Three-nucleon force at large distances: Insights from chiral effective field theory and the large-N_c expansion

TL;DR

This paper confirms a minimal operator set for three-nucleon forces, derives relations between different operator representations, and discusses their chiral and large-N_c expansions up to high order, enhancing understanding of nuclear interactions.

Contribution

It provides explicit relations between operator sets and analyzes the three-nucleon force using chiral effective field theory and large-N_c expansion, extending previous work.

Findings

20 operators suffice for local isospin-invariant three-nucleon forces

Derived explicit relations between different operator representations

Analyzed the chiral expansion up to N4LO without explicit Delta degrees of freedom

Abstract

We confirm the claim of Ref. [D.R. Phillips, C. Schat, Phys. Rev. C88 (2013) 3, 034002] that 20 operators are sufficient to represent the most general local isospin-invariant three-nucleon force and derive explicit relations between the two sets of operators suggested in Refs. [D.R. Phillips, C. Schat, Phys. Rev. C88 (2013) 3, 034002] and [H. Krebs, A.M. Gasparyan, E. Epelbaum, Phys.Rev. C87 (2013) 5, 054007]. We use the set of 20 operators to discuss the chiral expansion of the long- and intermediate-range parts of the three-nucleon force up to next-to-next-to-next-to-next-to-leading order in the standard formulation without explicit Delta(1232) degrees of freedom. We also address implications of the large-N_c expansion in QCD for the size of the various three-nucleon force contributions.