we will present the TRV chiral Lagrangian up to order $Q^2$ relevant for the calculation of the TRV potential, while in Sec. \[sec:trvpot\] we derive the TRV potential at N2LO. In Sec. \[sec:res\], we report the results obtained for the EDM of $\det$, $\tri$ and $\hel$ using the N2LO potential. Finally, in Sec. \[sec:conc\] we present our conclusions and perspectives. The technical details relative to the contributions of the various diagrams, and of the derivation of the potential in configuration space are given in Appendices \[app:vertex\],  \[app:pot\] and \[app:rpot\]. Moreover, in Appendix \[app:NNNconv\] we will give some details of the calculation of the trinucleon wave function negative-parity component and about the convergence of the TRV three body force contribution.

The TRV Lagrangian {#sec:trvlag}
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The various possible sources of TRV in SM induce a TRV $NN$ and $NNN$ potential. This potential can be constructed starting from a pion-nucleon effective Lagrangian which includes, in principle, an infinite set of terms which violates the chiral symmetry as the fundamental (quark-level) Lagrangian. The effective Lagrangian can be ordered by a power counting scheme which permits to select the most important interactions. In literature the chiral order of the TRV Lagrangian is determined by 