Nucleon-nucleon interaction in the ${}^3{S}_1$-${}^3{D}_1$ coupled channel for a pion mass of 469 MeV

Abstract

In this work, we apply the relativistic chiral nuclear force to describe the state-of-the-art lattice simulations of the nucleon-nucleon scattering amplitude. In particular, we focus on the ${}^3{S}_1$-${}^3{D}_1$ coupled channel for a pion mass of 469 MeV. We show that at leading order the relativistic chiral nuclear force can only describe $\hat{I}{´}_{3S1}$ and ${\epsilon }_1$ up to $T_{lab.}\approx 10$ MeV, while at the next-to-leading order it can do much better up to $T_{\mathrm{lab}}=200$ MeV. However, at the next-to-next-to-leading order, the description deteriorates, which can be attributed to the fact that the pion-mass dependence of the pion-nucleon couplings $c_{1,2,3,4}$ may not be negligible. Furthermore, all the studies consistently yield negative $\hat{I}{´}_{3D1}$, contrary to the lattice QCD results which are positive but consistent with zero. The present study is relevant to a better understanding of the lattice QCD nucleon-nucleon force and more general baryon-baryon interactions.

Accepted for publication in PLB