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

TL;DR

This paper systematically classifies lepton-number-violating dimension-9 operators in SMEFT, exploring their ultraviolet completions and implications for neutrinoless double beta decay and neutrino mass generation.

Contribution

It provides a comprehensive diagram-based classification of minimal UV completions of LNV dimension-9 operators and analyzes their impact on $0 uetaeta$ and neutrino masses.

Findings

Identifies minimal models avoiding lower-dimensional LNV operators.

Maps models onto SMEFT and assesses their experimental detectability.

Highlights scenarios where dimension-9 contributions dominate neutrino mass effects.

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 ($0\nu\beta\beta$) 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 $0\nu\beta\beta$ are analysed, delineating regions of parameter space where upcoming experiments can be sensitive to genuinely short-range LNV dynamics.