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

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 $\Delta L=2$ 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.