Nucleon-nucleon interaction in the $^3S_1$-$^3D_1$ 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 $^3S_1$-$^3D_1$ coupled channel for a pion mass of 469 MeV. We show that at leading order the relativistic chiral nuclear force can only describe $\delta_{3S1}$ and $\varepsilon_1$ up to $T_\mathrm{lab.}\approx10$ 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 $\delta_{3D1}$, 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.