Electromagnetic Dirac Cogenesis

Arnab Dasgupta; Debasish Borah

REVIEW 3 major objections 4 minor 1 cited by

Electromagnetic Dirac Cogenesis

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper proposes that one two-body decay through an electromagnetic dipole operator generates both the baryon asymmetry and dark matter, fixing the dark matter mass near 1.9 proton masses.

desk verdict Novel cogenesis idea with a clean DM-mass prediction, but the printed Boltzmann equations swap chiralities and vanish for massless final states, so the benchmark is not supported by the equations. read the letter →

arxiv 2507.11607 v1 pith:EJGXF4LZ submitted 2025-07-15 hep-ph astro-ph.CO

Debasish Borah , Arnab Dasgupta This is my paper

classification hep-phastro-ph.CO

keywords cogenesisasymmetricdarkmatterDiracleptogenesiselectromagneticdipoleoperatorbaryonasymmetryoftheUniverseradiationNeffvector-likefermions

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

This paper tries to show that the observed matter–antimatter imbalance and the dark matter abundance can both come from one set of out-of-equilibrium decays, with no net lepton-number violation anywhere. Heavy vector-like singlet fermions decay through an electromagnetic dipole operator into a right-handed Dirac neutrino and into a dark fermion, generating equal and opposite CP asymmetries in the two sectors. The neutrino asymmetry is transferred to ordinary leptons and then to baryons by electroweak sphalerons, while the dark fermion asymmetry survives as asymmetric dark matter. Because the two asymmetries are tied together and the Universe has roughly five times as much dark matter as baryonic matter, the model fixes the dark matter mass near 1.9 proton masses, with a long-lived three-body decay into two photons and a neutrino. It also predicts extra dark radiation, ΔNeff ≈ 0.14, from thermalized right-handed neutrinos, which future CMB experiments could see.

What carries the argument

The engine is the out-of-equilibrium two-body decay of a heavy vector-like singlet fermion $N_1$ through electromagnetic dipole operators, $(1/\Lambda) N \sigma^{\mu\nu} \nu_R B_{\mu\nu}$ and $(1/\Lambda) N \sigma^{\mu\nu} \chi B_{\mu\nu}$. Interference between tree-level and one-loop diagrams produces CP asymmetries $\epsilon_{\nu_R}$, $\epsilon_{\chi_L}$, $\epsilon_{\chi_R}$ whose sum vanishes by lepton-number conservation. Coupled Boltzmann equations track the comoving asymmetries in $\nu_R$, $\chi_L$, $\chi_R$ and the $N_1$ densities, with inverse decays and $2\to2$ processes as washouts; an out-of-equilibrium condition $\Gamma^{\rm wo}_{LR} < H$ keeps the $\nu_R$ and $\chi$ asymmetries from equilibrating. The relation $|\eta_{\Delta\chi_L}+\eta_{\Delta\chi_R}|\approx\eta_{\Delta\nu_R}$, combined with $\Omega_{\rm DM}\approx 5\Omega_B$, is what converts the asymmetry bookkeeping into the mass bound $m_\chi\lesssim 1.9\, m_p$.

What would settle it

Solve the full coupled Boltzmann equations (10)–(14) over a dense grid in the $\Lambda$ – $M_1$ plane and check the asymptotic relation $|\eta_{\Delta\chi_L}+\eta_{\Delta\chi_R}|\approx\eta_{\Delta\nu_R}$. If the two final asymmetries differ by an order-one factor in most of the allowed region, the predicted dark matter mass $m_\chi\approx1.9\, m_p$ and the $\Omega_\chi$ – $\Omega_B$ link break. A separate observational falsifier: observation of neutrinoless double $\beta$ decay would rule out the pure-Dirac neutrino assumption on which the equal-opposite asymmetry rests.

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Extended reading notes

Core claim

The central claim is that a single two-body decay channel, $N_i \to \chi B_\mu$ and $N_i \to \nu_R B_\mu$ via the dimension-five electromagnetic dipole operator, can simultaneously create the baryon asymmetry and the dark matter relic. Because the fermions are all Dirac-type and a global $U(1)_D$ symmetry is conserved, the loop-generated CP asymmetries satisfy $\epsilon_{\nu_R}+\epsilon_{\chi_L}+\epsilon_{\chi_R}=0$; the dark and neutrino sectors therefore carry exactly opposite asymmetries. Once the $\nu_R$ asymmetry is transferred to left-handed leptons through the neutrinophilic Higgs Yukawa and reprocessed by sphalerons, and the $\chi$ asymmetry is identified with asymmetric dark matter, the observed ratio $\Omega_{\rm DM}\approx 5\Omega_B$ forces $m_\chi \lesssim 1.9\, m_p$. The same framework predicts a TeV-scale cogenesis scale without resonant enhancement, a long-lived $\chi$ with the three-body decay $\chi \to \gamma \gamma \nu_R$, and $\Delta N_{\rm eff}\approx 0.14$ from thermalized right-handed neutrinos.

Load-bearing premise

The central claim depends on the final imbalance in the dark particle and the final imbalance in the neutrino coming out equal in magnitude after all the early-universe processes that could erase or transfer asymmetries; the paper shows this equality for one benchmark and does not demonstrate it across the full allowed parameter space.

Editorial extensions

If this is right

Dark matter has a fixed mass around 1.9 proton masses and decays as $\chi \to \gamma \gamma \nu_R$, making it a long-lived particle that can be sought in gamma-ray telescopes.
Successful cogenesis can happen at scales as low as a TeV, with no resonant enhancement of the CP asymmetry needed.
Three thermalized right-handed Dirac neutrinos give $\Delta N_{\rm eff}\approx 0.14$, within reach of future CMB experiments.
The heavy fermions $N$ can be searched at colliders through their dipole-induced mono-photon signatures.
The scenario is falsified if neutrinoless double beta decay is observed, since the mechanism requires Dirac neutrinos.

Reading between the lines

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

The paper fixes the DM mass using one benchmark where $|\eta_{\Delta\chi_L}+\eta_{\Delta\chi_R}|\approx\eta_{\Delta\nu_R}$; a full parameter scan might reveal that differing washout rates let the final asymmetries decouple, in which case the sharp $1.9\, m_p$ prediction would loosen into a range.
If a future CMB experiment measures $\Delta N_{\rm eff}$ between 0.1 and 0.15, it would align with exactly three thermalized right-handed neutrinos; a null measurement below 0.02 would exclude this model's dark-radiation signature while leaving the cogenesis mechanism itself untouched.
Replacing the effective dipole operator with a renormalizable UV completion would turn the cutoff $\Lambda$ into physical mediator masses and likely add charged-lepton flavor or electric-dipole observables, giving a low-energy test of the same cogenesis setup.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The paper has a clean idea: use two-body electromagnetic dipole decays of heavy vector-like fermions N into νR and χ to create equal and opposite CP asymmetries, then transfer the νR asymmetry into B−L while χ becomes asymmetric dark matter. That combination is new relative to the ALP-portal paper [51] and the electromagnetic leptogenesis paper [42], and the model gives sharp observables—mχ ~ 1.9 mp, ΔNeff ~ 0.14, and a χ→γγνR decay. If the mechanism works, it is a useful TeV-scale cogenesis variant. The detection discussion is concrete and well-grounded.

The problem is that the printed equations do not support the central quantitative claims. Eq. (1) has N_L coupling to νR and χR, and N_R coupling to χL. Eqs. (13)–(14) have N1L decaying to BμχL and N1R decaying to BμχR and BμνR—the reverse of what the Lagrangian permits. Consequently Eqs. (10)–(12) source and wash out the wrong species. Separately, Eq. (18) defines γ_{A→B} with K2(m_B/T) in the denominator; for massless B (photon or νR), K2(0) diverges, making γ=0. That kills the decay source terms, so the benchmark in Fig. 4 cannot be reproduced from the equations as written.

The DM mass prediction also rests on a weaker footing than the abstract implies. U(1)_D conservation gives ϵνR + ϵχL + ϵχR = 0, but that fixes the CP asymmetries, not the final comoving asymmetries after different washout rates operate. The paper asserts |ηΔχL + ηΔχR| ≈ ηΔνR after one benchmark; without a correct Boltzmann solution covering the parameter space, mχ ≤ 1.9 mp is an assumed relation, not a derived prediction.

Some of this may be typographical in the draft. The physics idea is coherent and the intended calculation is plausible. But as submitted, the numerical results are not supported by the equations, and the mass prediction is not derived from the model. A careful revision with corrected chiral assignments, a finite decay reaction density, and a real scan showing the asymmetry equality would make this a solid paper.

Would I send it to peer review? Yes—the idea is novel and the observables are sharp enough to deserve referee time, with the expectation of major revision. But I would not cite the current version, and I would flag the Boltzmann equations as the load-bearing issue.

Referee Report

3 major / 4 minor

Summary. The paper proposes a cogenesis mechanism in which the out-of-equilibrium decay of heavy vector-like fermions N into dark fermions χ and right-handed Dirac neutrinos ν_R through electromagnetic dipole operators generates equal and opposite CP asymmetries in the lepton and dark sectors. The ν_R asymmetry is transferred to left-handed lepton doublets by a neutrinophilic Higgs Yukawa coupling and subsequently converted to the baryon asymmetry by electroweak sphalerons, while the χ asymmetry forms asymmetric dark matter. The authors claim that total lepton number conservation fixes the dark matter mass to m_χ ≲ 1.9 m_p, that χ decays via χ → γγν_R giving indirect-detection signals, and that thermalized ν_R yields ΔN_eff ≈ 0.14. Quantitative results are obtained from a set of Boltzmann equations in Sec. III and illustrated by one benchmark in Fig. 4 and parameter-space plots in Fig. 5. The central quantitative claims, however, rest on Boltzmann equations that are internally inconsistent with the Lagrangian and contain a divergent reaction-density formula, and on an assumed equality of final asymmetries that is not derived from the dynamics.

Significance. If the mechanism works as advertised, the paper would be of considerable interest: it connects the baryon and dark matter abundances through a calculable relic asymmetry, predicts a specific O(GeV) dark matter mass, and gives falsifiable signatures in ΔN_eff, gamma-ray telescopes, and heavy neutral lepton searches. The setup is economical and the use of electromagnetic dipole operators for two-body decays is a distinctive twist on Dirac leptogenesis and asymmetric dark matter. The paper also makes a clean, testable prediction that neutrinos are purely Dirac, testable by neutrinoless double beta decay. However, the current manuscript does not support these claims as written: the printed Boltzmann equations do not describe the model defined by Eq. (1), the decay reaction densities vanish for massless final states as defined, and the key asymmetry-equality relation underlying the dark matter mass prediction is asserted rather than demonstrated. These are load-bearing deficiencies, not presentation issues.

major comments (3)

[Sec. III, Eqs. (10)-(14) vs Eq. (1)] The Boltzmann equations assign decay channels opposite to the chiral structure of the Lagrangian. In Eq. (1), N_{iL} couples to ν_R and χ_R (couplings λ_iα, h_Ri), while N_{iR} couples to χ_L (coupling h_Li). But Eq. (10) sources η_{Δν_R} from γ(N_{1R} → B_μν_R), Eq. (11) sources η_{Δχ_R} from γ(N_{1R} → B_μχ_R), and Eq. (12) sources η_{Δχ_L} from γ(N_{1L} → B_μχ_L). These are precisely the wrong chiral assignments, so the system solved in Fig. 4 produces asymmetries in species that do not couple to the stated initiator. The source and washout terms in Eqs. (10)-(14) therefore do not describe the model of Eq. (1); the authors must correct the channel assignments and re-solve the system.
[Sec. III, Eq. (18)] Equation (18) defines γ_{A→B} = n_eq^A K_1(m_A/T)/K_2(m_B/T) Γ_{A→B}. Since the final-state particles are taken to be massless in Eqs. (4)-(6) (and the photon is massless regardless), K_2(m_B/T) with m_B = 0 diverges, so every decay reaction density vanishes identically. Consequently, all decay source terms and inverse-decay washout terms in Eqs. (10)-(14) are zero, and the evolution shown in Fig. 4 cannot be generated by the printed equations. The standard thermal decay density uses the decaying particle mass in the K_2 factor; this should be corrected and the numerical benchmark recomputed.
[Sec. IV, derivation of m_χ ≲ 1.9 m_p] The load-bearing relation |η_{Δχ_L} + η_{Δχ_R}| ≈ η_{Δν_R} is introduced only by inspection of one benchmark, after the statement in the paragraph containing Eq. (24). It is not derived from the Boltzmann equations. Equations (10)-(12) contain distinct inverse-decay and scattering washout terms for ν_R, χ_R, and χ_L, so even if the CP-sum rule ϵ_νR + ϵ_χL + ϵ_χR = 0 holds, the final comoving asymmetries can differ substantially from the initially produced ones. The dark matter mass bound and the Ω_χ/Ω_B relation follow only if this equality is robust. The authors should either prove the equality from the (corrected) Boltzmann system, demonstrate it numerically across the allowed parameter space, or replace the sharp mass prediction with a range; without this, the headline O(1) GeV dark matter mass is unsupported.

minor comments (4)

[Sec. IV and Fig. 4 caption] The text and figure caption refer to an 'axion decay constant' when describing the scale Λ of the dipole operators; this should be the cutoff scale Λ, not an axion decay constant.
[Sec. III, Eq. (18)] Apart from the divergent K_2(m_B/T), the notation in Eq. (18) should specify whether Γ_{A→B} is the zero-temperature rest-frame partial width; as written the reader cannot check dimensions without guessing.
[Fig. 4] The axis labels and legend in Fig. 4 are corrupted ('= 10 5', '| R|', etc.), making the benchmark difficult to interpret; the figure should be regenerated with clear labels.
[General] Equation (2) is described as following from 'total lepton number conservation.' Since the symmetry is actually the global U(1)_D discussed in Sec. II, the wording should be aligned to avoid confusion with SM lepton number.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the m_chi <= 1.9 m_p bound is a standard asymmetric-dark-matter constraint using measured abundances and unitarity, not a fit or self-citation chain.

full rationale

The paper's central quantitative claim, m_chi <= 1.9 m_p, follows from the net-lepton-number-conservation relation epsilon_nuR + epsilon_chiL + epsilon_chiR = 0 (Eq. 2), the observed ratio Omega_DM ~ 5.36 Omega_B, and the final-asymmetry relation |eta_Delta chi_L + eta_Delta chi_R| ~ eta_Delta nu_R stated after the Fig. 4 benchmark. The last relation is asserted for one benchmark rather than proven over the parameter space, and the Boltzmann equations contain apparent technical defects (chiral assignments in Eqs. 13-14 relative to Eq. 1; Eq. 18 involves K2(m_B/T) which diverges for massless B). These are correctness or supportability concerns, not circularity: the mass bound is not obtained by defining the prediction in terms of itself, and the CP-asymmetry sum is derived from the displayed loop-level expressions rather than imported from a fit. The self-citations [42] and [51] are background references for the two-body decay kinematics and for a related ALP cogenesis mechanism; neither is used as the exclusive justification for the central claim. No equation in the paper reduces to its input by construction, and no fitted parameter is renamed as a prediction. Accordingly, no circular step can be exhibited under the required standard, and the appropriate finding is no significant circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 4 invented entities

The model introduces a new set of free parameters (mass, cutoff, couplings, Yukawa) constrained by BAU, DM relic, washout, and lifetime conditions. The only assumption that is both load-bearing and underjustified is the equality of the final asymmetries. Invented entities are standard BSM additions with some independent phenomenological handles.

free parameters (6)

M1 (heavy fermion mass) = 10^3 to 10^12 GeV
Central scale of cogenesis, scanned over to satisfy BAU, DM relic, washout, and EFT constraints.
Lambda (dipole operator cutoff) = 10^6 to 10^14 GeV; benchmark 1.5e9 GeV
Controls all decay rates and washout; chosen by fitting to observed BAU and DM relic.
m_chi (dark fermion mass) = about 1.9 GeV
Set to saturate Omega_chi = Omega_DM using the asymmetry equality.
lambda, h_L, h_R couplings = 1 or 0.1
Order-one values that set the CP asymmetries; smaller values open up more parameter space.
CP asymmetry scale epsilon = 10^-5 or 10^-2
An input parametrization for the scan; the underlying phases are not specified.
Dirac Yukawa y = >= 10^-8
Lower bound for nu_R equilibration; no specific value chosen.

assumptions (5)

domain assumption Global U(1)_D symmetry is exactly conserved, forbidding Majorana mass terms and keeping neutrinos purely Dirac.
Invoked in Section II to eliminate lepton-number violation and enforce Eq. (2).
domain assumption The dimension-5 dipole EFT is valid with Lambda > M1.
Used throughout; parameter space below Lambda > M1 is shaded as invalid in Fig. 5.
standard math The electroweak sphaleron conversion factor C_sph = 8/23 with N_H=2, N_f=3 and S=27.3 is applied.
Standard result, Eq. (21).
domain assumption The nu_R Yukawa interaction with H2 is in equilibrium before sphaleron decoupling (y >= 10^-8), and nu_R <-> chi scatterings remain out of equilibrium (Gamma_wo_LR < H).
Required for successful transfer of asymmetry to leptons without washout, Eqs. (19)-(20).
ad hoc to paper The final asymmetries satisfy |eta_Delta chi_L + eta_Delta chi_R| approx eta_Delta nu_R.
Asserted in Section IV before Eq. (24); needed for m_chi <= 1.9 m_p but not proven over the parameter space.

invented entities (4)

Heavy vector-like singlet fermions N_L,R independent evidence
purpose: Out-of-equilibrium decay sources that generate CP asymmetries in nu_R and chi via dipole operators.
Can be searched at colliders through dipole-induced mono-photon signatures; no specific mass prediction is given.
Dark fermion chi_L,R independent evidence
purpose: Long-lived asymmetric dark matter candidate with three-body decay chi -> nu_R gamma gamma.
Gives a continuum gamma-ray signature with m_chi around GeV within reach of future MeV/GeV telescopes; lifetime constraint applied.
Right-chiral Dirac neutrino nu_R (three copies) independent evidence
purpose: Carries the lepton asymmetry and, once thermalized, contributes Delta Neff about 0.14.
Probeable via future CMB-S4/CMB-HD measurements of Neff and excluded if neutrinoless double beta decay is observed.
Neutrinophilic second Higgs doublet H2
purpose: Transfers nu_R asymmetry to left-handed leptons via a tiny VEV.
Required for the model but has no distinctive collider signature identified in the paper.

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Cite this review

Pith. "Pith review of Electromagnetic Dirac Cogenesis." pith.science (2026). https://pith.science/paper/EJGXF4LZ

@misc{pith2026250711607,
  author       = {Pith},
  title        = {Pith review of: Electromagnetic Dirac Cogenesis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EJGXF4LZ}},
  note         = {Machine review of arXiv:2507.11607}
}

abstract

We propose a novel cogenesis mechanism by utilising the two-body decay of heavy vector-like fermions to dark matter (DM) $\chi$ and right chiral part of light Dirac neutrino $\nu_R$ via the electromagnetic dipole operator. This leads to generation of asymmetry in dark fermion $\chi$ as well as $\nu_R$ with the latter getting transferred to left-handed lepton doublets via Yukawa interactions with a neutrinophilic Higgs doublet. While lepton asymmetry is converted into baryon asymmetry of the Universe via electroweak sphalerons, the dark fermion asymmetry results in asymmetric dark matter. Since CP asymmetries in lepton and dark sector are equal and opposite due to net lepton number conservation, DM mass is restricted to a fixed value $\sim \mathcal{O}(1)$ GeV. Long-lived nature of DM keeps indirect detection prospects at gamma-ray telescopes alive while thermalised light Dirac neutrinos lead to observable dark radiation at cosmic microwave background (CMB) experiments. Heavy vector-like fermions can be probed at terrestrial experiments via their electromagnetic dipole interactions.

Figures

Figures reproduced from arXiv: 2507.11607 by the authors.

**Figure 2.** FIG. 2: Feynman diagrams of processes responsible for gen [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3: Three-body decay of dark matter [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4: Evolution of comoving number densities for [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5: Allowed parameter space of electromagnetic Dirac cogenesis in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Forward citations

Cited by 1 Pith paper

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