term is associated to a low-energy constants (LECs) which are then determined by fits to experimental data.

The $\chi$EFT method permits to construct also an effective TRV Lagrangian treating all possible sources of TRV. The TRV Lagrangian induced by the $\theta$-term was derived in Refs. [@EM10; @JB150]. Also BSM terms such as supersymmetry, multi-Higgs scenarios, left-right symmetric model [*etc.*]{} induce TRV operators at the quark-gluon level which appear at level of dimension six (see for example Ref. [@BG10]). The $\chi$EFT Lagrangians for these sources were derived in Refs. [@JB150; @JV13; @WD13; @JV11]. This approach permits not only to determine the TRV interactions but also to estimate the chiral order of the LECs and their values as function of the fundamental parameters, providing a direct connection between the fundamental theories and the nuclear observables  [@EM10; @JB150; @JV13]. To be noticed that the chiral order of the Lagrangian terms, which is determined by the products of the chiral order of the dynamical part and that of the LECs, really depends on the particular source of TRV. Therefore, when the LECs will be determined experimentally it will be possible to identify the dynamical properties of the TRV source [@JV11; @WD14].

Starting from the 