Radiative neutrino masses from dim-7 SMEFT: a simplified multi-scale approach

TL;DR

The paper analyzes radiative Majorana neutrino masses from ΔL=2 dimension-7 SMEFT operators by mapping all minimal two-field UV completions via covariant derivative expansion and by introducing a dimensional-regularisation-based, simplified multi-scale approach to estimate loop masses. It demonstrates that conventional single-scale cut-off EFT estimates fail when heavy new-physics masses are hierarchically arranged, while the multi-scale dim-reg method reproduces exact UV results for both one- and two-loop masses, capturing the impact of mass hierarchies. A concrete leptoquark model with two scalars illustrates the method, showing good agreement with full calculations and highlighting cancellations and hierarchy effects that cut-off methods miss. The phenomenological analysis combines collider, 0νββ, kaon decay, and direct neutrino-mass constraints, revealing viable parameter regions near current experimental reach and emphasizing the role of internal mass hierarchy in expanding the allowed space for ΔL=2 new physics.

Abstract

Lepton-number-violating interactions occur in the Standard Model Effective Field Theory (SMEFT) at odd dimensions starting from the dimension-5 Weinberg operator. Although the operators at dimension-7 and higher are more suppressed by the heavy new scale, they can be crucial when traditional seesaw mechanisms leading to tree-level dimension-5 contributions are absent. We identify all minimal tree-level UV-completions for dimension-7 $ΔL=2$ SMEFT operators without covariant derivatives and propose a new simplified approach for estimating the radiative neutrino masses arising from such operators. This dimensional-regularisation-based approach provides a more accurate estimate for the loop neutrino masses when the new physics fields are hierarchical in mass, as compared to the cut-off-regularisation-based approach often employed in the literature. This allows us to identify viable regions of parameter space in the full list of relevant simplified models close to the current limits set by neutrinoless double beta decay and the LHC that would previously have been thought to be excluded by neutrino-mass constraints.

Figures (9)

• Figure 1: Radiative neutrino mass realised via topology I (left) and topology II (right).
• Figure 2: Tree-level neutrino mass realised via topology III (left), topology IV (centre) and topology V (right).
• Figure 3: Left column: Operators $\mathcal{O}_{\bar{d}LQLH1}$ (top) and $\mathcal{O}_{\bar{d}LueH}$ (bottom) generated by the model described in the text. Right column: Radiative neutrino mass diagrams generated in the model described in the text, corresponding to the set of coupling constants that lead to $\mathcal{O}_{\bar{d}LQLH1}$ (top) and $\mathcal{O}_{\bar{d}LueH}$ (bottom).
• Figure 4: The sum of neutrino masses as a function of the degree of hierarchy between $m_{\tilde{R}_2}$ and $m_{S_1}$, assuming $m_{\tilde{R}_2}>m_{S_1}$, as quantified by the parameter $\xi$, at 1-loop (left) and 2-loop (right) using $\mu=10^8$ GeV. The green line shows the cut-off estimate from Eq. \ref{['eq:LQEFTmass']}, the blue line shows the full model-based expression from Eqs. \ref{['eq:LQ1loopmass']} (1-loop) and \ref{['eq:thefinalnumass']} (2-loop). The red line shows the expression obtained in the simplified model estimate.
• Figure 5: One-loop neutrino mass diagrams in the full and effective theories. The crosses represent fermion mass insertions, and the thick circle represents contact interactions.