Systematical decomposition of dimension-11 short-range neutrinoless double beta decay operators

TL;DR

This work addresses the origin of short-range contributions to neutrinoless double beta decay arising from gauge-invariant dimension-11 operators. It develops a systematic framework to classify all tree-level UV completions with scalar and fermion mediators, uncovering eight topologies and 28 diagrams that, after imposing SM gauge invariance, require 61 new beyond-SM fields. Most completions involve colored mediators, but two minimal colorless models are analyzed in detail, including a representative model with three colorless scalars that generate neutrino masses at two loops and contribute to $0\nu\beta\beta$ via short-range operators. The results yield concrete predictions for $0\nu\beta\beta$ half-lives and neutrino masses, and establish a general toolkit for exploring exotic short-range lepton-number-violating effects in current and future experiments.

Abstract

Neutrinoless double beta decay ($0νββ$) may receive sizable contributions from short-range physics beyond the Standard Model. We present a systematical classification of all tree-level ultraviolet completions of the dimension-11 short-range $0νββ$ decay operators, renormalizable scenarios with scalar and fermion mediators are considered. We identify eight distinct topologies and twenty-eight viable diagrams, from which all consistent UV completions are generated by imposing Standard Model gauge invariance. All these models involve a total of 61 new fields beyond the Standard Model and they typically feature fractionally charged fermions and exotic bosons such as dileptons, diquarks, and leptoquarks. We further study a representative model without colored mediators and analyze its implications for the $0νββ$ decay half-life and light neutrino masses. We find that current and future $0νββ$ decay experiments impose stringent constraints. Our systematic decomposition provides a general framework for exploring exotic short-range contributions to $0νββ$ decay in future experiments.

Figures (13)

• Figure 1: The tree-level topologies for the UV completions of the $d=11$$0\nu\beta\beta$ decay operators. The topologies requiring non-renormalizable interaction vertices are omitted here.
• Figure 2: All possible diagrams for the topologies in figure \ref{['fig:topology']}, where the Lorentz nature (scalar and fermion) of each field is indicated by (dashed and solid) line.
• Figure 3: The $0\nu\beta\beta$ diagrams in which the two external Higgs bosons are attached to a single 3-point vertex.
• Figure 4: The tree-level diagrams for the UV completion of the dim-11 $0\nu\beta\beta$ decay effective operators, we here dropped the cases in which the two external Higg fields are attached to a 3-point vertex.
• Figure 5: The Feynman diagrams for the short-range $0\nu\beta\beta$ decay in the example model of section \ref{['sec:representative-model']}. Notice that the panels of F1$\sim$F7 are UV completions of the $0\nu\beta\beta$ operators $\mathcal{O}_{1a}$ and $\mathcal{O}_{1b}$, F8$\sim$F11 are UV completions of $\mathcal{O}_{2a}$ and $\mathcal{O}_{2b}$, F12$\sim$F15 are UV completions of the operators $\mathcal{O}_{3a}$ and $\mathcal{O}_{3b}$.