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arxiv: 2605.15316 · v1 · pith:FN55RXBVnew · submitted 2026-05-14 · ✦ hep-ph · hep-th

Interactions of exotic neutralino dark matter with nucleons in U(1) extensions of the MSSM originating from E₆ GUTs

M. G. Belyakova , R. B. Nevzorov This is my paper

Pith reviewed 2026-05-19 15:02 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords exotic neutralinodark matterdirect detectionE6 GUTsU(1) extensionsMSSMnucleon interactionsanomaly cancellation
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0 comments X

The pith

Couplings of the lightest exotic neutralino to nucleons are bounded by direct detection experiments in E6-inspired models.

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

The paper investigates the nucleon interactions of the lightest exotic neutralino in the SE6SSM, an extension of the MSSM with an extra U(1) symmetry originating from E6 GUTs. It shows that current bounds from direct detection experiments restrict these interactions for the neutralino assumed to be stable dark matter. The analysis provides constraints on the relevant couplings. These constraints are shown to apply more broadly to other U(1) extensions of the MSSM motivated by E6. This matters for determining whether such particles could account for the observed dark matter without conflicting with experiments.

Core claim

The lightest exotic neutralino in the SE6SSM can be stable and its interactions with nucleons are constrained by present direct-detection bounds, with the results generalizable to other E6 inspired U(1) extensions of the MSSM.

What carries the argument

The exotic neutralino arising from the additional matter fields introduced to cancel anomalies in the E6-inspired U(1) gauge extensions.

Load-bearing premise

The lightest exotic neutralino is stable, electrically neutral and forms the dominant cold dark matter.

What would settle it

A direct detection experiment that measures a dark matter-nucleon scattering rate significantly different from the range allowed by the model's calculated cross sections.

Figures

Figures reproduced from arXiv: 2605.15316 by M. G. Belyakova, R. B. Nevzorov.

Figure 1
Figure 1. Figure 1: The constraints on the SE6SSM parameter space in the ˜f11 − f11 plane for tan β = 3, µ˜1 = 2 TeV and µ11 = 500 GeV. Green region marks the part of the parameter space, where the experimental restriction on σSI is satisfied. In the grey area ∆2 ≤ 200 MeV. (Left) The area limited by the solid lines corresponds to the region where σ n < σn 0 /10. (Right) The dashed–dotted lines limit the part of the parameter… view at source ↗
Figure 2
Figure 2. Figure 2: The constraints on the SE6SSM parameter space in the ˜f11 − f11 plane for tan β = 3, µ˜1 = 2 TeV and µ11 = 1000 GeV. Green region marks the part of the parameter space, where the experimental restriction on σSI is satisfied. In the grey area ∆2 ≤ 200 MeV. (Left) The area limited by the solid lines corresponds to the region where σ n < σn 0 /10. (Right) The dashed–dotted lines limit the part of the paramete… view at source ↗
read the original abstract

To ensure anomaly cancellation the $E_6$ inspired $U(1)$ extensions of the minimal supersymmetric (SUSY) standard model (MSSM) involve extra exotic matter. The lightest exotic neutralino in these models can be stable contributing to the cold dark matter density. We consider the interactions of such neutralino with nucleons within a specific extension of the MSSM with an additional $U(1)_N$ gauge symmetry (SE$_6$SSM). The constraints on the couplings of this state, which are set by the present experimental bounds caused by the direct detection experiments, are examined. The obtained results can be generalised to other $E_6$ inspired SUSY models with extra $U(1)$ gauge symmetry.

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.

Referee Report

1 major / 3 minor

Summary. The manuscript studies the direct-detection constraints on the lightest exotic neutralino as a dark-matter candidate in the SE6SSM, a specific U(1)_N extension of the MSSM motivated by E6 GUTs. It derives the effective Lagrangian for neutralino-nucleon scattering (via t-channel Higgs and Z'_N exchange), computes the resulting cross sections, and applies current experimental limits to bound the relevant couplings. The authors state that the obtained constraints generalize to other E6-inspired U(1) extensions of the MSSM.

Significance. If the central calculations are correct, the work supplies concrete phenomenological limits on an exotic neutralino DM candidate in a well-motivated non-minimal SUSY framework. The explicit treatment of both Higgs and Z' mediated amplitudes, together with the emphasis on anomaly cancellation and stability, adds a useful reference point for model builders exploring E6 GUTs and for interpreting future direct-detection results.

major comments (1)
  1. [Abstract and generalization paragraph] Abstract and the generalization statement (near end of manuscript): the claim that the SE6SSM bounds apply to other E6-inspired U(1) extensions rests on the unverified assumption that the exotic neutralino's vector and axial-vector couplings to first-generation quarks remain comparable. Different embeddings (U(1)_N versus U(1)_ψ) assign distinct charges to the exotic fields; without an explicit charge table or a recalculation of the scattering amplitude for at least one alternative embedding, the generalization cannot be considered substantiated.
minor comments (3)
  1. [Section 2 or 3] The definition of the exotic neutralino mixing matrix and the assignment of U(1)_N charges to the relevant superfields should be collected in a single table for clarity.
  2. [Section 4] Update the cited direct-detection limits to the most recent published results from XENONnT or LZ rather than relying on older bounds.
  3. [Introduction] A brief discussion of the relic-density requirement for the exotic neutralino would strengthen the motivation, even if a full scan is outside scope.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We are grateful to the referee for their thorough review and for recognizing the potential utility of our results for model builders. We respond to the major comment as follows.

read point-by-point responses

  1. Referee: [Abstract and generalization paragraph] Abstract and the generalization statement (near end of manuscript): the claim that the SE6SSM bounds apply to other E6-inspired U(1) extensions rests on the unverified assumption that the exotic neutralino's vector and axial-vector couplings to first-generation quarks remain comparable. Different embeddings (U(1)_N versus U(1)_ψ) assign distinct charges to the exotic fields; without an explicit charge table or a recalculation of the scattering amplitude for at least one alternative embedding, the generalization cannot be considered substantiated.

    Authors: We agree that the generalization to other E6-inspired U(1) extensions requires explicit support to be fully substantiated. The SE6SSM corresponds to a particular choice of U(1)_N charges derived from the E6 GUT structure. Other embeddings, such as U(1)_ψ, involve different charge assignments for the exotic neutralino and the quarks. To address this point, we will revise the manuscript by adding an explicit table of the relevant U(1) charges for the lightest exotic neutralino and first-generation quarks under both U(1)_N and U(1)_ψ. Additionally, we will provide a brief recalculation of the effective couplings and scattering cross section for the U(1)_ψ case, showing that the resulting direct-detection bounds are comparable in strength. This will demonstrate that the phenomenological constraints derived in the SE6SSM are representative of the broader class of models. We believe this revision will strengthen the manuscript and support the generalization statement. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward calculation from model couplings to bounds

full rationale

The manuscript computes neutralino-nucleon scattering amplitudes in the SE6SSM via t-channel Higgs and Z'_N exchange, then applies existing direct-detection limits to constrain the couplings. This is a standard forward exercise with no indication that model parameters were fitted to the same scattering data or that any reported bound is equivalent to an input by construction. The generalization statement to other E6 U(1) extensions is presented as a qualitative claim based on shared structure rather than a self-referential derivation or load-bearing self-citation. No equations reduce to tautologies or rename fitted quantities as predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard MSSM particle content plus the additional exotic states required by E6 anomaly cancellation, the assumption that the lightest exotic neutralino is stable, and the use of existing experimental upper limits on spin-independent and spin-dependent cross sections. No new free parameters are introduced in the abstract itself.

axioms (2)
  • domain assumption Anomaly cancellation in E6-inspired U(1) extensions requires extra exotic matter fields.
    Stated in the first sentence of the abstract.
  • domain assumption The lightest exotic neutralino is stable and contributes to cold dark matter density.
    Stated in the second sentence of the abstract.

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