Simplification of chiral nuclear forces near the unitarity limit

Abstract

Modern theory approaches for describing atomic nuclei often make use of on an effective theory that constructs the interaction between nucleons systematically based on Quantum Chromodynamics (QCD), exploiting constraints arising from the approximate chiral symmetry of QCD. The tensor nuclear force produced by one-pion exchange is an important feature that arises naturally in this framework. In this work we show that, however, the tensor force is suppressed by the large nucleon-nucleon scattering lengths in combination with the smallness of the pion mass. Based on this observation, we propose a new scheme for a chiral nuclear force that is able to describe $NN$ phase shifts up to the center-of-mass momenta $k \simeq 300$ MeV while treating pion exchange as a perturbation. Our much simplified leading-order force provides a microscopic explanation for the recent success of various short-range nuclear forces from the perspective of chiral effective field theory, and it shares with those approaches an approximate Wigner SU(4) symmetry, as well as the closeness to the unitarity limit (infinite nucleon-nucleon scattering lengths), as guiding principles. Compared to previous approaches to perturbative-pion interactions, our force also adjusts the ordering of short-range contact interactions, by means of which we overcome convergence problems of the expansion that were previously assumed to severely limit its usefulness. We demonstrate the performance of our approach with numerical calculations of $NN$ scattering up to fourth order, in addition to studies of $3N$ and $4N$ bound-state properties.