Three-nucleon forces in the 1/Nc expansion

TL;DR

This paper classifies three-nucleon force operators within the 1/Nc expansion, showing consistency with phenomenological models and providing a comprehensive operator basis up to next-to-leading order.

Contribution

It provides a systematic classification of three-nucleon force operators in the 1/Nc expansion and explicitly constructs a complete basis up to next-to-leading order.

Findings

Leading order includes spin-flavor independent and Fujita-Miyazawa structures.

Corrections are suppressed by 1/Nc^2.

Complete operator basis provided up to next-to-leading order.

Abstract

The operator structures that can contribute to three-nucleon forces are classified in the 1/Nc expansion. At leading order in 1/Nc a spin-flavor independent term is present, as are the spin-flavor structures associated with the Fujita-Miyazawa three-nucleon force. Modern phenomenological three-nucleon forces are thus consistent with this O(Nc) leading force, corrections to which are suppressed by a power series in 1/Nc^2. A complete basis of operators for the three-nucleon force, including all independent momentum structures, is given explicitly up to next-to-leading order in the 1/Nc expansion.