Cartography of LNV dim-9 SMEFT: Implications for Radiative Neutrino Masses and $0νββ$

TL;DR

This work develops a systematic framework to study lepton-number-violating (LNV) dimension-9 SMEFT operators that can mediate neutrinoless double beta decay ($0\nu\beta\beta$) at tree level, mapping them to ultraviolet completions and isolating minimal two-particle models that avoid generating the Weinberg operator or dimension-7 LNV operators at tree level. Using a diagram-based approach, the authors enumerate 1474 UV completions, narrow them to 315 models free of lower-dimension LNV at tree level, and identify 14 minimal, non-vector models that can yield tree-level dimension-9 contributions alongside loop-induced lower-dimension operators. They analyse representative 1-loop and 2-loop classes, perform SMEFT matching (via Matchete) to obtain the relevant Wilson coefficients, and study implications for neutrino masses, charged-lepton flavour violation, and $0\nu\beta\beta$ in diverse flavor scenarios; they find that dimension-9 tree-level contributions can dominate in certain parameter regions (notably with flavor-tuned Yukawas and TeV-scale new physics), while in more generic flavor setups the loop-suppressed Weinberg operator often dominates. The results highlight the importance of flavor structure in realizing a genuine short-range LNV signal and provide concrete benchmarks showing how upcoming $0\nu\beta\beta$ experiments can probe these short-range dynamics. The framework offers a concrete path to test BSM short-range LNV dynamics through a combination of $0\nu\beta\beta$, neutrino-mass constraints, and charged-lepton flavour-violation probes.

Abstract

We perform a systematic study of lepton-number-violating (LNV) dimension-9 operators in the Standard Model Effective Field Theory (SMEFT) that can mediate neutrinoless double beta decay ($0νββ$) at tree level, and map them to their possible tree-level ultraviolet completions. Using a diagram-based classification, we enumerate all such completions and isolate minimal two-particle models that avoid generating the dimension-5 Weinberg operator or dimension-7 LNV operators at tree level. We then chart how these minimal models populate the operator landscape and organise them by the loop order at which they radiatively induce lower-dimensional LNV operators, highlighting scenarios in which the tree-level dimension-9 contribution can compete with or dominate loop-suppressed neutrino-mass (dimension-5) effects. Representative one-loop and two-loop classes are matched onto the SMEFT, and their implications for neutrino masses, charged-lepton flavour violation, and the relative size of dimension-9 versus dimension-5 contributions to $0νββ$ are analysed, delineating regions of parameter space where upcoming experiments can be sensitive to genuinely short-range LNV dynamics.

Figures (20)

• Figure 1: Step (i) and (ii) of the diagram based approach: topologies and diagrams at tree level and 1-loop level for the Weinberg operator.
• Figure 2: Step (iii) of the diagram based approach: model diagrams at tree level and 1-loop level for the Weinberg operator.
• Figure 3: Diagrams for the dimension-9 operators for the minimal models. All models with one BSM scalar $S$ and one BSM vectorlike fermion $F$ generate operators of the class $\Psi^6$ via the diagram on the left. Models with two BSM scalars $S_1$ and $S_2$ generate $\Psi^6$ operators via the diagram on the right.
• Figure 4: Tree-level diagrams for dimension-9 operator $\mathcal{O}^{(9)}_{LLH^4D^2}$ with one $W$ boson (left) and two $W$ bosons (right) for the model M3. Note that the operator with no $W$ boson, i.e. with only partial derivatives $\partial_{\mu}$, vanishes due to symmetries.
• Figure 5: Black box theorem for the Weinberg operator: every model that generates operator $\mathcal{O}_{dQdQLL}^{(9)}$ at tree level (left) will generate the Weinberg operator at maximally 2-loop level by closing both pairs of external $Q$ and $d_R$ legs into a loop via a Yukawa interaction with a Higgs boson (right).