Chiral three-nucleon force at N^4LO II: Intermediate-range contributions

TL;DR

This paper derives subleading contributions to three-nucleon forces in chiral effective field theory at N^4LO, analyzing their structure and impact on convergence, with a focus on intermediate-range interactions and the role of Delta(1232) excitations.

Contribution

It provides the first complete derivation of subleading two-pion-one-pion exchange and ring three-nucleon force contributions at N^4LO without unknown parameters, and develops a comprehensive operator basis for local three-nucleon forces.

Findings

Subleading contributions are large, indicating significant intermediate-range effects.

The operator basis consists of 22 independent structures for local three-nucleon forces.

Convergence of the chiral expansion is analyzed through potential comparisons.

Abstract

We derive the subleading contributions to the two-pion-one-pion exchange and ring three-nucleon force topologies emerging at next-to-next-to-next-to-next-to-leading order in chiral effective field theory. The resulting expressions do not involve any unknown parameters. To study convergence of the chiral expansion we work out the most general operator structure of a local isospin-invariant three-nucleon force. Using the resulting operator basis with 22 independent structures, we compare the strength of the corresponding potentials in configuration space for individual topologies at various orders in the chiral expansion. As expected, the subleading contributions from the two-pion-one-pion-exchange and ring diagrams are large which can be understood in terms of intermediate excitation of the Delta(1232) isobar.