arxiv: 2603.19358 · v2 · submitted 2026-03-19 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

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

Hao-Lin Li , Yu-Han Ni , Ming-Lei Xiao , Jiang-Hao Yu , Xiao-Long Zheng

Authors on Pith no claims yet

Pith reviewed 2026-05-15 07:52 UTC · model grok-4.3

classification ✦ hep-ph

keywords SMEFTUV completionsneutrinoless double beta decaydimension-9 operatorsvector resonancesmediatorstree-level

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The pith

A systematic classification yields 324 minimal UV completions with vector resonances for dimension-9 SMEFT operators in short-range neutrinoless double beta decay.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper classifies all tree-level ultraviolet completions of dimension-nine operators in the SMEFT that contribute to short-range neutrinoless double beta decay. It identifies the smallest sets of heavy particles required for each operator, reporting that 440 of 505 distinct mediator combinations qualify as minimal and that 12 cases need only two heavy species. The work reproduces earlier scalar and fermion results while delivering the first full list of 324 minimal completions that involve vector resonances.

Core claim

Using the SMEFT J-basis framework the authors enumerate all distinct mediator combinations for both all-boson and boson-fermion-boson topologies, then isolate the minimal genuine heavy degrees of freedom that generate each operator; the resulting catalog contains 324 minimal vector-resonance completions.

What carries the argument

The SMEFT J-basis framework that organizes distinct UV completions by mediator combinations and topologies.

Load-bearing premise

The J-basis framework captures every distinct UV completion and minimality is correctly identified by the smallest set of genuine heavy degrees of freedom.

What would settle it

Observation of a short-range neutrinoless double beta decay signal whose operator cannot be generated by any of the enumerated mediator combinations would falsify the claimed completeness.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finishes the classification of minimal tree-level UV completions for these dim-9 operators by adding the first full set of 324 vector cases on top of the known scalars and fermions.

read the letter

The main takeaway is that this work gives a complete catalog of minimal UV completions for the dim-9 SMEFT operators that drive short-range neutrinoless double beta decay. Using the J-basis, it identifies 505 mediator combinations, labels 440 as minimal, and supplies the first systematic list of 324 vector resonance cases that earlier papers left out. Twelve operators need only two distinct heavy fields. The reproduction of the prior scalar and fermion results is a solid check on the method, and the split into all-boson versus boson-fermion-boson topologies keeps the enumeration organized and readable. That is the useful part: anyone building models for 0νββ now has a reference list instead of having to redo the counting themselves. The soft spot sits with the vector resonances. Vectors allow more Lorentz and gauge structures than scalars or fermions, so it is not automatic that the chosen topologies catch every tree-level diagram or that integrating the vectors out never produces extra light states. The headline numbers rest on the claim that the topologies are exhaustive, but without explicit matching to a few known vector-mediated examples it is hard to rule out omissions or double-counting. The paper is still worth referee time because the classification is systematic, the numbers are concrete, and the vector extension fills a genuine gap. People working on BSM explanations for neutrinoless double beta decay will cite it as a reference even if some vector counts need tightening in revision.

Referee Report

1 major / 1 minor

Summary. The manuscript systematically classifies tree-level UV completions of dimension-9 SMEFT operators relevant to short-range neutrinoless double beta decay. Using the SMEFT J-basis, it enumerates all-boson and boson-fermion-boson topologies, identifies 505 unique mediator combinations (440 minimal), reproduces prior scalar/fermion results, and provides the first compilation of 324 minimal vector-resonance completions.

Significance. If the enumeration is exhaustive and free of omissions or double-counting, the work supplies a useful catalog of minimal UV realizations, especially for the previously unexplored vector sector. This could inform model-building and experimental constraints on short-range 0νββ mechanisms. The reproduction of Ref. [1] results for scalars and fermions lends some methodological support.

major comments (1)

[vector mediator classification section] The central claim of completeness for the 324 vector-resonance cases rests on the assertion that the J-basis plus the listed topologies exhausts every tree-level mediator combination. However, vectors admit multiple Lorentz and gauge representations, and the manuscript does not provide explicit matching or a proof that every possible vector-mediated diagram is captured or that no additional light degrees of freedom are induced upon integration. This directly affects the headline numbers (505 combinations, 440 minimal) and the 'complete' title claim.

minor comments (1)

The citation to Ref.[1] should be given in full in the bibliography rather than left as a placeholder.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We appreciate the acknowledgment of the utility of our classification, especially the new vector sector results. We address the major comment below.

read point-by-point responses

Referee: The central claim of completeness for the 324 vector-resonance cases rests on the assertion that the J-basis plus the listed topologies exhausts every tree-level mediator combination. However, vectors admit multiple Lorentz and gauge representations, and the manuscript does not provide explicit matching or a proof that every possible vector-mediated diagram is captured or that no additional light degrees of freedom are induced upon integration. This directly affects the headline numbers (505 combinations, 440 minimal) and the 'complete' title claim.

Authors: We agree that the manuscript would be strengthened by a more explicit demonstration of completeness for the vector cases. The J-basis together with the all-boson and boson-fermion-boson topologies is designed to enumerate all possible tree-level diagrams, and we have cross-checked against known scalar and fermion results. However, we did not include a dedicated matching appendix for the vector representations. In the revised version we will add a new subsection (or appendix) that (i) lists all Lorentz and gauge representations of vector mediators that can appear in the topologies, (ii) shows the explicit matching to the dim-9 operators, and (iii) confirms that integration does not induce additional light degrees of freedom beyond those already accounted for in the minimal sets. This will substantiate the headline numbers without changing them. We therefore plan to revise the presentation accordingly. revision: yes

Circularity Check

0 steps flagged

Enumeration of UV completions is independent enumeration without self-referential reductions

full rationale

The paper performs a systematic classification of tree-level UV completions for dim-9 SMEFT operators using the established J-basis framework, enumerating 505 mediator combinations and identifying 440 as minimal via all-boson and boson-fermion-boson topologies. It reproduces scalar/fermion results from Ref.[1] but presents the 324 vector cases as a new extension. No load-bearing step reduces by construction to fitted parameters, self-definitions, or unverified self-citations; the counts derive directly from applying the framework to operator topologies. The derivation chain is self-contained against external benchmarks of the J-basis and does not invoke uniqueness theorems or ansatze from overlapping prior work in a circular manner.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

No free parameters are introduced as the work is a combinatorial classification. Axioms are standard in the SMEFT approach for effective field theories. No new particles or entities are invented; the focus is on possible heavy degrees of freedom.

axioms (2)

domain assumption The SMEFT J-basis provides a complete basis for dimension-9 operators
Invoked in the classification of UV completions.
domain assumption Only tree-level completions are considered
The paper specifies tree-level ultraviolet completions.

pith-pipeline@v0.9.0 · 5456 in / 1227 out tokens · 76066 ms · 2026-05-15T07:52:06.747539+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

J-basis organization of the local operator space... channel-wise Casimir construction... common eigenbasis... UV interpretation reduced to a problem in representation theory
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

minimal UV realizations... 440 minimal... 324 minimal UV completions featuring vector resonances

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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