Nucleon-nucleon scattering matrix and its Nc scaling

TL;DR

This paper investigates how the nucleon-nucleon scattering matrix scales with Nc in large Nc QCD, proposing a proportional relationship between the logarithm of the S-matrix elements and Nc, supported by theoretical and heuristic arguments.

Contribution

It introduces a scaling law for the nucleon-nucleon S-matrix in large Nc QCD, extending previous potential models to more realistic scattering scenarios.

Findings

Logarithm of S-matrix scales with Nc

Scaling derived from potential models applies to realistic scattering

Heuristic arguments support the proposed Nc scaling

Abstract

This paper focuses on the scaling of the S-matrix for elastic nucleon-nucleon scattering at large Nc. It is argued that the logarithm of a typical S-matrix element is proportional to Nc in the regime where the large Nc limit is taken with momentum of the incident nucleons proportional Nc. The suggested scaling was previously derived within the framework of potential scattering models for purely elastic scattering in which the parameters scale the same way as in large Nc QCD. A variety of heuristic arguments strongly suggest that the same scaling holds in the realistic case where both elastic and inelastic scattering are possible.