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

Neutrinoless double beta decay ($0\nu\beta\beta$) 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 $0\nu\beta\beta$ 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 $0\nu\beta\beta$ decay half-life and light neutrino masses. We find that current and future $0\nu\beta\beta$ decay experiments impose stringent constraints. Our systematic decomposition provides a general framework for exploring exotic short-range contributions to $0\nu\beta\beta$ decay in future experiments.