$ limit of QCD to obtain relations between proton-proton and proton-neutron total cross sections for both polarized and unpolarized scattering. The formalism used is valid in the semiclassical regime in which the relative momentum of the incident nucleons is much larger than the inverse size of the nucleon, provided that certain technical assumptions are met. The relations should be phenomenologically useful provided that $N_c=3$ is sufficiently large so that the large $N_c$ results have at least semiquantitative predictive power. The relations are model independent in the sense that they depend on properties of large $N_c$ QCD only and not on any particular model-dependent details of the nucleon-nucleon interaction. We compare these model-independent results to the experimental data. We find the relation for spin-unpolarized scattering works well empirically. For the case of polarized scattering, the data are consistent with the relations, but the cross sections are too small to make sharp predictions.

• Received 21 November 2011

DOI:https://doi.org/10.1103/PhysRevC.85.024001