*2.2. EFT Approach to* 0*νββ Decay*

As mentioned in the introduction, a more general approach could be constructed based on the effective field theory extension of the Standard Model. Such an EFT analysis is preferable because it does not rely on specific models and the parameters could be constrained by the existing 0*νββ* data and by data from the Large Hadron Collider and other experiments. In addition, the models considered in Equation (1) always lead to a subset of terms in the low-energy (∼200 MeV) effective field theory Lagrangian. EFT considers all terms in the BSM Lagrangian allowed by the symmetries, some of them corresponding to the model terms incorporated in Equation (1), but the couplings might have a wider meaning. Other terms in the EFT Lagrangian are new, not directly identifiable with those originating from specific models.

At the quark level, Figure 1 shows the generic 0*νββ* Feynman diagrams contributing to the 0*νββ* process. I consider contributions coming from the light left-handed Majorana neutrino (Figure 1b) and a long-range part coming from the low-energy fourfermion charged-current interaction (see Ref. [17] for details). After hadronization (see Figure 2), the extra terms in the Lagrangian require the knowledge of about 20 individual NMEs [22–24,75,80,89]. One can write the half-life in a factorized compact form:

$$\mathbb{E}\left[T\_{1/2}^{0\nu}\right]^{-1} = \mathbf{g}\_A^4 \left[\sum\_i |\mathcal{E}\_i|^2 \mathcal{M}\_i^2 + \text{Re}\left(\sum\_{i \neq j} \mathcal{E}\_i \mathcal{E}\_j \mathcal{M}\_{ij}\right)\right].\tag{4}$$

Here, the E*<sup>i</sup>* contain the neutrino physics parameters, E<sup>1</sup> = *η*0*<sup>ν</sup>* represent the exchange of light left-handed neutrinos, <sup>E</sup>2–6 <sup>=</sup> { *<sup>V</sup>*+*<sup>A</sup> <sup>V</sup>*−*A*,  *<sup>V</sup>*+*<sup>A</sup> <sup>V</sup>*+*A*,  *<sup>S</sup>*+*<sup>P</sup> <sup>S</sup>*±*P*,  *TR TR*, *ηπν*} are the long-range LNV parameters, and E7–14 = {*ε*1, *ε*2, *ε LLz*(*RRz*) <sup>3</sup> , *ε LRz*(*RLz*) <sup>3</sup> , *ε*4, *ε*5, *η*1*π*, *η*2*π*} denote the short-range LNV parameters at the quark level (see Ref. [17] for definitions of notations and details). The contributions of pion-exchange diagrams are also included in the so-called "higher-order term in nucleon currents" [80]. However, they are constrained by partial conservation of axial current (PCAC) and are only included in the light neutrino exchange contribution in Figure 2a. This contribution changes the associated NMEs by only 20%, and one concludes that it does not represent a serious double counting issue.

In Equation (4), M<sup>2</sup> *<sup>i</sup>* and M*ij* are combinations of NMEs and integrated PSFs [27] denoted with *G*01–*G*<sup>09</sup> (see Ref. [17] for definitions and details). In some cases, the interference terms E*i*E*j*M*ij* are small [90] and can be neglected, but not all of them [91]. In Ref. [15], I analyzed a subset of terms contributing to the half-life formula, with Equation (1) originating from the left-right symmetric model. In that restrictive case, I showed that one can disentangle different contributions to the 0*νββ* decay process using two-electron angular and energy distributions as well as the half-lives of two selected isotopes.
