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Decaying scalar dark matter in the minimal left-right symmetric model

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The real neutral scalar of the right-handed triplet is claimed to be a viable decaying dark-matter candidate in the keV-to-multi-MeV range if v_R is at least 10^15 GeV, at the cost of severe fine-tuning.

desk verdict New candidate, clean vacuum-stability bound, but the scenario's radiative stability is not demonstrated and the abstract oversells what is shown. read the letter →

arxiv 2501.14669 v2 pith:H4G3VPM2 submitted 2025-01-24 hep-ph

P. S. Bhupal Dev , Julian Heeck , Anil Thapa This is my paper · ORCID
classification hep-ph PACS 95.35.+d12.60.Cn14.60.Pq98.80.-k
keywords left-rightsymmetricmodelscalardarkmatterdecayingtwo-photondecayright-handedneutrinosseesawmechanismleptogenesisvacuumstability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes that the real neutral component of the SU(2)_R triplet Higgs field, denoted χ ≡ Re($Δ_R^{0}$), can serve as the dark matter in the minimal left-right symmetric model, decaying slowly into two photons. To be cosmologically long-lived, χ must be very light while the left-right breaking scale v_R is very high: the viable window is roughly m_χ in the keV-to-multi-MeV range with v_R ≳ $10^{15}$ GeV. The authors show that such a hierarchy can be arranged, though only by fine-tuning the triplet quartic coupling ρ_1 to about 5 × $10^{-43}$, and that the resulting vacuum-stability constraint forbids right-handed neutrino masses in the window $\sqrt$(m_χ v_R) ≲ m_N ≲ v_R. The remaining parameter space still accommodates neutrino masses through the seesaw mechanisms and the observed baryon asymmetry through leptogenesis. If correct, this gives the minimal left-right model a way to explain dark matter, neutrino masses, and matter-antimatter asymmetry simultaneously without adding new particles.

What carries the argument

The load-bearing object is the scalar χ = Re($Δ_R^{0}$), whose mass is set by $m_χ^{2}$ ≈ 2ρ_1 $v_R^{2}$ in the limit of small mixing angles θ_1 and θ_2. Keeping m_χ at keV-MeV with v_R ≳ $10^{15}$ GeV forces the quartic coupling to ρ_1 ≈ $m_χ^{2}$/($2v_R^{2}$) ≈ 5 × $10^{-43}$ at the scale m_χ. The lifetime comes from the one-loop decay width Γ(χ → γγ) through W_R^± and charged triplet/bidoublet scalars, which scales as $α^{2}$ $m_χ^{3}$/($1028π^{3}$ $v_R^{2}$) times a loop-factor combination. The argument then hinges on renormalization-group stability: the right-handed neutrino Yukawa coupling f feeds a negative -16|f|^4 contribution into the running of ρ_1, which is what produces the forbidden neutrino mass window of Eq. (12). Production of the observed abundance can proceed through thermal freeze-out followed by entropy dilution, through UV freeze-in with reheating below v_R, or via late decays of a long-lived right-handed neutrino.

What would settle it

Measure the χ → γγ line from a dark-matter-rich region and compare its rate with Eq. (9): a detected line whose rate is incompatible with the claimed m_χ and v_R, or a W_R discovery at the LHC implying v_R around the TeV scale, would rule the scenario out; equally, a complete threshold-corrected two-loop RGE calculation that finds no positive ρ_1 trajectory from m_χ up to v_R would falsify it.

Watch

Extended reading notes

Core claim

The central claim is that Re($Δ_R^{0}$) ≡ χ, the same scalar whose vacuum expectation value breaks SU(2)_R × U(1)_{B-L} down to Standard Model hypercharge, is a viable decaying dark-matter candidate. For m_χ between roughly 10 keV and a few MeV, and v_R ≳ $10^{15}$ GeV, the one-loop decay χ → γγ has a lifetime longer than the age of the Universe and evades existing X-ray and gamma-ray line searches. The authors derive the decay width, the allowed region, and the constraint that vacuum stability forbids right-handed neutrino masses in the window $\sqrt$(m_χ v_R) ≲ m_N ≲ v_R. In the allowed windows the model can generate active neutrino masses by type-I or type-II seesaw and can produce the baryon asymmetry through resonant or flavor-enhanced leptogenesis. They present this as an economical alternative to the usually considered right-handed-neutrino dark matter in the same model, and conjecture that the candidate survives in Pati-Salam and SO(10) embeddings.

Load-bearing premise

The load-bearing premise is that the triplet self-coupling ρ_1 can be tuned to about 5 × $10^{-43}$ at the dark-matter mass scale and remain positive up to v_R ≈ $10^{17}$ GeV; the paper labels this severe fine-tuning and did not find a consistent two-loop solution when lighter scalars were used to offset the negative neutrino contribution.

Editorial extensions

If this is right

  • If the central claim is right, χ can make up all the dark matter and should produce a sharp two-photon line from dark-matter-rich regions; a detected line whose strength matches Eq. (9) would be direct evidence.
  • The model predicts that any right-handed neutrino with mass between sqrt(m_χ v_R) and v_R is excluded, so future searches for heavy neutrinos can either confirm or falsify the scenario.
  • Discovering a W_R boson at the LHC, or any other indication that v_R is far below 10^15 GeV, would kill this dark-matter candidate.
  • The same χ candidate should remain viable when the left-right model is embedded in Pati-Salam or SO(10), giving those unification frameworks a built-in decaying dark-matter option.
  • Future MeV gamma-ray telescopes should probe most of the currently allowed mass range up to multi-MeV, as the paper's future-reach line indicates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the ρ_1 tuning is the real bottleneck, so any ultraviolet symmetry that suppresses this quartic would turn the candidate from a fine-tuned option into a robust prediction and would also erase the forbidden neutrino window of Eq. (12).
  • Beyond the paper: the forbidden window supplies a sharp global test—if a future experiment measures a right-handed neutrino mass inside sqrt(m_χ v_R) ≲ m_N ≲ v_R at the same time a χ → γγ line is reported, the two observations cannot both be explained by this model.
  • Beyond the paper: by setting the mixing angles θ_1 and θ_2 to zero the paper chooses the most constrained branch; nonzero mixing introduces extra loop contributions and can even tune the diphoton rate to zero, which would allow a much lower v_R and make the candidate testable at colliders.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes that the lightest neutral component of the SU(2)_R triplet, Re(Delta_R^0)=chi, can serve as a decaying dark matter candidate in the minimal left-right symmetric model. The authors compute the loop-induced chi -> gamma gamma width, derive the allowed parameter space from X-ray, gamma-ray, and structure-formation constraints, and show that m_chi in the keV-to-multi-MeV range forces v_R ≳ 10^15 GeV. They then analyze the vacuum-stability constraints on the right-handed neutrino mass that follow from the very small quartic coupling rho_1, and discuss two viable mass windows for the N's, with mechanisms for the DM abundance, neutrino masses, and leptogenesis.

Significance. If the radiative-stability issue for the chi-h mixing angle is resolved, this would be a genuinely new and economical DM candidate in a well-motivated extension of the Standard Model, with falsifiable predictions (a monochromatic X-ray/gamma-ray line and the absence of W_R at colliders). The paper is transparent about the extreme fine-tuning in rho_1, and it provides a detailed scalar-sector analysis, a standard decay-width calculation in Appendix B, and a careful application of astrophysical constraints. The numerical RGE work in Appendix D is cross-checked against known results, which is a strength. However, the central DM longevity claim is not yet established because the tree-level vanishing of the chi-h mixing is not shown to be radiatively stable, and the combined benchmark for all cosmological requirements is not supplied.

major comments (3)
  1. [Sec. III, Eq. (A11), Appendix D] The DM lifetime is controlled by the assumption theta_1,2 << 1, but the radiative stability of the tree-level cancellation C1 = 0 in Eq. (A12) is never analyzed. For the benchmark m_chi = 1 MeV, v_R = 10^17 GeV, the intrinsic Gamma(chi -> gamma gamma) in Eq. (9) is ~10^-50 GeV, so the h-mediated width theta_1^2 Gamma(h -> gamma gamma)(m_chi/m_h)^3 keeps tau_chi ≳ 10^25 s only if theta_1 ≲ 10^-15. From Eq. (A11), C1 = theta_1 kappa_+(m_h^2 - m_chi^2)/v_R, so theta_1 ≲ 10^-15 requires C1 ≲ 4 x 10^-26 GeV^2, i.e., a cancellation in alpha_1 at the 10^-30 level. The scalar potential has no symmetry enforcing C1 = 0, and one-loop W_R/charged-scalar corrections generically shift alpha_1 by ~g_R^4/(16 pi^2) ~ 10^-5, which would give theta_1 many orders of magnitude above the allowed value. Appendix D tracks rho_1 and the effective low-energy quartics but not alpha_1, alpha_2, alpha_3, or C1, so the paper does not address this issue. Unless a protective symmetry is identified or the required extra fine-tuning is quantified, the chi -> gamma gamma lifetime and hence the DM candidate are not established.
  2. [Secs. IV-V and Conclusion] The abstract and conclusion claim that the scenario simultaneously explains DM, neutrino masses, and the baryon asymmetry, but the paper does not provide a complete parameter point satisfying all constraints. In the late-entropy dilution mechanism of Sec. IV, the needed lifetime tau_N ~ 10^-12 s (Eq. (18)) is many orders of magnitude longer than the seesaw estimate following from Eq. (14); the text addresses this only by saying that one of the three N's must have much smaller Yukawa couplings, without demonstrating that neutrino oscillation data can still be fitted or that the same N can also provide resonant leptogenesis without spoiling the dilution. The UV freeze-in and heavy-N options similarly require additional inputs (reheating temperature, inflaton decay, or new particles) that are not part of the minimal model. Thus the claim to simultaneously explain all three observables is stronger than what is demonstrated.
  3. [Appendix D, Eq. (11)] The numerical benchmark stated in Appendix D (m_chi = 1 MeV, v_R = 10^17 GeV, f ≲ 6 x 10^-11) appears inconsistent with the vacuum-stability bound derived from Eq. (11). For one N, |f| < sqrt(pi) rho_1^{1/4}/4 gives f ≲ 3.7 x 10^-11 (m_N ≲ 5 x 10^6 GeV), and even the three-N version of Eq. (12) gives f ≲ 5.4 x 10^-11. The quoted f = 6 x 10^-11 exceeds both, so the statement that this benchmark yields a consistent solution needs clarification or a corrected value, with the actual values of f and m_N used in the RGE run.
minor comments (4)
  1. [Sec. V] The sentence 'with v_R ≳ 10^15 GeV from Fig. 1' should refer to Fig. 2, which displays the v_R-m_chi constraints; Fig. 1 is the loop diagram for chi -> gamma gamma.
  2. [Eq. (12)] Please write the lower bound as sqrt(m_chi v_R) rather than the ambiguous notation '√m_chi v_R'.
  3. [Eq. (16)] The formula uses g_*(T_f) = 106.75, but at T_f ~ v_R the LR model contains many additional degrees of freedom; please clarify whether 106.75 is used only as a reference value, since this affects the numerical statement about m_chi ~ 170 eV.
  4. [Appendix D] Please state explicitly whether the two-loop search with lighter scalars was performed in the same parameter region as the f << 1 benchmark, so that the reader can separate the negative result from the benchmark solution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DM mass and mixing angles are tuned inputs, not derived predictions; the decay width is re-derived in an appendix, and the abundance discussion explicitly treats dilution and freeze-in as accommodations rather than predictions.

full rationale

The paper's central claim is that Re(Delta_R^0) can be a long-lived decaying DM candidate if the quartic coupling rho_1 is tuned to approximately m_chi^2/(2 v_R^2) and the scalar mixing angles are set to zero. These are inputs, not outputs of a derivation: the paper explicitly calls the required hierarchy 'severe fine-tuning' and 'the price we pay for this DM candidate.' No equation is used to derive these parameters in a way that then masquerades as a prediction. The decay width in Eq. (9) is derived in Appendix B from standard one-loop functions; the citation to Ref. [37], which shares an author, is convenient but not load-bearing because the formula is reproduced in the paper. The vacuum-stability constraint of Eq. (12) follows from the explicit RGE beta function for rho_1 in Eq. (D1), with the negative f^4 contribution shown in Eq. (11), and it is checked with the public PyR@TE package; it is a consistency condition rather than an imported uniqueness theorem. The abundance formula Eq. (16) is the standard thermal freeze-out result and is used to show that the naive relic abundance overcloses for the target mass range; the subsequent dilution and freeze-in mechanisms are parameter choices that accommodate, not predict, the observed Omega h^2. Appendix D honestly admits the failure to find a two-loop solution with lighter scalars, which is a limitation on the scenario's radiative viability, not a circular argument. The main unresolved weakness is the radiative stability of theta_1 = 0, which the paper does not analyze; this is a correctness and fine-tuning risk, not circularity, because the tree-level cancellation in Eq. (A12) is stated as an assumption. Self-citations in Refs. [14-16,30,37,39,51,64] either concern background material or are supported by the paper's own equations, so none reduces the derivation to its inputs. No circular step can be exhibited from the text.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The ledger makes the hidden cost explicit: the 'economical' scenario rests on eight free choices (the tuned quartic rho_1, the DM mass, the LR scale, the triplet Yukawa f, the right-handed neutrino masses, vanishing mixings, the abundance machinery, and near-degenerate N for resonant leptogenesis), plus the standard assumptions of the LR framework and early-universe cosmology. No new particles are invented: chi is an existing field of the model, which is a genuine virtue. The derived content is the vacuum-stability window (Eq. 12) and the lifetime relation (Eq. 9); everything else is parameter choice.

free parameters (8)
  • rho_1 (quartic coupling of Delta_R) = ~5 x 10^-43 (m_chi/100 keV)^2 (10^17 GeV/v_R)^2
    Chosen tiny so that m_chi is much smaller than v_R (Eqs. 8-10); this tuning is the price of entry for the DM candidate and is acknowledged by the authors.
  • m_chi (scalar DM mass) = keV to multi-MeV (free scan parameter)
    The DM mass is an input scanned over in Fig. 2, not predicted by the model.
  • v_R (left-right breaking scale) = 10^15 to ~10^19 GeV (allowed band in Fig. 2)
    Free scale; lower values excluded by X-ray and gamma-ray limits on chi to gamma gamma, higher values by v_R below the Planck mass requirement.
  • f (triplet Yukawa coupling to N) = |f| ≲ (pi rho_1/4)^(1/4), i.e. m_N ≲ sqrt(m_chi v_R)
    Must be tiny in the light-N window to keep rho_1 positive (vacuum stability, Eqs. 11-12).
  • m_N (right-handed neutrino mass) = m_N < sqrt(m_chi v_R) ~ 3 x 10^6 GeV or m_N > v_R
    The intermediate window is forbidden by vacuum stability (Eq. 12); both windows are free choices.
  • theta_1, theta_2 (chi mixing angles with h, H) = set to zero
    For concreteness the authors effectively set theta_1,2 = 0 (Sec. III); nonzero mixings would add decay channels and possible fine-tuned loop cancellations.
  • tau_N or T_reh (abundance machinery) = tau_N long enough for S ≳ 25, or T_reh in a 'sweet spot' below v_R
    The observed DM abundance is not reproduced from the model; it is enforced via entropy dilution (Eq. 19, requiring an assumed long-lived N with small Yukawa) or UV freeze-in with a tuned reheat temperature (Sec. IV.3).
  • Near-degeneracy of N for resonant leptogenesis = two or more almost degenerate N
    The Davidson-Ibarra bound (m_N ≳ 10^9 GeV) is violated, so the observed asymmetry requires resonant leptogenesis, an additional fine-tuning (Secs. IV.2 and IV.3).
assumptions (7)
  • domain assumption The minimal LR gauge group SU(3)c x SU(2)L x SU(2)R x U(1)B-L with parity symmetry and the stated particle content (Eqs. 1-2)
    The framework itself, cited to Refs. [1-5]; unproved background.
  • standard math The most general renormalizable scalar potential of Eq. (A1), with real VEVs and no CP violation
    Standard LR scalar potential from Ref. [59]; BSM content pulled from prior literature.
  • ad hoc to paper A parameter region with rho_1, theta_1,2 much less than 1 exists and is self-consistent
    The central fine-tuning assumption (Sec. III, Eqs. 8-10); the authors acknowledge it but the two-loop stability is not demonstrated, and Appendix D admits no consistent solution with scalar mitigation.
  • domain assumption (Semi-)thermal DM production mechanism
    Sec. III: 'we do, however, assume a (semi-)thermal mechanism rather than condensation or misalignment', used to justify the Lyman-alpha mass bounds.
  • standard math One-loop RGE for rho_1 with the f^4 contribution (Eq. 11) and standard beta functions (Eq. D1)
    Standard perturbative RGE framework; the negative f^4 term is the driver of the m_N constraint.
  • standard math Standard cosmology: relativistic freeze-out abundance (Eq. 16), entropy dilution (Eqs. 17-19), UV freeze-in
    Standard early-universe formulas from Refs. [48-51].
  • standard math Loop-function asymptotics A0(0) ~ 1/3 and A1(0) ~ -7 in Eq. (9)
    Standard one-loop results for scalar and W-boson contributions to diphoton amplitudes; valid for m_chi much smaller than the loop masses.

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Pith. "Pith review of Decaying scalar dark matter in the minimal left-right symmetric model." pith.science (2026). https://pith.science/paper/H4G3VPM2

@misc{pith2026250114669,
  author       = {Pith},
  title        = {Pith review of: Decaying scalar dark matter in the minimal left-right symmetric model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H4G3VPM2}},
  note         = {Machine review of arXiv:2501.14669}
}
abstract

In the minimal left-right symmetric theory, the dark matter candidate is usually ascribed to the lightest right-handed neutrino. Here we present an alternative decaying dark matter candidate in this model in terms of the lightest neutral scalar from the $SU(2)_R$-triplet field. This setup requires a vast hierarchy between the scalar mass and the left-right symmetry breaking scale, which renders the scalar dark matter sufficiently stable on cosmological time scales. The stability of the dark matter imposes constraints on the right-handed neutrino mass, which has consequences for the neutrino mass generation, as well as for leptogenesis. Although somewhat fine-tuned, it provides a very economical scenario wherein the minimal left-right model can simultaneously explain dark matter, neutrino masses, and the matter-antimatter asymmetry of the Universe.

Figures

Figures reproduced from arXiv: 2501.14669 by the authors.

Figure 1
Figure 1. FIG. 1. Loop-induced decay of scalar DM into photons [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. One-loop contribution to the quartic-coupling con [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Allowed parameter space (unshaded) for the DM [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of the quartic couplings to show that the electroweak vacuum is stable all the way up to Planck scale. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Loop-Level Lepton Flavor Violation and Diphoton Signals in the Minimal Left-Right Symmetric Model

    hep-ph 2025-12 conditional novelty 6.0 of 10

    Recasting axion limits onto the one-loop H3 couplings of the minimal left-right symmetric model excludes the right-handed scale up to 2×10^9 GeV and could eventually probe 6×10^11 GeV.

Reference graph

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Reviewed August 10, 2026 · model on record in the stance chip above.