Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory

TL;DR

This paper examines the differences between chiral and pionless effective field theories for nucleon interactions, concluding that a three-nucleon contact term is essential at leading order and that fewer low energy constants may suffice.

Contribution

It demonstrates the necessity of including a three-nucleon contact term at leading order in both theories and suggests that a single low energy constant could explain scattering lengths.

Findings

A three-nucleon contact term is required at LO in both theories.

Subleading three-nucleon contact terms should be promoted to lower orders.

A single low energy constant may account for large scattering lengths.

Abstract

In chiral effective field theory the leading order (LO) nucleon-nucleon potential includes two contact terms, in the two spin channels $S=0,1$, and the one-pion-exchange potential. When the pion degrees of freedom are integrated out, as in the pionless effective field theory, the LO potential includes two contact terms only. In the three-nucleon system, the pionless theory includes a three-nucleon contact term interaction at LO whereas the chiral effective theory does not. Accordingly arbitrary differences could be observed in the LO description of three- and four-nucleon binding energies. We analyze the two theories at LO and conclude that a three-nucleon contact term is necessary at this order in both theories. In turn this implies that subleading three-nucleon contact terms should be promoted to lower orders. Furthermore this analysis shows that one single low energy constant might be sufficient to explain the large values of the singlet and triplet scattering lengths.