Total nucleon-nucleon cross sections in large N(c) QCD

TL;DR

This paper derives model-independent relations between proton-proton and proton-neutron total cross sections in large Nc QCD, valid in the semi-classical regime, and compares these theoretical predictions with experimental data.

Contribution

It introduces a large Nc QCD-based formalism to relate nucleon-nucleon cross sections, providing semi-quantitative predictions without relying on specific interaction models.

Findings

Relation for unpolarized scattering agrees well with data

Polarized scattering relations are consistent but less precise

Formalism applicable in semi-classical high-momentum regime

Abstract

We use contracted spin-flavor symmetry which emerges in the large Nc 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 semi-classical 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 Nc=3 is sufficiently large so that the large Nc results have at least semi-quantitative predictive power. The relations are model-independent in the sense that they depend on properties of large Nc QCD only and not on any particular model-dependent details of the nucleon-nucleon interaction. We compare these model-independent results to experimental data. We find the relation for spin-unpolarized scattering works well empirically. For the case of polarized scattering, the data is consistent with the relations but the cross sections are too small to make sharp predictions.