Chiral three-nucleon force at N^4LO I: Longest-range contributions

TL;DR

This paper derives the longest-range contributions to the three-nucleon force at N^4LO in chiral effective field theory, analyzing pion-nucleon scattering to determine low-energy constants and discussing the convergence of the chiral expansion.

Contribution

It provides the derivation of sub-subleading two-pion exchange three-nucleon forces at N^4LO and determines relevant low-energy constants using pion-nucleon scattering data.

Findings

Derived the N^4LO three-nucleon force contributions.

Analyzed the convergence of the chiral expansion.

Provided low-energy constants for realistic three-nucleon force modeling.

Abstract

We derive the sub-subleading two-pion exchange contributions to the three-nucleon force which appear at next-to-next-to-next-to-next-to-leading order in chiral effective field theory. In order to determine the low-energy constants, a complete analysis of pion-nucleon scattering at the subleading-loop order in the heavy-baryon expansion is carried out utilizing the power counting scheme employed in the derivation of the nuclear forces. We discuss the convergence of the chiral expansion for this particular three-nucleon force topology and give the values of the low-energy constants which provide the most realistic description of the three-nucleon force when the chiral expansion is truncated at next-to-next-to-leading order.