addresses the same physics of the EDM, posing, for the future, as a complementary and independent test for TRV in nuclei. Also other TRV observables in proton- and neutron-nucleus scattering have been proposed as probes of TRV effects [@YH11; @JDB14; @YNU16; @VG18; @PF19].

The use of light nuclei to study TRV results to be advantageous because the nuclear physics of the systems is theoretically under control and so the TRV effects can be easily highlighted. In particular, the chiral effective field theory ($\chi$EFT) has provided a practical and successful scheme to study two and many-nucleon interactions [@DR15; @EE15] and the interaction of electroweak probes with nuclei  [@Park96; @Park03; @Koelling09; @Pastore09; @Koelling11; @Pastore11; @Piarulli13]. The $\chi$EFT approach is based on the observation that the chiral symmetry exhibited by QCD has a noticeable impact in the low-energy regime. Therefore, the form of the strong interactions of pions among themselves and other particles is severely constrained by the transformation properties of the fundamental Lagrangian under Lorentz, parity, time-reversal, and chiral symmetry [@W66; @CCWZ69]. The Lagrangian terms can be organized as an expansion in powers of $Q/\Lx$, where $\Lx\simeq1$ GeV specifies the chiral symmetry breaking scale and $Q$ is the exchanged pion momentum. Each 