Scrutiny of the new class of three-nucleon forces

TL;DR

This paper critically examines recent claims about enhanced three-nucleon forces involving short-range operators, analyzing their scheme dependence and impact on nuclear matter properties within chiral effective field theory.

Contribution

It provides a detailed analysis of the scheme dependence of three-nucleon forces and assesses their actual impact on nuclear matter, challenging previous assertions of enhancement.

Findings

Short-range 3NFs yield small contributions after scheme-dependent components are removed.

Comparison with pion-exchange diagrams supports standard power counting expectations.

Estimated effects on nuclear matter properties align with traditional chiral EFT predictions.

Abstract

In a recent publication, Cirigliano {\it et al.} [Phys. Rev. Lett. 135, 022501 (2025)] argue that three-nucleon forces (3NFs) involving short-range operators that couple two pions with two nucleons are enhanced beyond what is expected in chiral effective field theory based on naive dimensional analysis. Here, we scrutinize the arguments and conclusions of that paper by taking into account renormalization scheme dependence of the corresponding low-energy constants. We gain further insights into the expected impact of these 3NFs by comparing them with contributions of similar type, induced by pion-exchange diagrams at lower orders in the chiral expansion. We also estimate the impact of these 3NFs on properties of nuclear matter. After removal of scheme-dependent short-distance components in pion loops, the 3NFs considered by Cirigliano {\it et al.} are shown to yield reasonably small contributions to the equation of state of neutron and symmetric nuclear matter in agreement with expectations based on Weinberg's power counting.