are discussed (additional details are given in Appendix \[app:pot\]). We will give also some hints in the renormalization of the coupling constants.

From amplitudes to potentials
-----------------------------

We start considering the conventional $NN$ scattering amplitude ${\langle}N'N' |T|NN{\rangle}$, where $|NN{\rangle}$ and $|N'N'{\rangle}$ represent the initial and final two nucleon state and $T$ can be written as, $$\begin{aligned}
 T =  H_I \sum_{n=1}^\infty \left( 
 \frac{1}{E_i -H_0 +i\, \eta } H_I \right)^{n-1} \ ,
\label{eq:pt}\end{aligned}$$ where $E_i$ is the initial energy of the two nucleons, $H_0$ is the Hamiltonian describing free pions and nucleons, and $H_I$ is the Hamiltonian describing interactions among these particles. To be noticed that in Eq. (\[eq:pt\]) the interaction Hamiltonian $H_I$ is in the Schrödinger picture and that, at the order of interest here, it follows simply from $H_I=-\int {\rm d} \bmx\; {\cal L}_I (t=0,\bmx)$, where ${\cal L}_I$ is the interaction Lagrangian in interaction picture. Vertices from $H_I$ are listed in Appendix \[app:vertex\].

The $NN$ scattering amplitude can be organized as an expansion in powers of $Q/{\Lambda_\chi}\ll 1$, where ${\Lambda_\chi}\simeq1$ GeV is the typical hadronic mass scale, $${\langle}N'N' |T|NN{\rangle}=\sum_n T^{(n)}\,,
  \label{eq:teft}$$ where $T^{(n)}\sim Q^n$.

The $T$ matrix in Eq. (\[eq:teft\]) is generated, order by order in the power counting, by 