Nonperturbative $^3S_1$-$^3D_1$ NN scattering in pionless EFT

Abstract

The rigorous on-shell $T$-matrices for $NN$ scattering in the coupled channels $^3S_1$$-$$^3D_1$ are briefly presented in the context of EFT($\not\pi$) with the contact potentials truncated at order $\Delta=4$. 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.