Nucleon-nucleon interaction in the S13-D13 coupled channel for a pion mass of 469 MeV

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 S13-D13 coupled channel for a pion mass of 469 MeV. We show that at leading order the relativistic chiral nuclear force can only describe δ_3S1 and ε₁ up to T_lab.≈10 MeV, while at the next-to-leading order it can do much better up to T_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 δ_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.