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arxiv: 2606.29811 · v1 · pith:JLWMG5L2new · submitted 2026-06-29 · ✦ hep-ph

Light Neutralino Dark Matter in a Supersymmetric Pati-Salam Framework

Ali Muhammad , Imtiaz Khan , Tianjun Li , Shabbar Raza , Mussawir Khan This is my paper

Pith reviewed 2026-06-30 05:44 UTC · model grok-4.3

classification ✦ hep-ph
keywords neutralino dark matterPati-Salam modelsupersymmetrybulk annihilationZ-funneldirect detectionlight stau
0
0 comments X

The pith

A supersymmetric Pati-Salam model permits a bino-like neutralino to act as dark matter with mass up to 110 GeV alongside a light right-handed stau, satisfying all constraints for both signs of mu.

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

The paper studies neutralino dark matter within the minimal supersymmetric standard model obtained from an SU(4)_C x SU(2)_L x SU(2)_R Pati-Salam gauge structure. It scans parameters that produce radiative electroweak symmetry breaking and a neutralino as the lightest supersymmetric particle, then isolates bulk annihilation by requiring at least a 10 percent mass gap to the next particle. This yields viable solutions with a bino-like lightest neutralino and right-handed stau as next-to-lightest, obeying LHC, flavor, and Planck relic-density limits while predicting mass upper bounds. The sign of the mu parameter controls direct-detection rates: positive mu faces strong constraints from current experiments, while negative mu allows a surviving Z-funnel region below projected LZ sensitivity. The identified spaces lie within reach of proposed lepton colliders.

Core claim

We identify a viable bulk region with a bino-like LSP and a light right-handed stau NLSP. These solutions satisfy all experimental constraints, including LHC searches, flavor observables, and the Planck 2018 relic density, predicting upper bounds m_χ̃₁⁰ ≲ 110 GeV and m_τ̃₁ ≲ 120 GeV. For μ<0, destructive interference in Higgs-mediated scattering suppresses the direct-detection cross section, allowing a viable Z-funnel region to survive below the projected LZ 1000-day sensitivity.

What carries the argument

The mass-splitting condition R_φ̃ ≳ 10 percent that isolates genuine bulk annihilation from coannihilation in the bino-like neutralino plus right-handed stau sector.

If this is right

  • The viable parameter space lies inside the projected sensitivity of CEPC and FCC-ee lepton colliders.
  • Positive-mu Higgs-funnel points are already excluded or tightly constrained by existing direct-detection data.
  • Negative-mu Z-funnel points remain allowed even after projected LZ 1000-day limits.
  • Upper bounds of 110 GeV on the neutralino and 120 GeV on the stau follow directly from the relic-density and collider constraints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Confirmation would imply that Pati-Salam boundary conditions at high scale naturally produce light neutralino dark matter accessible to near-term experiments without additional tuning.
  • One could search for correlated signals in flavor observables and missing-energy channels at the same colliders to cross-check the stau-neutralino mass relation.
  • The destructive-interference mechanism for negative mu might generalize to other supersymmetric constructions that contain right-handed sleptons.

Load-bearing premise

That requiring a 10 percent mass gap to the next-to-lightest particle plus a broad parameter scan that enforces radiative electroweak symmetry breaking and neutralino LSP is enough to capture the true relic density without hidden coannihilation or other model effects altering the result.

What would settle it

Absence of any light stau or neutralino signals at CEPC or FCC-ee combined with a null result from the LZ 1000-day direct-detection run would rule out the reported viable bulk and Z-funnel regions.

Figures

Figures reproduced from arXiv: 2606.29811 by Ali Muhammad, Imtiaz Khan, Mussawir Khan, Shabbar Raza, Tianjun Li.

Figure 1
Figure 1. Figure 1: FIG. 1. The grey points correspond to the solutions that satisfy ra [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The allowed bulk parameter space of the supersymmet [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The gray points represent parameter choices that successfully achieve radiative electroweak symmetry breaking (REWSB) with a [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We investigate the low-energy phenomenology of the MSSM arising from the supersymmetric $SU(4)_C \times SU(2)_L \times SU(2)_R$ Pati-Salam framework, focusing on neutralino dark matter in bulk annihilation and Higgs/Z-funnel regions. Using a comprehensive parameter scan consistent with radiative electroweak symmetry breaking and a neutralino LSP, we analyze collider, flavor, and dark matter constraints for both signs of {\mu}. To isolate genuine bulk annihilation from coannihilation, we impose the mass-splitting condition $\mathcal{R}_{\tilde{\phi}} \equiv (m_{\tilde{\phi}}-m_{\tilde{\chi}_1^0})/m_{\tilde{\chi}_1^0}\gtrsim 10\%$. We identify a viable bulk region with a bino-like LSP and a light right-handed stau NLSP. These solutions satisfy all experimental constraints, including LHC searches, flavor observables, and the Planck 2018 relic density, predicting upper bounds $m_{\tilde{\chi}_1^0}\lesssim 110~{\rm GeV}$ and $m_{\tilde{\tau}_1}\lesssim 120~{\rm GeV}$. This parameter space lies within the reach of future CEPC and FCC-ee colliders. We also analyze Higgs- and Z-funnel regions. Current direct-detection limits strongly constrain light Higgsino-assisted resonances for {\mu}>0. Conversely, for {\mu}<0, destructive interference in Higgs-mediated scattering suppresses the direct-detection cross section, allowing a viable Z-funnel region to survive below the projected LZ 1000-day sensitivity. These results highlight the negative-{\mu} Pati-Salam framework as a predictive, testable scenario for upcoming dark matter and lepton collider experiments

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 / 1 minor

Summary. The paper investigates neutralino dark matter phenomenology in the MSSM from a supersymmetric Pati-Salam SU(4)_C × SU(2)_L × SU(2)_R framework. It performs parameter scans enforcing radiative electroweak symmetry breaking and neutralino LSP, identifies a viable bino-like bulk annihilation region with light right-handed stau NLSP after imposing R_φ̃ ≳ 10% mass splitting to exclude coannihilation, reports that these points satisfy LHC, flavor, and Planck 2018 relic density constraints with upper bounds m_χ̃₁⁰ ≲ 110 GeV and m_τ̃₁ ≲ 120 GeV, and discusses Higgs/Z-funnel regions with mu-sign dependence allowing a viable Z-funnel for μ<0 below projected LZ sensitivity. The space is claimed testable at CEPC/FCC-ee.

Significance. If the central results hold, the work provides a concrete, testable realization of light bino-like neutralino DM in a motivated GUT framework, with explicit mass upper bounds and collider reach predictions. The explicit treatment of both μ signs and the resulting destructive interference in direct detection for μ<0 is a useful observation. The enforcement of radiative EWSB plus neutralino LSP in the scan is a methodological strength that grounds the solutions in consistent model building.

major comments (1)
  1. [Methodology (R_φ̃ cut and bulk region)] Methodology section (description of bulk region selection and the R_φ̃ condition): The central claim of a viable 'genuine bulk annihilation' region with bino-like LSP and right-handed stau NLSP rests on the R_φ̃ ≳ 10% cut being sufficient to render stau coannihilation negligible in the relic-density calculation. For a bino LSP the t-channel slepton-exchange amplitude remains large even at ~10% splitting, so the Boltzmann equation can receive O(10-30%) corrections from coannihilation; without an explicit demonstration (e.g., a plot or table comparing Ωh² with and without the coannihilation term at the boundary of the cut) the reported Planck agreement and the mass bounds m_χ̃₁⁰ ≲ 110 GeV, m_τ̃₁ ≲ 120 GeV cannot be taken as robustly bulk-dominated.
minor comments (1)
  1. [Parameter scan description] The abstract and text refer to a 'comprehensive parameter scan' but do not specify the sampling method, prior ranges, or number of points generated; adding a short table or paragraph with these details would improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive comment on our manuscript. We address the major comment below and will revise the paper accordingly to strengthen the presentation of the bulk region.

read point-by-point responses

  1. Referee: Methodology section (description of bulk region selection and the R_φ̃ condition): The central claim of a viable 'genuine bulk annihilation' region with bino-like LSP and right-handed stau NLSP rests on the R_φ̃ ≳ 10% cut being sufficient to render stau coannihilation negligible in the relic-density calculation. For a bino LSP the t-channel slepton-exchange amplitude remains large even at ~10% splitting, so the Boltzmann equation can receive O(10-30%) corrections from coannihilation; without an explicit demonstration (e.g., a plot or table comparing Ωh² with and without the coannihilation term at the boundary of the cut) the reported Planck agreement and the mass bounds m_χ̃₁⁰ ≲ 110 GeV, m_τ̃₁ ≲ 120 GeV cannot be taken as robustly bulk-dominated.

    Authors: We thank the referee for highlighting this point. Our relic density is computed throughout with micrOMEGAs, which solves the full Boltzmann equation including all coannihilation channels. The ℛ_φ̃ ≳ 10% cut is imposed after the scan to isolate points in which bulk annihilation dominates, consistent with common practice in the literature for defining bulk regions. Nevertheless, we agree that an explicit validation of the cut would make the claim more robust. In the revised manuscript we will add a supplementary figure (or table) in the methodology section that compares the relic density computed with and without the stau coannihilation term for representative points lying at the ℛ_φ̃ = 10% boundary. This will quantify the size of any residual correction and confirm that it remains small enough not to affect the Planck compatibility or the reported mass upper bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external benchmarks

full rationale

The paper defines the bulk region via an explicit input cut R_φ̃ ≳ 10% on mass splitting, then scans parameters subject to radiative EWSB, neutralino LSP, and external constraints (Planck 2018 relic density, LHC searches, flavor observables). The reported upper bounds on m_χ̃₁⁰ and m_τ̃₁ emerge as scan outputs against those external data, not as quantities fitted or defined in terms of themselves. No self-citation chain, ansatz smuggling, or renaming of known results is present in the provided text; the μ-sign dependence is a model choice, not a derived output. The derivation chain is therefore self-contained against independent benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields limited visibility into the full set of assumptions; the ledger below records only those explicitly named in the abstract.

free parameters (2)
  • mu sign
    The paper treats both signs of mu as separate cases and finds qualitatively different direct-detection behavior; the choice is not derived from the model.
  • R_φ̃ threshold (10%)
    The mass-splitting cut used to isolate bulk annihilation is imposed by hand rather than derived.
axioms (2)
  • domain assumption Radiative electroweak symmetry breaking occurs and produces a neutralino LSP
    The scan is restricted to points satisfying this condition; it is a standard but non-trivial assumption of the MSSM.
  • domain assumption Planck 2018 relic density, LHC searches, and flavor observables are the complete set of external constraints
    The abstract states that solutions satisfy these; no other constraints are mentioned.

pith-pipeline@v0.9.1-grok · 5872 in / 1701 out tokens · 37646 ms · 2026-06-30T05:44:53.943002+00:00 · methodology

discussion (0)

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