Two-pion exchange as a leading-order contribution in chiral effective field theory

TL;DR

This paper demonstrates that including two-pion exchange and contact terms in chiral effective field theory leads to accurate, renormalization group invariant phase shifts in nucleon-nucleon interactions, especially in the $^1S_0$ partial wave.

Contribution

It introduces a leading-order potential with TPE and contact terms that systematically improves phase shift predictions and maintains RG invariance in chiral EFT.

Findings

TPE and contact terms yield accurate phase shifts in $^1S_0$ partial wave.

Adding a quadratic contact improves the systematic behavior of the potential.

Including the $ riangle$ isobar does not alter TPE's strong contributions.

Abstract

Pion exchange is the central ingredient to nucleon-nucleon interactions used in nuclear structure calculations, and one pion exchange (OPE) enters at leading order in chiral effective field theory. In the $^{2S+1}L_J={^1S_0}$ partial wave, however, OPE and a contact term needed for proper renormalization fail to produce the qualitative, and quantitative, features of the scattering phase shifts. Cutoff variation also revealed a surprisingly low breakdown momentum of about 330 MeV in this partial wave. Here we show that potentials consisting of OPE, two pion exchange (TPE), and a single contact address these problems and yield accurate and renormalization group (RG) invariant phase shifts in the $^1S_0$ partial wave. We demonstrate that a leading-order potential with TPE can be systematically improved by adding a contact quadratic in momenta. For momentum cutoffs below about 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the $\Delta$ isobar degree of freedom in the potential does not change the strong contributions of TPE.