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Leptogenesis in a Majoron+Triplet model

T0 review · 2 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Leptogenesis in the majoron+triplet model is controlled by the coupled out-of-equilibrium evolution of the neutrino, the scalar, the majoron, and the triplet, and neutrino-only Boltzmann equations can misestimate the efficiency by up to a…

desk verdict First coupled-Boltzmann treatment of leptogenesis in the majoron+triplet model; the factor-of-six claim holds up, but the Y_N^0 normalization is sloppy and must be fixed before absolute numbers are trusted. read the letter →

arxiv 2501.11529 v2 pith:3IJAOMXC submitted 2025-01-20 hep-ph

Tim Brune This is my paper · ORCID
classification hep-ph
keywords leptogenesismajorontripletfermioncoupledBoltzmannequationsleptonasymmetrybaryondarkmatterseesawmechanism
topics Dark MatterMatter-Antimatter Asymmetry
open problems Dark 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 sets out to show that leptogenesis in the majoron+triplet model cannot be reduced to a single Boltzmann equation for the heavy neutrinos. The model adds a CP-even scalar $\sigma$, the majoron $J$ (a Goldstone boson from broken lepton number), and a fermion triplet $T$ under the weak gauge group; all three scatter with neutrinos and can themselves leave thermal equilibrium. The final lepton asymmetry is therefore shaped by the coupled evolution of all four species. Solving only the neutrino equation, with the other species held in equilibrium, underestimates the efficiency by up to a factor of about six in the scanned parameter space. If correct, this means simplified one-species treatments can misjudge whether this class of seesaw extensions produces the observed baryon asymmetry.

What carries the argument

The load-bearing element is the coupled system of Boltzmann equations (3.12)–(3.15) for the abundances $Y_N$, $Y_T$, $Y_\sigma$, and $Y_J$, together with the efficiency equation (3.9). The summed scattering rate $\gamma_S$ collects the processes that change the neutrino abundance, and the $\rho$ term encodes how deviations of $\sigma$, $J$, and $T$ from thermal equilibrium feed back into neutrino production. The named diagnostic is the efficiency factor $\eta$, defined through $Y_L = \varepsilon Y_N^0 \eta$, whose final value $\eta(z_N\to\infty)$ is the quantity compared across scenarios. Cases $\hat{A}$ and $\hat{B}$ impose $\delta_T=\delta_\sigma=\delta_J=1$, reducing the system to a single neutrino equation; cases A and B solve the full system for $g_T=1$ and $g_T=10^{-7}$, respectively. The contrast between these two levels of treatment is what exposes the sixfold effect.

What would settle it

Re-run the numerical solution of the Boltzmann equations at $g_N \approx 0.7$ and $\tilde m \approx 10^{-3}$ eV with $\delta_\sigma=\delta_J=\delta_T\equiv 1$, keeping all scattering terms in $\gamma_S$; the paper predicts this simplified efficiency is roughly six times smaller than the full coupled result, so agreement within a few percent would refute the central claim. Independently, at $g_N = 0.1$ and $\tilde m = 5\times 10^{-5}$ eV with all initial abundances zero, the paper predicts a negative final efficiency in case $B_z$; a positive sign there would also falsify it.

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Extended reading notes

Core claim

The central claim is that the new particles in the majoron+triplet model do not merely rescale the vanilla leptogenesis efficiency; they change how the heavy neutrino $N$ is populated and depleted. Scattering processes involving $\sigma$, $J$, and $T$ keep $N$ near thermal equilibrium early on and push its decays to later times, and in the simplified treatment with $\delta_T=\delta_\sigma=\delta_J=1$ this suppresses the efficiency. In the full coupled system the deviations of $\sigma$, $J$, and $T$ from equilibrium feed back into the neutrino abundance, producing a larger efficiency in cases A and B. The author further finds that the initial abundances of the new fields are irrelevant in most of parameter space but matter in a narrow region of small $g_N$ and small effective neutrino mass with vanishing initial abundances, where the final efficiency can be negative. The paper also derives a modified sphaleron conversion relation for the model and uses dark matter bounds to exclude the large-triplet-coupling case, leaving only the small-coupling case B as cosmologically viable.

Load-bearing premise

The calculation assumes that at the symmetry-breaking scale the new fields start either exactly thermal or exactly absent, with zero pre-existing lepton asymmetry; if the earlier universe left different abundances or an asymmetry, the final efficiency, especially its sign in the small-parameter region, could change.

Editorial extensions

If this is right

  • For large parts of the $g_N$\u2013$\tilde m$ plane, efficiencies from neutrino-only Boltzmann equations are not reliable; quantitative leptogenesis predictions in this model require the coupled system.
  • In the strong-washout limit, $\tilde m\to 10^{-1}$ eV, inverse neutrino decays dominate and the efficiencies converge to the vanilla-leptogenesis values, so the simplification is safe there.
  • In the small $g_N$ and small $\tilde m$ region with zero initial abundances, the sign of the final lepton asymmetry is not fixed: the model permits a negative efficiency, which would translate into the wrong sign of the baryon asymmetry.
  • Dark matter bounds force the triplet Yukawa coupling below about $2.9\times 10^{-7}$, excluding the large-coupling case A and leaving case B, where the triplet barely affects the efficiency, as the viable version.
  • The triplet changes the sphaleron conversion from $Y_B = (28/79)Y_{B-L}$ to $Y_B = (76/679)Y_{B+3L}$; the numerical factor is similar, but the conserved combination is different.

Reading between the lines

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

  • The sixfold sensitivity to spectator dynamics probably extends beyond this specific model: any leptogenesis setup in which additional fields scatter strongly with heavy neutrinos should be checked with the full coupled system, not just the neutrino equation.
  • Including flavour effects or resonant CP enhancement, which the paper leaves out, could move the boundary of the negative-efficiency region; computing the same cases in a flavour-basis Boltzmann treatment would test how robust the initial-abundance dependence is.
  • The paper's division of parameter space by $z_N^{\mathrm{eq}} = 1$ could serve as a practical diagnostic for when initial abundances matter in other multi-species leptogenesis models.
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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

2 major / 6 minor

Summary. The manuscript studies leptogenesis in a singlet-majoron model extended by a Z2-odd right-handed SU(2)L triplet fermion. It derives the full set of coupled Boltzmann equations for the heavy neutrino N, the CP-even scalar σ, the majoron J, and the triplet T, including on-shell subtraction of σ-mediated scatterings. The equations are solved numerically for four parameter cases (full dynamics with gT=1 or gT=10^-7, and a simplified scenario where σ, J, T are pinned to equilibrium), with either thermal or vanishing initial abundances at the spontaneous-symmetry-breaking scale. The central finding is that the simplified neutrino-only treatment can misestimate the final efficiency by up to about a factor of six in parts of the scanned (gN, m-tilde) plane, and that initial abundances of the new fields matter only in a restricted 'IA' region of the small-gT scenario. The paper also derives the modified sphaleron conversion relation in this model, computes the CP violation required to match the observed baryon asymmetry, and discusses dark-matter constraints on the majoron and triplet.

Significance. If the numerical results are sound, the paper provides a concrete, fairly comprehensive demonstration that in a well-motivated majoron+triplet extension of type-I seesaw, the non-equilibrium dynamics of σ, J, and T can substantially change the efficiency of leptogenesis relative to the usual one-species treatment. The Boltzmann equations are written out explicitly, the on-shell subtraction is discussed, and several analytic approximations (e.g., Eqs. (4.15) and (4.25)) give physical insight that goes beyond a black-box numerical scan. The paper also quantifies the change in the sphaleron conversion factor and connects the analysis to dark-matter and baryon-asymmetry constraints. The author is explicit about the main assumptions (neglect of λmix, flavor effects, pre-existing asymmetries) and about the origin of the sphaleron relation [25]. Overall, this is a useful contribution to leptogenesis model-building, provided the normalization and robustness issues identified below are resolved.

major comments (2)
  1. [Sec. 3.2, Eqs. (3.8)–(3.9)] The efficiency normalization Y_N^0 is defined as Y_N(z→∞) in Eq. (3.8). For a decaying heavy neutrino, the asymptotic abundance is negligible and is not the standard normalization in leptogenesis, where Y_N^0 is normally the ultra-relativistic equilibrium abundance (or the initial abundance at z→0). Taken literally, the source term in Eq. (3.9) proportional to 1/Y_N^0 would be singular in a physically irrelevant limit. Since all reported absolute values of η in Figs. 4.1, 4.2, and the derived CP-violation requirements in Sec. 6 depend on this normalization, the definition must be corrected (e.g., to Y_N^eq(z→0) or Y_N(z_I)) and the numerical implementation must be checked to use a consistent constant normalization. If the intended quantity is indeed Y_N^eq(z→∞) in some limiting sense, that limit should be stated precisely.
  2. [Sec. 4.4.3.1, Eq. (4.28), and Fig. 4.19] The IA/IA boundary is defined by the explicit criterion z_N^eq(m-tilde^IA, g_N^IA)=1, and the text admits that there is no fundamental reason for this choice, arguing that the exact value is irrelevant because the thermalization transition is rapid. Since this boundary determines the location and extent of the region in which initial abundances are claimed to be relevant (including the negative-efficiency triangle in Fig. 4.2 and the discussion in Sec. 4.4.3.2), the paper should substantiate the claimed insensitivity with a concrete robustness check. For example, show how the IA/IA boundary and the |η_z^B/η_t^B| contours change when the criterion is varied to z_N^eq=2 and z_N^eq=0.5. This would also make clear whether the boundary is best thought of as a sharp transition or as a convenient contour.
minor comments (6)
  1. [Sec. 4.2.3 and Figs. 4.12, 4.16] The two regimes labeled 'WO' and 'WO' (with and without washout) are typographically indistinguishable in the typeset text and figure labels; the overline or other diacritic is lost. Please use distinct unambiguous labels, e.g., 'WO' and 'no-WO', and define them in the caption.
  2. [Sec. 4.1 and Fig. 4.4] The text says the efficiency is split into an 'IA (initial abundance) regime' and an 'IA regime' where initial abundances have no effect; both labels appear identical in the plain text. This makes the central dichotomy hard to follow. Please introduce distinct names (e.g., 'IA-sensitive' and 'IA-insensitive') and use them consistently.
  3. [Sec. 4.4.3.1, Eq. (4.28)] The notation (g_N^IA, m-tilde^IA) suggests a single point, but Eq. (4.28) defines a one-dimensional curve in the (g_N, m-tilde) plane. Please clarify that the pair denotes the boundary curve (e.g., by writing z_N^eq(m-tilde, g_N)=1 for the boundary) and that g_N^IA and m-tilde^IA refer to representative values along it, as used in Fig. 4.20.
  4. [Sec. 6.1, Eq. (6.10)] The factors 3×76/679 and 28/79 are correct only if the initial hypercharge and charge constraints are imposed as in [25]; the sign conventions for Y_L and Y_{B-L} should be stated explicitly so that the 'apart from the different signs' remark is unambiguous. A one-sentence derivation of the factor 3 would help the reader.
  5. [Abstract and Sec. 4.1] The abstract states that solving the coupled Boltzmann equations is essential 'for large parts of the considered parameter space,' but Fig. 4.3 shows that the ratio η_hat/η is close to unity over a sizable fraction of the scanned plane, with the largest deviations (factor ~6) concentrated near g_N~0.7 and small m-tilde. Consider softening the wording or adding a quantitative statement about the region where the difference exceeds, say, a factor of two.
  6. [Throughout] The manuscript contains numerous typographical and grammatical errors (e.g., 'condtions', 'seperate', 'dicuss', 'substraction', 'squablack' in App. A.3, 'inital', 'indentical'). A careful proofreading pass is needed before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is a direct numerical comparison of two Boltzmann-equation setups, not a fit or a self-referential derivation.

full rationale

The paper's central result is the comparison between the simplified neutrino-only Boltzmann equation (3.18), obtained by setting delta_T,sigma,J = 1, and the full coupled system (3.12)-(3.15). The efficiency maps in Figs. 4.1-4.4 are numerical solutions of these equations for the parameter grid of Table 1; no parameter is fitted to the quantities being compared, and no 'prediction' is reconstructed from a fitted input. The IA/IA boundary in Sec. 4.4.3.1 is explicitly acknowledged as conventional: 'There is no fundamental reason to explicitly choose z_N^eq(tilde m_IA, g_N^IA) = 1', so it is a classification choice rather than a hidden fit. The initial-condition assumption in Sec. 3.3, 'that no other mechanisms generated an lepton asymmetry for z_N < z_I', is a stated cosmological assumption and not a circular use of the final asymmetry. The only same-author citation that is load-bearing in any section is [25] for the sphaleron conversion coefficient Y_B = (76/679) Y_(B+3L) (Eq. 6.8); this is a published parameter-free chemical-potential computation used only in Sec. 6.1, and it does not feed back into the coupled-Boltzmann efficiency claim that forms the paper's main conclusion. Hence there is no circular step that reduces a claimed prediction to its inputs.

Assumptions & free parameters 6 free parameters · 8 assumptions · 0 invented entities

The model ingredients (sigma, majoron J, triplet T) are taken from prior literature, not invented here. The free parameters are hand-picked values for the model couplings and scales; none are fitted to data. The main assumptions are the Z2 symmetry, the single-source CP violation, the hierarchy of heavy neutrinos, and the initial condition at z_I.

free parameters (6)
  • f = 10^10 GeV
    VEV of the sigma field setting the seesaw scale; chosen and fixed, with a discussion in Sec. 6.2 of its effect on the efficiency.
  • lambda_sigma = 1
    Singlet quartic coupling fixing sigma mass; chosen for convenience, varied in Fig. 4.24 to show weak dependence.
  • g_T = 1 (case A) and 10^-7 (case B)
    Triplet Yukawa coupling scanned between strong and weak values; the weak value is below the DM bound g_T less than about 2.9e-7.
  • m_J = 10^-3 GeV
    Small majoron mass, stated not to affect the numerical results; motivated by majoron DM.
  • g_N = range [0.1, 1]
    Neutrino Yukawa coupling scanned; controls sigma to NN kinematics and scattering rates.
  • m_tilde = range [5e-5, 0.1] eV
    Effective neutrino mass parameter, input from neutrino mass models; scanned.
assumptions (8)
  • standard math Maxwell-Boltzmann approximation for distribution functions and thermal rates (App. A.1).
    Used throughout to compute equilibrium abundances and reaction densities.
  • domain assumption Z2 symmetry forbids the triplet Yukawa coupling to SM leptons and Higgs (Sec. 2).
    This is the defining feature of the model; if absent, the triplet would directly participate in LNV processes and alter all conclusions.
  • domain assumption No additional CP violation beyond the standard neutrino decay loops; epsilon is given by the vanilla formula (Sec. 3.1).
    The paper assumes the only CP source is the interference in N decays, ignoring potential CP phases in the scalar or triplet sector.
  • domain assumption Heavy neutrinos N2,3 are strongly hierarchical with MN1 much less than MN2,3 for the DI bound and epsilon formula (Sec. 3.1).
    The Davidson-Ibarra bound and the standard epsilon rely on this hierarchy; the authors note in Sec. 6 that relaxing it can enhance epsilon.
  • domain assumption The sphaleron conversion relation Y_B = (76/679) Y_{B+3L} from [25] (Sec. 6.1).
    Used to translate the lepton asymmetry into a baryon asymmetry; this is the author's own previous published result.
  • domain assumption The singlet-doublet mixing lambda_mix is neglected (Sec. 2).
    The scalar potentials for sigma and H decouple; the authors note this may affect the efficiency if included.
  • domain assumption No pre-existing lepton asymmetry for z_N < z_I (Sec. 3.3).
    The Boltzmann equations are initialized with eta(z_I)=0, assuming no asymmetry was generated before the seesaw scale.
  • standard math Radiation-dominated universe with g_* = 106.75 (App. A.1).
    Standard cosmological background used for the Hubble rate and entropy density.

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Pith. "Pith review of Leptogenesis in a Majoron+Triplet model." pith.science (2026). https://pith.science/paper/3IJAOMXC

@misc{pith2026250111529,
  author       = {Pith},
  title        = {Pith review of: Leptogenesis in a Majoron+Triplet model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3IJAOMXC}},
  note         = {Machine review of arXiv:2501.11529}
}
abstract

We discuss leptogenesis in a majoron model extended by a right-handed $SU(2)_L$ triplet fermion. We study several different parameter assignments and find that the interactions of neutrinos with the new particles in the majoron+triplet model can significantly alter the way leptogenesis proceeds. We show that for large parts of the considered parameter space, it is essential to solve the set of coupled Boltzmann equations for the evolution of the neutrinos and the additional particles rather than solving the Boltzmann equations for the neutrino evolution only.

Figures

Figures reproduced from arXiv: 2501.11529 by the authors.

Figure 3.1
Figure 3.1. Feynman diagrams contributing to the CP violating [PITH_FULL_IMAGE:figures/full_fig_p006_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Branching ratios of σ → NN and σ → JJ as functions of gN . We stress that in cases A, Aˆ the decay σ → T T is kinematically forbidden while in cases B, Bˆ, the branching ratio Brσ→T T is of order 10−13 and can therefore be neglected. As a result, the branching ratios Brσ→JJ and Brσ→NN are practically the same in all considered scenarios. Moreover, we note that σ-decays to a pair of majorons are clearly the dominant … view at source ↗
Figure 4.1
Figure 4.1. Left: Density plots of ηAˆ (upper plot) and ηBˆ (lower plot) in the gN − m˜ plane. The black lines indicates at which ˜m the efficiency reaches its maximum. Middle: ηAˆ (upper plot) and ηBˆ (lower plot) as functions of gN . Right: ηAˆ (upper plot) and ηBˆ (lower plot) as functions of ˜m. See text for discussion. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_4_1.png] view at source ↗
Figures from the paper (27 more)
Figure 4.2
Figure 4.2. Figure 4.2: Left: Density plots of ηA (top column), η t B (middle column) and η z B (bottom column) in the gN − m˜ plane. The black lines indicates at which ˜m the efficiency reaches its maximum. Middle: ηA (top column), η t B (middle column) η z B (bottom column) as functions o…
Figure 4.3
Figure 4.3. Figure 4.3: Upper plots: Density plots of ηAˆ/ηA (left) and ηBˆ/η t B (right) in the gN − m˜ plane. Lower plots: Density plots of ηAˆ/ηBˆ (left) and ηA/η t B (right) in the gN − m˜ plane. See text for discussion. 0.1 0.2 0.3 𝑔𝑁 10−4 10−3 ̃𝑚/eV |𝜂 𝑧 𝐵/𝜂 𝑡 𝐵 | 0.3 0.4 0.5 0.6 0.1 …
Figure 4.4
Figure 4.4. Figure 4.4: Left: Density plot of | η z B/η t B | in the gN − m˜ plane. Right: Schematic density plot of IA, IA and (g IA N , m˜ IA). See text for discussion. the cases A, ˆ Bˆ. This is highlighted in [PITH_FULL_IMAGE:figures/full_fig_p014_4_4.png]
Figure 4.5
Figure 4.5. Figure 4.5: z eq S (gN ) as defined in (4.3) with the blue solid line corresponding to case Aˆ und the orange dashed line corresponding to case Bˆ. For gN ≪ 0.7 and gN > 0.7, both z eq,Aˆ S and z eq,Bˆ S increase with gN due to the Boltzmann suppression of the relevant thermal r…
Figure 4.6
Figure 4.6. Figure 4.6: Thermal rates of scattering processes that appear in the majoron+triplet model [PITH_FULL_IMAGE:figures/full_fig_p018_4_6.png]
Figure 4.7
Figure 4.7. Figure 4.7: Thermal rates relevant for the evolution of [PITH_FULL_IMAGE:figures/full_fig_p018_4_7.png]
Figure 4.8
Figure 4.8. Figure 4.8: Upper plots: Left: Density plot of z Aˆ S in the gN − m˜ plane. Middle: z Aˆ S (solid) and z Bˆ S (dashed) as functions of ˜m. Right: z Aˆ S (solid) and z Bˆ S (dashed) as functions of gN . Note that for gN ≤ 0.7, we have z Aˆ S ∼ z Bˆ S . We stress the striking simi…
Figure 4.9
Figure 4.9. Figure 4.9: Evolution of Y t NAˆ (zN ) and Y t,z NV L (zN ), compared to Y eq N . The red region denotes the scatter regime where the neutrino evolution in the majoron+triplet model is dominated by scattering processes while the blue region denotes the decay regime where (invers…
Figure 4.10
Figure 4.10. Figure 4.10: Evolution of the efficiencies η t,z V L and η t,z Aˆ for gN = [0.1, 0.7, 1] and ˜m = [5 × 10−5 , 10−3 , 10−1 ]eV. The blue region in panels 7–9 indicates where inverse neutrino decays are in thermal equilibrium, the solid vertical line denotes z eq S and the dashed …
Figure 4.11
Figure 4.11. Figure 4.11: Thermal rate γD/n eq L H relevant for (3.9). We can easily see that inverse decays are thermalized only for ˜m > 10−3 eV. the efficiency are Boltzmann suppressed and additionally, they are never thermalized when m˜ is small. In this case, washout processes are not e…
Figure 4.12
Figure 4.12. Figure 4.12: Comparison of ˜mS and mˆ˜ max for case Aˆ (solid) and case Bˆ (dashed). In the red region, the final efficiency is determined by scattering processes and neutrino decays and thus proportional to ˜m. On the other hand, the final efficiency in the blue regions is dete…
Figure 4.13
Figure 4.13. Figure 4.13: Thermal rates relevant for the evolution of [PITH_FULL_IMAGE:figures/full_fig_p026_4_13.png]
Figure 4.14
Figure 4.14. Figure 4.14: Evolution of ∆NA = δNA − 1 (solid lines) and ∆NAˆ = δNAˆ − 1 (dashed lines) for m˜ = [5 × 10−5 , 10−1 ]eV and gN = 0.1 (panel 1), gN = 0.7 (panel 2), gN = 1 (panel 3). The vertical solid lines indicate z A ρ while the vertical dashed lines denote z Aˆ S . Note that …
Figure 4.15
Figure 4.15. Figure 4.15: Evolution of the abundances of N, σ, T and J for gN = [0.1, 0.7, 1] and m˜ = [5 × 10−5 , 10−2 ]eV. In the right plot, we have gN = gT and therefore Y eq NA = Y eq T . Note that the lower limits of the zN range are given by zI and hence depend on gN . Scattering proc…
Figure 4.16
Figure 4.16. Figure 4.16: Comparison of ˜mmax and mˆ˜ max for case A, A ˆ (solid) and case B, B ˆ (dashed). In the red region, the final efficiency in cases A, B is determined by scattering processes and neutrino decays and thus proportional to ˜m. On the other hand, the final efficiencyy in…
Figure 4.17
Figure 4.17. Figure 4.17: Efficiencies η t,z A , η t Aˆ and η t,z V L as functions of zN . The blue region indicates where inverse decays are in thermal equilibrium, the solid vertical line denotes zρ and the dashed vertical line denotes zS. Note that the lower limits of the zN range are giv…
Figure 4.18
Figure 4.18. Figure 4.18: Evolution of ∆NA = δNA − 1 (solid lines) and ∆NB = δNB − 1 (dashed lines) for different values of ˜m = [5 × 10−5 , 10−1 ]eV and gN = 0.1 (panel 1), gN = 0.7 (panel 2), gN = 1(panel 3). The vertical solid lines indicate z A ρ while the vertical dashed lines belong to…
Figure 4.19
Figure 4.19. Figure 4.19: Density plots of z (N,σ,J) eq in the gN − m˜ plane. In the green region, thermalization proceeds rapidly so that z i eq ≪ 1 while in the grey region, the respective particle is not thermalized until zN = 10. They white line indicate z i eq = 1. Note that we do not s…
Figure 4.20
Figure 4.20. Figure 4.20: Left: z N eq as a function of gN for ˜m = [5 × 10−5 , 5 × 10−4 ]eV, compared to z V L eq and zI . Right: z N eq as a function of ˜m for gN = [0.1, 0.2], compared to z V L eq and zI . We note that z V L eq (zI ) is constant in the left(right) panel as it does not dep…
Figure 4
Figure 4. Figure 4: , we show [PITH_FULL_IMAGE:figures/full_fig_p037_4.png]
Figure 4.21
Figure 4.21. Figure 4.21: Evolution of YN,σ,J (zN ), compared to the respective equilibrium abundances, for gN = [0.1, 0.2, 0.24] and ˜m = [5×10−5 , 5×10−4 , 2.5×10−3 ]eV. The vertical solid line indicates z N eq while the vertical dashed line indicates z V L eq . We do not show YT as it is …
Figure 4.22
Figure 4.22. Figure 4.22: Left: Evolution of |η z B|(zN ) for gN = [0.1, 0.15, 0.2](dashed, dash-dotted, dotted) and ˜m = 5 × 10−5 eV, compared to |η z V L| (solid). For zN ≪ z N eq, zV L eq , the evolution of the efficiency is dominated by (inverse) neutrino decays and therefore independent…
Figure 4.23
Figure 4.23. Figure 4.23: Left: |η z B|, |η − B |, η + B and z N eq as functions of gN with ˜m = 5 × 10−5 eV. In the blue region, the final efficiency depends on the initial abundances while in the red region, the final efficiency is independent from the initial abundance. The vertical line …
Figure 4.24
Figure 4.24. Figure 4.24: Efficiency η(gT , m˜ ) (left) and η(λσ, m˜ ) (right) for gN = 0.1. Note that we used the same color scaling as in [PITH_FULL_IMAGE:figures/full_fig_p042_4_24.png]
Figure 5.1
Figure 5.1. Figure 5.1: Left, middle: Upper limits on the majoron mass that does not overproduce DM for case A, Bt (left) and Bz (middle) in the gN − m˜ plane. Note that these constraints are only valid if majoron decays to light neutrinos are sufficiently slow. Right: Triplet relic density…
Figure 6.1
Figure 6.1. Figure 6.1: Left: Density plots of the CP violation |ε t B| (top) and |ε z B| (bottom) required to explain the experimentally observed baryon asymmetry in case B in the majoron+triplet model. Middle: |ε t B| (top) and |ε z B| (bottom) as functions of ˜m (solid lines) for gN = [0…
Figure 6.2
Figure 6.2. Figure 6.2: Efficiency η t B for gN = 0.1 and ˜m = 10−3 eV as a function of the VEV f, compared to η DI as defined in (6.14). In the green region, η t B is sizable enough to reproduce the experimentally observed baryon asymmetry with a CP violation ε that fulfills the DI bound. …

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Cited by 2 Pith papers

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