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

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.

💡 Research Summary

This paper addresses the often‑overlooked class of short‑range contributions to neutrinoless double‑beta decay (0νββ) that arise from dimension‑11 effective operators. While the standard “mass mechanism” involves the exchange of light Majorana neutrinos and is described by dimension‑5 (Weinberg) and dimension‑9 operators, the authors focus on higher‑dimensional operators that require two Higgs insertions and therefore generate a distinct set of low‑energy four‑fermion structures.

First, the authors catalog the nineteen independent gauge‑invariant dimension‑11 operators that can contribute to 0νββ after electroweak symmetry breaking. These operators are grouped into seven families (O₁–O₇) distinguished by the chiralities of the lepton currents (right‑handed electrons, left‑handed lepton doublets, or mixed left‑handed lepton–right‑handed electron currents) and by whether color generators λ⁽ᴬ⁾ appear. By inserting the Higgs vacuum expectation value, each operator reduces to one of twelve short‑range low‑energy operators of the form J J j, where J denotes a quark bilinear and j a lepton bilinear.

The core of the work is a systematic tree‑level UV decomposition of these operators. Using a custom Mathematica routine, the authors generate all possible renormalizable diagrams with scalar or fermion mediators that have eight external legs (four quarks, two leptons, two Higgs fields). They find eight distinct topologies, which, after assigning Lorentz nature and Standard Model gauge quantum numbers to each internal line, yield twenty‑eight viable diagrams. These diagrams involve a total of 61 new fields beyond the Standard Model. Many of the new particles carry fractional electric charge and belong to exotic representations such as dileptons (charge ±2), diquarks (color triplets with unconventional hypercharge), and leptoquarks (scalar lepton–quark composites).

A representative “colorless” model is studied in detail. It contains two scalar mediators that are singlets under SU(3)₍C₎ and a vector‑like fermion. After electroweak symmetry breaking the scalars mix, and the mass eigenstates are used to compute the effective coefficients ϵ_X that appear in the master formula for the 0νββ half‑life. The analysis shows that, for mediator masses in the 1–10 TeV range and moderate mixing angles, the predicted half‑life comfortably exceeds the current experimental limits from KamLAND‑Zen (⁸⁶Xe) and GERDA (⁷⁶Ge). The same particle content also generates Majorana neutrino masses at the two‑loop level; the authors provide explicit expressions for the loop integrals and demonstrate that realistic neutrino masses (∼10 meV) can be obtained without fine‑tuning.

Appendices supplement the main text: Appendix A lists the non‑renormalizable tree‑level topologies; Appendix B derives the low‑energy effective operators and presents the master half‑life formula; Appendix C supplies the two‑loop integral results needed for neutrino‑mass calculations; Appendix D offers several additional illustrative models, including ones with a single color‑triplet mediator and others that remain color‑neutral.

In conclusion, the paper delivers a comprehensive map of all possible tree‑level UV completions of dimension‑11 short‑range 0νββ operators. By enumerating the required new particles and their gauge quantum numbers, it provides a valuable reference for model builders and experimentalists alike. The work highlights that future 0νββ experiments, which aim to push half‑life sensitivities to 10²⁸ yr, will probe a wide swath of exotic physics—particularly scenarios involving fractionally charged fermions and exotic bosons that are otherwise difficult to access at colliders. This systematic framework thus opens new avenues for exploring lepton‑number violation and the origin of neutrino mass beyond the traditional dimension‑5 and dimension‑9 paradigms.