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REVIEW 3 major objections 5 minor 1 cited by

Two-component Dark Matter and low scale Thermal Leptogenesis

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Two dark matter species are made to share one coupling with the cosmic matter–antimatter asymmetry, and the paper maps where all constraints overlap.

desk verdict Novel two-component DM/leptogenesis correlation, but the quantitative BAU regions rest on an incomplete Boltzmann treatment that needs a referee. read the letter →

arxiv 2412.21202 v2 pith:G5DAOFO5 submitted 2024-12-30 hep-ph

Subhaditya Bhattacharya , Devabrat Mahanta , Niloy Mondal , Dipankar Pradhan This is my paper · ORCID
classification hep-ph
keywords two-componentdarkmatterthermalleptogenesisscotogenicmodelradiativeneutrinomassCPasymmetryWIMPconversionleptonflavorviolation
topics Matter-Antimatter AsymmetryDark Matter
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 tries to show that a single extension of the Scotogenic model can tie together three unrelated cosmic puzzles: the observed baryon asymmetry, the small neutrino masses, and the dark matter relic abundance. It proposes two-component dark matter, an inert doublet and a real singlet, and arranges the same couplings that generate the CP asymmetry in right-handed neutrino decay to also control dark matter conversion and relic density. This establishes a direct interdependence, so a point that produces the right baryon asymmetry is immediately constrained by dark matter bounds and neutrino data. A sympathetic reader would care because this makes the dark matter sector experimentally testable through leptogenesis observables and vice versa.

What carries the argument

The central object is the one-loop vertex correction to $N_1\to\ell_\alpha\eta_1$, where the internal line is cut on the singlet $\phi$ and the second inert doublet $\eta_2$. Its imaginary part, computed in Appendix C, is proportional to $\mathrm{Im}(h_{22\alpha}\,y_{12\phi}\,\mu_{12\phi}\,h^*_{11\alpha})$, and it is this imaginary part that generates the CP asymmetry $\varepsilon_{N_1}$. The same $\mu_{12\phi}\,\eta_1^\dagger\eta_2\phi$ interaction controls the $\eta_1\leftrightarrow\phi$ conversion processes used in the dark matter Boltzmann equations, and a small mass splitting between the two dark matter components makes the conversion efficient enough to share the relic density correctly. The second load-bearing element is the scotogenic one-loop neutrino mass formula with two inert doublets, which through the Casas–Ibarra parametrization determines the Yukawa couplings $h_{kk\alpha}$ from neutrino data.

What would settle it

Include the omitted scattering terms, such as $N_1\phi\to\ell_\alpha\eta_2^\dagger$ and $N_1\eta_1\to\ell_\alpha V_\mu$, in the $Y_{N_1}$ evolution equation and recompute $Y_{B-L}$ for the benchmark points of Table 2; if the final asymmetry shifts by more than an order of magnitude, the BAU-allowed region shown in Figures 5 and 10 is not stable under the full Boltzmann dynamics.

Watch

Extended reading notes

Core claim

The paper claims that in a model with two inert doublets ($\eta_1,\eta_2$), two right-handed neutrinos ($N_1,N_2$), and a real singlet $\phi$, stabilized by a $\mathbb{Z}_2\otimes\mathbb{Z}_2'$ symmetry, the CP asymmetry in $N_1\to \ell_\alpha \eta_1$ decay receives a one-loop vertex correction whose imaginary part is proportional to $\mathrm{Im}(h_{22\alpha}\,y_{12\phi}\,\mu_{12\phi}\,h^*_{11\alpha})$. Because this correction is independent of the tiny Yukawa couplings fixed by neutrino masses, the Davidson–Ibarra bound is evaded and TeV-scale leptogenesis becomes possible even though the decay parameter $K_{N_1}$ is always in the strong-washout regime. The same couplings $y_{12\phi}$ and $\mu_{12\phi}$ enter the $\eta_1\leftrightarrow\phi$ conversion processes that set the two dark matter relic densities, and the inert doublets also appear in the one-loop radiative neutrino mass formula. The paper therefore establishes a concrete correlation: baryon asymmetry, active neutrino masses, and both dark matter components are governed by overlapping parameters, and it identifies the surviving parameter space after imposing the observed baryon asymmetry, neutrino oscillation data, relic density, direct and indirect detection limits, and collider bounds.

Load-bearing premise

The account assumes that the coupled Boltzmann equations track the asymmetry accurately even though some scattering processes that change the right-handed neutrino abundance are left out.

Editorial extensions

If this is right

  • If the central claim is correct, thermal leptogenesis can proceed at the TeV scale in a two-right-handed-neutrino setup without invoking the Davidson–Ibarra bound, because the new vertex-coupling combination is free from the neutrino-mass constraints.
  • The same parameter point that reproduces the observed baryon asymmetry must also reproduce the dark matter relic density, so future direct detection experiments such as LUX-ZEPLIN, PandaX-xT, and XLZD can directly probe the leptogenesis-favored region.
  • The two-component structure relaxes the restrictive inert-doublet relic-density window, because the singlet $\phi$ can carry the missing abundance through $\eta_1\leftrightarrow\phi$ conversion, opening parameter space that a single-component inert doublet model would exclude.
  • The $\eta_1$-$\phi$ conversion requires a small mass splitting $\Delta m\lesssim 10$ GeV, giving a sharp, testable prediction for the mass spectrum that connects the dark matter sector to leptogenesis.

Reading between the lines

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

  • The same vertex-loop relation should generate a correlation between the neutrino mass ordering and the size of the CP asymmetry, since the imaginary part $\mathrm{Im}(h_{22\alpha}\,y_{12\phi}\,\mu_{12\phi}\,h^*_{11\alpha})$ depends on the Casas–Ibarra rotation parameters; scanning both orderings could reveal which ordering makes the baryon asymmetry easier to generate.
  • The paper leaves the WIMP-pFIMP branch ($\lambda_{\phi H}\sim 10^{-12}$) for future work; in that branch the singlet would decouple from direct detection while still contributing through conversions, so the two dark matter components would separate cleanly in future detection channels.
  • The charged components of the inert doublets are within collider reach for the benchmark points, so a search for the associated charged-scalar signatures at the HL-LHC could provide an indirect probe of the leptogenesis scale even if the right-handed neutrinos are too heavy to produce directly.
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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 / 5 minor

Summary. The manuscript proposes an extension of the scotogenic model with two inert doublets, two right-handed neutrinos, and a real scalar singlet, stabilized by a Z2 x Z2' symmetry, so that the lightest inert doublet component and the singlet form a two-component dark matter sector. Neutrino masses arise radiatively at one loop, while the baryon asymmetry is generated by thermal leptogenesis from the decay of the lightest right-handed neutrino N1, with the CP asymmetry sourced by a vertex correction that involves the two DM scalars through the couplings y12phi and mu12phi. The authors solve coupled Boltzmann equations for N1 and B-L, scan over model parameters satisfying neutrino oscillation data and the observed baryon asymmetry, and then impose DM relic density, direct and indirect detection limits, and collider and lepton-flavor constraints. The central claim is that the same couplings and masses control the CP asymmetry, DM-DM conversion, and the radiative neutrino mass generation, establishing a three-way correlation among baryon asymmetry, DM, and neutrino masses, with several benchmark points and combined plots shown in Figs. 5 and 10.

Significance. If the correlation holds, the model is a useful proof of principle that low-scale leptogenesis and a two-component DM sector can be tied together by explicit couplings, rather than merely coexisting in the same model. The paper has clear strengths: the appendices contain a detailed analytic derivation of the neutrino mass matrix and the CP asymmetry, including an explicit comparison with the literature in the limiting case; the DM analysis uses micrOMEGAS-6.0 for coupled Boltzmann equations; and the parameter scans incorporate a broad set of current constraints from LEP, LHC, MEG II, LUX-ZEPLIN, and Fermi-LAT. The manuscript is also honest about the residual sign discrepancy with reference [47] and about the fact that some scattering processes affect N1 number densities. However, the reliability of the leptogenesis calculation in the strong-washout regime is the main load-bearing element, and the completeness of the scattering set in the Boltzmann equations is not established, which makes the claimed quantitative correlation provisional until that point is addressed.

major comments (3)
  1. [Section 4, eq. (4.2)] The Boltzmann equation for Y_B-L omits the crossed ΔL=1 washout processes N_i + l -> eta_i + V and N_i + l -> eta_j + phi, together with their CP conjugates. These processes are kinematically open for the benchmark points (for example, the condition m_N1 > m_eta2 + m_phi in eq. (4.5)) and they involve the same Yukawa and gauge couplings as the included processes eta_i N_i -> l V and N_i phi -> l eta_j. In the strong-washout regime, where the final Y_B-L is set by a balance between production and washout, the omission could shift the BAU-satisfying regions in Figs. 5 and 10. The text after eq. (4.4) concedes that 'some scattering processes significantly impact the number density of N1', which shows that the scattering set is not demonstrated to be complete. Please include the missing terms or provide a quantitative rate comparison showing that they are negligible for Y_B-L in the scanned parameter region.
  2. [Appendix C, text after eq. (C.14)] The authors state that their CP asymmetry agrees with reference [47] in the limit m_eta -> 0 and m_phi -> 0 'except for a negative sign'. Since the overall sign of epsilon_N1 determines whether the resulting baryon asymmetry has the observed positive sign, and since the scan in Fig. 5 implicitly depends on the sign through Im(F_vertex), this discrepancy must be resolved rather than reported. Please trace the sign difference to a specific convention (for example, the definition of the C matrix or the orientation of the loop momentum) and demonstrate that the positive-BAU solutions are not an artifact of this convention choice.
  3. [Equations (4.5) and (5.3), and Fig. 2 caption] The Casas-Ibarra rotation angles are fixed differently in different parts of the paper: eq. (4.5) sets a=1, b=0.4 for the leptogenesis scan, the caption of Fig. 2 uses a=0.1, b=0.3 for the decay parameter plot, and eq. (5.3) uses a=0, b=0.175 for the DM scan. Because Fig. 14 shows that epsilon_N1 can vary by orders of magnitude in some regions of the (a,b) plane, the choice of different angles in the leptogenesis and DM analyses could affect the claimed correlation. Please clarify which parameter sets were used for Figs. 5 and 10 and justify that the overlap between BAU-satisfying and DM-allowed regions is not an artifact of choosing different CI angles in the two analyses.
minor comments (5)
  1. [Section 4, after eq. (4.4)] The sentence admitting that 'some scattering processes significantly impact the number density of N1' does not identify which processes are meant; please list them explicitly and state whether they are included in the dY_N1/dz equation, since otherwise the reader cannot evaluate the consistency of the Boltzmann treatment.
  2. [Fig. 10 caption] The caption states that the color bar shows the baryon asymmetry for each point, but it does not say whether the plotted points are selected by requiring Y_DeltaB to match the observed value or merely colored by its value; please state the selection criterion explicitly.
  3. [Section 5.2, text after eq. (5.5)] The sentence beginning 'The annihilation cross-section, <sigma v>_etaI1 etaI1 -> b b, proportionally depends on the parameters m_etaI1 0. 0.2 0.4' contains garbled or missing content and should be rephrased as a complete sentence.
  4. [Section 2, Table 1] The table caption reads 'T able 1' rather than 'Table 1'; please fix the typo.
  5. [Equations (4.1) and (4.5)] The notation for the inert doublet masses is inconsistent: eq. (4.1) uses mu_eta2 while eq. (4.5) uses m_etaI2; please unify the notation throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the baryon asymmetry is used as an external constraint, while the DM, neutrino-mass, and lepton-flavor outputs are independently computed.

full rationale

The paper's central claim is that the couplings y12phi and mu12phi enter both the N1 decay vertex correction (hence the CP asymmetry epsilon_N1, eqs. C.12-C.13) and DM-DM conversion / relic density (eqs. 5.2). This is a parameter-overlap claim, not a derivation of an output from its own input. The observed baryon asymmetry is imposed as a constraint in Figs. 5 and 10: y12phi and mu12phi are free parameters scanned to satisfy Y_DeltaB, and the same couplings are then fed into independent Boltzmann equations for the two DM components. The relic density, direct-detection cross sections, and lepton-flavor-violating rates are not forced by the BAU fit; they depend on additional couplings and processes that do not enter epsilon_N1. Neutrino masses are imported through the Casas-Ibarra parametrization (B.14), which re-expresses the Yukawa couplings in terms of the measured neutrino masses and mixings; this is standard parameterization practice and does not by itself produce the observed baryon asymmetry. The self-citations present (e.g., ref. [53] for two-component DM cross sections, and refs. [48, 51] for related leptogenesis studies) supply standard or externally checkable formulas and are not load-bearing for the central derivation; no uniqueness theorem or ansatz is smuggled in via citation. The admitted incompleteness of scattering processes in eq. (4.2) is a robustness/correctness concern about the size of the leptogenesis result, not a circularity.

Assumptions & free parameters 7 free parameters · 8 assumptions · 5 invented entities

The model rests on a large number of free parameters, including Casas-Ibarra angles, new Yukawa and trilinear couplings, masses, and quartic couplings. The central claim is not a parameter-free prediction; it is a constraint-satisfying scan. The new particles are introduced without independent detection, so all carry the burden of future falsification.

free parameters (7)
  • CI rotation angles (a, b) = a=1, b=0.4 (leptogenesis scan); a=0, b=0.175 (DM scan)
    Free complex orthogonal matrix R in the Casas-Ibarra parametrization (eq. B.14); scanned to reproduce neutrino masses and the baryon asymmetry, and it controls the phase in the CP asymmetry.
  • y12ϕ = 2.555 to 3.001 (Table 2)
    Yukawa coupling for N2-N1-ϕ; enters the CP asymmetry (eq. C.11) and DM-DM conversion; fitted to the observed baryon asymmetry.
  • µ12ϕ = 0.5 mϕ to 2 mϕ
    Trilinear η1-η2-ϕ coupling; enters the CP asymmetry and DM conversion; fitted to the baryon asymmetry and relic density.
  • mN1 = 2.2 to 6.4 TeV (Table 2)
    Lightest right-handed neutrino mass; sets the leptogenesis scale and appears in neutrino mass loop; mN2 is fixed to 3mN1.
  • mη0_I1, mϕ = scanned from 25 to 700 GeV
    The two DM masses; enter the CP asymmetry through η1 and σ, the neutrino mass loop, and the relic density; chosen to satisfy DM and BAU constraints.
  • λ11ϕ, λϕH, λ'11H, λ''11H = scanned up to 1; λϕH ~ 0.1 for WIMP-WIMP
    Quartic couplings controlling DM annihilation, direct detection, and the inert doublet mass splittings; tuned to match relic density and direct detection limits.
  • λij, λkkϕ = set to 1 in the scans
    Additional quartic couplings in the scalar potential; fixed to simplify the scans rather than fitted.
assumptions (8)
  • domain assumption The Standard Model is the correct low-energy description apart from the new fields.
    The paper extends the SM with two inert doublets, two right-handed neutrinos, and a real scalar, and assumes all SM constraints apply.
  • domain assumption The Z2⊗Z2' symmetry is exact, ensuring the stability of the two DM candidates and forbidding tree-level lepton-number-violating decays.
    This symmetry assignment is introduced in Section 2 and is essential for the two-component DM picture and the leptogenesis mechanism.
  • domain assumption The one-loop radiative diagram (fig. 12) is the sole source of neutrino mass; no tree-level seesaw contributes.
    The neutrino mass formula in eq. (B.7) assumes only the scotogenic loop generates mass, which is standard for this model class.
  • domain assumption Electroweak sphalerons convert the B-L asymmetry to baryon asymmetry at T_sph ~ 130 GeV with the standard conversion factor, though the explicit coefficient is not stated.
    Used throughout Section 4 to relate Y_B-L to Y_ΔB; the sphaleron conversion factor is standard but not written out.
  • ad hoc to paper All model parameters are real except the Yukawa couplings h_iiα, which carry the CP-violating phase.
    Stated in Section 2; this is a modeling choice that isolates the CP violation in the Yukawa sector.
  • domain assumption The unflavored Boltzmann equations in eq. (4.2) are adequate for computing the final baryon asymmetry.
    The equations sum over lepton flavors and do not track flavor-dependent washouts, a common but non-trivial approximation in TeV-scale leptogenesis.
  • ad hoc to paper Scatterings that are not explicitly included in the asymmetry evolution do not significantly change the result.
    The paper states that scattering processes are less important than decays, but also admits some scatterings significantly impact N1 number density (Section 4). This tension is unresolved.
  • domain assumption Only the WIMP-WIMP regime (λϕH ~ 0.1) is considered for dark matter.
    The paper explicitly limits to WIMP-WIMP and leaves WIMP-FIMP and WIMP-pFIMP for future work (Section 5).
invented entities (5)
  • N1 (lightest right-handed neutrino)
    purpose: Generates the lepton asymmetry through out-of-equilibrium decay; also participates in the neutrino mass loop.
    No direct laboratory evidence; its mass and couplings are scanned to fit the baryon asymmetry and neutrino data.
  • N2 (heavier right-handed neutrino)
    purpose: Internal line in the CP asymmetry vertex correction; sets the mass hierarchy for the mechanism.
    No independent signal; its mass is fixed to 3mN1 in the scans.
  • η1 (inert doublet)
    purpose: Responsible for radiative neutrino mass, is the decay product in leptogenesis, and its neutral CP-odd component is a dark matter candidate.
    Could be searched via charged scalar production at colliders and dark matter detection, but no signal is observed and the masses are fitted.
  • η2 (second inert doublet)
    purpose: Enables the new η2-η1-ϕ vertex that enhances the CP asymmetry; also contributes to co-annihilation.
    New particle without independent evidence; its mass is tied to mη1 and mϕ by construction.
  • ϕ (real scalar singlet)
    purpose: Second dark matter candidate; enters the CP asymmetry vertices N2-N1-ϕ and η2-η1-ϕ.
    Could be detected through Higgs-portal dark matter searches, but no observation exists and the coupling λϕH is fitted.

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Cite this review

Pith. "Pith review of Two-component Dark Matter and low scale Thermal Leptogenesis." pith.science (2026). https://pith.science/paper/G5DAOFO5

@misc{pith2026241221202,
  author       = {Pith},
  title        = {Pith review of: Two-component Dark Matter and low scale Thermal Leptogenesis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G5DAOFO5}},
  note         = {Machine review of arXiv:2412.21202}
}
abstract

The observable cosmos exhibits sizable baryon asymmetry, small active neutrino masses, and the presence of dark matter (DM). To address these phenomena together, we propose a two component DM scenario in an extension of Scotogenic model, imposing $\mathbb{Z}_2 \otimes \mathbb{Z}_2^{\prime}$ symmetry. The electroweak sphaleron process converts the $\rm Y_{B-L}^{}$ yield, generated through the Leptogenesis mechanism, into the baryon asymmetry ($\rm Y_{\Delta B}^{}$) at $\rm T_{\rm sph}\sim 130$ GeV, the sphalerons decoupling temperature. In this framework, the CP asymmetry as well as the radiative neutrino mass generation explicitly involve the two DM particles, thus establishing a correlation between the baryon asymmetry, DM and observed active neutrino masses. We study in details the allowed parameter space available after considering all the constraints from the three phenomena as well as from the collider search limits, and outline the region which could potentially be tested in future DM detection experiments through direct or indirect detection searches, lepton flavor-violating decays, etc.

Figures

Figures reproduced from arXiv: 2412.21202 by the authors.

Figure 1
Figure 1. 1-loop Feynman diagrams related to ℓα → ℓβγ. The branching fraction corresponds to ℓα → ℓβγ is given by [77–80], B(ℓα → ℓβγ) = 3(4π) 3αem 4G2 F |FD| 2 BR(ℓα → ℓβνανβ), (3.4) where αem and GF are the electromagnetic fine structure and Fermi constant, respectively. For SM leptonic decay branching, ℓα → ℓβνανβ, see [81]. FD is the dipole form factor, given by, FD = X 2 i=1 h ∗ iiβhiiα 2(4π) 2 1 m2 η + i G(xi), (3.5) wh… view at source ↗
Figure 2
Figure 2. We have used {mN1 > µη2 + mϕ , λ′ iiH = 0.01, mη 0 I1 = 0.5 TeV, mϕ = 0.4 TeV, mη 0 I2 = mη 0 I1 + mϕ + 1 GeV, µ12ϕ = mϕ, y12ϕ = 1, mN2 = 3mN1 , mη + i = mη 0 Ii + 3 GeV, mη 0 Ri = (m2 η 0 Ii + λ ′′ iiHv 2 ) 1/2 , a = 0.1, b = 0.3} to calculate the decay parameter, KN1 . 4 5 6 7 106 107 108 10-1 100 101 2.0 2.5 3.0 3.5 4.0 4.5 100 101 102 103 10-3 10-2 10-1 100 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Scan plot for the asymmetry parameter in mN1 − λ ′′ iiH plane. For the left panel plot, the other important parameters are mentioned in the figure inset (for 2 RHN and one inert). The figure on the right corresponds to our model and uses the same parameters as those in fig . 2. We calculate the CP asymmetry (εN1 ) parameter arising from the decay N1 −→ lαη1 in appendix . C. In fig . 3, we show the variation of the a… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: The left figure corresponds to the initial condition YN1 = Yeq N1 , while for the right figure YN1 ∼ 10−20. The horizontal and vertical gray dashed lines indicate Y obs ∆B and Tsph, respectively. The other solid and dashed lines represent the variation of parameters wi…
Figure 5
Figure 5. Figure 5: In this figure, the dark rainbow-colored points represent the RHN mass mN1 . All of these points respect the observed baryon asymmetry (Y obs ∆B ≃ 8.75+0.23 −0.23 ×10−11) and account for the correct active neutrino masses. In fig . 5 we show the points in m η 0 I1 −y12…
Figure 6
Figure 6. Figure 6: Feynman diagrams correspond to the direct detection of η 0 I1 (left) and ϕ (right). In fig . 7, we show the DM relic density allowed parameter space in mη 0 I1 − σ eff Nη 0 I1 plane (left panel) and mϕ − σ eff Nϕ plane (right panel). All plots in fig . 7 are filled wit…
Figure 7
Figure 7. Figure 7: Figs . 7a, 7c, 7e and 7b, 7d, 7f, represents the relic allowed parameter space in mη 0 I1 −σ eff Nη 0 I1 and mϕ−σ eff Nϕ plane, respectively. The rainbow colorbar represents the variation of µ12ϕ, ∆m = m η 0 I1 − mϕ, and %Ωih 2 = Ωih 2 P i Ωih 2 −1 100, where i = η 0…
Figure 8
Figure 8. Figure 8: The Feynman diagrams represents the self annihilation of η 0 I1 and ϕ into b b shown in figs . 8a, and 8b, respectively. where the cross-section is calculated at the WIMP freeze-out temperature, TFO ∼ mDM/25. The annihilation cross-section, ⟨σv⟩ η 0 I1 η 0 I1 →b b , pr…
Figure 9
Figure 9. Figure 9: Figures are shown the Indirect detection limit on relic allowed parameter space in mi − ⟨σv⟩ eff i i→b b plane, where i = η 0 I1 , and ϕ. The grey-shaded regions are excluded from the recent Fermi-LAT limit on the DM annihilation bottom pair. In this scan, we have take…
Figure 10
Figure 10. Figure 10: The red points represent the total relic density satisfied by both DM candidates. The blue points correspond to the total relic density satisfied and allowed by the DD constraint from the LZ-2022 experiment for both DMs. Lastly, the rainbow color points indicate the r…
Figure 11
Figure 11. Figure 11: The relevant Feynman diagrams for Leptogenesis where i = 1, 2 ; Vµ = Bµ, W3 µ , W± µ [9, 93] and α define the lepton generation. B Neutrino mass generation In this scenario, neutrino mass is generated via a one-loop radiative diagram, as shown in fig . 12. and the 1-l…
Figure 12
Figure 12. Figure 12: Radiative neutrino majorana mass generation where i, j are generation indices and k = 1, 2. The left and right figures correspond to before and after EWSB, respectively. Here C αk R(I) and C βk R(I) are the couplings, given by C αk R(I) = fR(I) √ 2 h ∗ kkα and C βk R(…
Figure 13
Figure 13. Figure 13: Feynman diagrams corresponds to N1 → ℓαη1 is relevant for Leptogenesis. The vertex factors for the processes in fig . 13 are, Nj → ℓαηj : −ihjjαPR; (C.1) N2 → N1ϕ : iy12ϕC † ; η2 → η1ϕ : −iµ12ϕ . (C.2) – 22 – [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]
Figure 14
Figure 14. Figure 14: This figure illustrates the dependency of the parameters a and b on the asymmetry (εN1 ) after accounting for the constraints imposed by neutrino masses. We are fixing other parame￾ters as: mN1 = 2 TeV, mN2 = 6 TeV, mϕ = 0.5 TeV, mη 0 I1 = 0.4 TeV, mη 0 I2 = mη 0 I1 +…

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