Complete UV Resonances of SMEFT Dim-9 Operators for Short-range Neutrinoless Double Beta Decay

TL;DR

This paper systematically classifies UV completions for dimension-nine SMEFT operators relevant to short-range neutrinoless double beta decay, highlighting minimal realizations and vector resonance contributions.

Contribution

It provides the first comprehensive catalog of 324 minimal UV completions with vector resonances, extending previous scalar and fermion mediator classifications.

Findings

Out of 505 mediator combinations, 440 are minimal.

12 cases require only two heavy species.

First detailed classification including vector resonances.

Abstract

We present a systematic classification of tree-level ultraviolet (UV) completions for dimension-nine SMEFT operators relevant to short-range neutrinoless double beta decay. Using the SMEFT J-basis framework, we categorize distinct UV completions, including both all-boson and boson-fermion-boson topologies. A primary objective is the identification of minimal UV realizations, defined as the smallest set of genuine heavy degrees of freedom required to generate each operator. Out of the 505 unique mediator combinations identified, 440 are found to be minimal, with 12 cases necessitating only two distinct heavy species. While our findings reproduce the scalar- and fermion-mediated results of Ref.[1], we significantly extend the classification by providing the first comprehensive compilation of 324 minimal UV completions featuring vector resonances -- a category previously unexplored in this context.