Nonperturbative ${}^3{S}_1$-${}^3{D}_1$ NN scattering in pionless EFT

The rigorous on-shell $T$-matrices for $NN$ scattering in the coupled channels ${}^3{S}_1$$-$${}^3{D}_1$ are briefly presented in the context of EFT($\mathrm{\pi ̸}$) with the contact potentials truncated at order $\mathrm{\Delta }=4$. The nonperturbative features of renormalization are highlighted and elaborated. A simple scenario for EFT power counting’s and renormalization prescriptions is also presented with its consequences being roughly analyzed and discussed.