the divergences coming from the TPE and $3\pi$ exchange diagrams.

In the calculation of the EDM in Sec. \[sec:res\], the configuration space version of the potential is needed. This formally follows from =1.0pt $$\begin{aligned}
 \!\!\!\!\!\!\!\!\!\!\!\! \langle \bmr_1'\bmr_2'|V|\bmr_1\bmr_2\rangle&=&
  \delta (\bmR-\bmR') \int {d^3k\over (2\pi)^3} {d^3K\over (2\pi)^3}
  \nonumber\\ 
 &\times& e^{i(\bmK+\bmk/2)\cdot\bmr'} V(\bmk,\bmK)
    e^{-i(\bmK-\bmk/2)\cdot\bmr}\ ,
    \label{eq:vrsp}\end{aligned}$$ where $\bmr=\bmr_1-\bmr_2$ and $\bmR=(\bmr_1+\bmr_2)/2$, and similarly for the primed variables. In order to carry out the Fourier transforms above, the integrand is regularized by including a cutoff of the form $$C_\Lambda(k)={\rm e}^{-(k/\Lambda)^4}\ ,\label{eq:cutoff}$$ where the cutoff parameter $\Lambda$ is taken in the range 450–550 MeV. With such a choice the $V^{ ({\rm OPE})}_{TRV}$, $V^{ ({\rm TPE})}_{TRV}$, $V^{ ({\rm 3\pi,0})}_{TRV}$, $V^{ ({\rm 3\pi,1})}_{TRV}$, and $V^{ ({\rm CT})}_{TRV}$ components of the resulting potential are local, i.e., $\langle \bmr_1'\bmr_2'|V|\bmr_1\bmr_2\rangle=
\delta (\bmR-\bmR')\, \delta (\bmr-\bmr') V(\bmr)$, while the RC component contains mild non-localities associated with linear and quadratic terms in the relative momentum operator $-i {{\bm \nabla}}$. Explicit expressions for all these components are listed in Appendix \[app:rpotNN\].

The $NNN$ TRV potential {#sec:NNNtrv}
-----------------------

The $3\pi$ TRV vertex gives rise to a three body contribution through the diagram (m) in Fig. \[fig:diagNN\]. The lowest contribution appears at NLO while at N2LO the various time 