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A non-supersymmetric modular A'_5 inverse seesaw model can simultaneously fit measured neutrino oscillations and explain the cosmic baryon asymmetry through TeV-scale leptogenesis.

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2026-08-02 17:49 UTC pith:SAW5R72F

load-bearing objection Three concrete non-SUSY A'_5 modular inverse-seesaw models with decent neutrino fits, but the leptogenesis claim is enforced by scanning a free scale r, so treat it as an existence proof, not a prediction. the 4 major comments →

arxiv 2603.19104 v2 pith:SAW5R72F submitted 2026-03-19 hep-ph

Neutrino mass and leptogenesis in the non-SUSY modular A^prime₅ inverse seesaw model

Xianshuo Zhang , Yakefu Reyimuaji This is my paper
classification hep-ph PACS 14.60.Pq11.30.Hv98.80.Cq
keywords neutrino massmodular symmetryA'_5 double coverinverse seesawleptogenesisTeV-scale new physicsneutrinoless double beta decayCP violation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper constructs three concrete neutrino-mass models based on a non-supersymmetric modular A'_5 symmetry, using the inverse seesaw mechanism to keep the new physics at the TeV scale. Each model reproduces the measured neutrino mixing angles and mass-squared differences within 3 sigma and makes definite predictions for the neutrino mass ordering, CP-violating phases, and the effective Majorana mass in neutrinoless double beta decay. The same framework also generates the observed baryon asymmetry via resonant leptogenesis, with heavy pseudo-Dirac neutrino pairs at TeV masses that could be probed at colliders. If correct, the models provide a parameter-sparse, testable origin for both neutrino flavor structure and matter–antimatter asymmetry without supersymmetry.

Core claim

The paper establishes that the non-holomorphic modular group A'_5 (the double cover of A5) can serve as the flavor symmetry for a non-SUSY inverse seesaw extension of the Standard Model, with all lepton flavor structure arising from the vacuum expectation value of a single complex modulus tau. Three benchmark models, differing in representation and modular-weight assignments, fit the global neutrino oscillation data: Model A prefers normal ordering with the atmospheric angle in the lower octant and m_beta_beta in 11.8–18.2 meV; Model B also prefers normal ordering but predicts an upper-octant atmospheric angle and m_beta_beta around 1 meV, beyond next-generation reach; Model C fits both orde

What carries the argument

The central objects are the finite modular group A'_5 and the non-holomorphic modular forms (polyharmonic Maaß forms) of weights between -4 and 3, which replace the usual holomorphic modular forms and allow non-SUSY modular invariance. Neutrino masses are generated by the inverse seesaw formula M_nu = M_D M_SN^{-1} M_S (M_SN^T)^{-1} M_D^T, where the smallness of M_S (a lepton-number-violating Majorana mass for singlet fermions S) naturally yields light neutrinos. A generalized CP symmetry reduces all coupling constants to real numbers, leaving the modulus tau as the only source of CP violation; the small mass splitting of the pseudo-Dirac pairs, tied to the small lepton-number-breaking param

Load-bearing premise

The inverse-seesaw hierarchy alpha_D v_h / Lambda is imposed by hand (set to 10^-3 for Models A/B and 10^-4 for Model C), and successful leptogenesis is achieved by scanning a free common scale factor r and selecting the ranges where the predicted baryon asymmetry matches the observed value, so the baryon asymmetry is reproduced rather than predicted from first principles.

What would settle it

A decisive test would be a null result in next-generation neutrinoless double-beta decay searches at the level of m_beta_beta < 5 meV combined with a measurement of the atmospheric angle in the lower octant: this would exclude Model C (NO) and simultaneously challenge Model A (NO), leaving only the nearly undetectable Model B, which could then be falsified by its tiny m_beta_beta prediction. Alternatively, detecting heavy neutrinos at the LHC with masses far outside the predicted TeV windows (e.g., below 0.4 TeV or above 2.5 TeV for the lightest pair) would rule out all three models.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If Model A or Model C is realized, next-generation neutrinoless double-beta decay experiments (LEGEND-1000, nEXO) should observe a signal in the predicted m_beta_beta ranges, while Model B would remain unobservable for the foreseeable future.
  • Precision measurements of the atmospheric mixing angle can discriminate between models: Model A favors sin^2 theta23 < 0.5 in normal ordering, while Models B and C in inverted ordering favor the upper octant.
  • The predicted correlations among Dirac and Majorana CP phases, if measured, would narrow the allowed modulus region and cross-check the modular symmetry assignment.
  • TeV-scale heavy neutrinos predicted by the models could produce observable lepton-number-violating signatures at the high-luminosity LHC or future colliders.
  • The non-unitarity of the leptonic mixing matrix, controlled by (alpha_D v_h / Lambda)^2, is kept within current bounds and could be probed further by electroweak precision and charged-lepton flavor-violation searches.

Where Pith is reading between the lines

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

  • A sharp experimental exclusion of m_beta_beta below roughly 10 meV would disfavor both Model A (NO) and Model C (NO), leaving only Model B's tiny m_beta_beta as a viable outcome, which would require a different discovery strategy.
  • The tendency of viable modulus values to sit near the boundary of the fundamental domain (Re(tau) ~ 0.5 or Im(tau) near fixed points) hints that modulus stabilization, not just flavor structure, might be the deeper constraint; future work could couple this to a dynamical mechanism.
  • The framework could be extended to the quark sector with the same A'_5 modular symmetry, potentially correlating quark and lepton CP violation, though the paper does not pursue this.
  • If future oscillation data pin down sin^2 theta23 and delta_CP with high precision, the model's correlations could be inverted to predict the absolute neutrino mass scale before direct kinematic measurements reach the sub-0.1 eV range.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper constructs three non-SUSY inverse seesaw models based on the modular double cover A'_5, with lepton fields assigned to specific representations and modular weights. After imposing a generalized CP symmetry, the remaining free parameters are coupling ratios and the modulus τ. The authors scan these parameters to fit two charged-lepton mass ratios and four neutrino oscillation observables, report best-fit points for normal and inverted ordering for Models A, B and C, and derive predictions for the mass ordering, CP phases, m_ββ, and absolute neutrino masses. They then restore physical scales by fixing α_D v_h/Λ and introduce a common scaling factor r; using approximate resonant-leptogenesis efficiency formulas, they identify r intervals in which the predicted η_B matches the Planck value.

Significance. The paper explores a relatively under-studied direction — non-holomorphic modular A'_5 symmetry in a non-SUSY inverse seesaw framework — and this is potentially a useful contribution to modular model building. Its strengths are the explicit construction of three concrete models, the numerical scans over the modulus and coupling ratios, the inclusion of both mass orderings, and the clear presentation of m_ββ and CP-phase targets that could be tested in next-generation experiments. The paper is also honest about the cosmological tension of some IO points. However, the combined-explanation claim is currently weaker than the abstract suggests: the leptogenesis part is an existence proof with a tuned overall scale, and the neutrino fit quality is not quantified in terms of degrees of freedom. If these points are addressed, the paper would be a solid model-building contribution.

major comments (4)
  1. [§5.2 (Figs. 13–14, Table 5)] The leptogenesis result is not a prediction. The common scale r multiplies both α_D v_h and Λ, so n=(α_D v_h/Λ)^2 α_S is independent of r; the neutrino fit is therefore completely decoupled from r. The paper then selects intervals r∈(4.0,6.0) for Model A NO, r∈(4.6,6.0) for Model B NO, etc., at which η_B crosses the observed value, and for Model C extends beyond the stated r∈(0.1,20) range. At the reference r=1 the quoted best-fit points do not reproduce η_B. Together with the hand-set hierarchies α_D v_h/Λ=10^-3 (Models A/B) and 10^-4 (Model C), the abstract's statement that the model 'realizes TeV-scale leptogenesis consistent with the observed baryon asymmetry' is an existence proof with a tunable scale, not a falsifiable prediction. Please reframe the claim as 'can accommodate', report the sensitivity of η_B to the choice of α_D v_h/Λ, and validate the approximate efficiency formulas
  2. [§4, Eqs. (22)–(28)] The fit quality is overstated. Models A and B have five dimensionless free parameters (β̃_CL, γ̃_CL, β̃_S, Re τ, Im τ) fitted to six observables (two charged-lepton mass ratios, three mixing angles, one mass-splitting ratio), while Model C has six parameters for the same six observables. Thus the χ²_min values quoted in Eqs. (23)–(28) (e.g., 0.092 for Model C NO) correspond to one or zero degrees of freedom; a low χ² is not evidence of predictive success but of the flexibility of the scan. Please report the number of dof, p-values, and the scan density, and discuss how much of the parameter space is actually excluded by the 3σ constraints. The arbitrary 0.1% uncertainty assigned to the charged-lepton mass ratios also needs justification.
  3. [§3.2, Eq. (21)] There are internal inconsistencies in the mass-matrix notation that affect the numerical implementation. In Model C, the Lagrangian Eq. (17) and the text state k_5=0, so M_S should depend on Y^{(0)}_1 and Y^{(0)}_5. Equation (21) instead uses Y^{(-2)}_5 and Y^{(-2)}_1, which are the Model A/B weights. Similarly, Eq. (6) has a superscript typo in the (2,2) entry, where β_CL Y^{(k2)}_{6I,-} should read β_CL Y^{(k1)}_{6II,-}. Since no code is provided, it is impossible to verify which modular forms were used in the scan; please correct the equations and confirm that the numerical results correspond to the intended k-values.
  4. [§5.1, Eqs. (33)–(40)] The leptogenesis numerics rest on approximate analytic efficiency factors and an effective washout parameter K^eff_i from Refs. [59,62,63]. These expressions are derived under specific quasi-degenerate conditions; the present model has three pseudo-Dirac pairs with very different mass hierarchies (Table 5), and the flavor-blind reduction is asserted rather than derived. The claim that η_B is reproduced should be tested with a full density-matrix Boltzmann calculation, or the regime of validity of the approximations should be demonstrated quantitatively. This is load-bearing because the abstract's combined-explanation claim depends directly on these η_B numbers.
minor comments (6)
  1. [§3.2, Eq. (21)] See Major Comment 3: the Y^{(-2)} superscripts in Eq. (21) should be Y^{(0)} for Model C. Please also check the analogous superscripts in Eq. (13) for Models A/B.
  2. [§3.2, text after Eq. (14)] Typo: 'modelular weight' should be 'modular weight'.
  3. [Figs. 2, 4, 6, 8, 10, 12] Several captions state 'cosmological upper bound m1 ≳ 0.037 eV' (and similarly for m3). Since the bound is an upper limit, the inequality should read m1 ≲ 0.037 eV. Please correct the notation.
  4. [§5.2 and Fig. 14] For Model C the successful NO region includes M1 ≈ 0.05 TeV, which is not 'TeV-scale' in the usual sense. The abstract's blanket 'TeV-scale leptogenesis' should be qualified, and Fig. 14's axis label M1[eV] is awkward; GeV would be clearer.
  5. [§5.2] The paper says Model C 'does not have a clear regularity' for r∈(0.1,20) and then extends the scan beyond r=20. This extension should be justified and its prior made explicit, since it is part of the leptogenesis matching.
  6. [§4] No data/code availability statement is given. FlavorPy is cited, but the scan configuration, the number of scan points, and the convergence criteria are not reported. This limits reproducibility.

Circularity Check

1 steps flagged

Leptogenesis agreement is obtained by scanning a free overall scale r that leaves the neutrino-sector fit invariant; the neutrino-sector predictions are self-contained, but the baryon-asymmetry consistency is enforced by construction.

specific steps
  1. fitted input called prediction [Sec. 5.2 (with n invariance defined in Sec. 3.1); Table 5]
    "In the numerical analysis, we introduce a common scaling factor r that multiplies both αDvh and Λ, therefore adjusting the overall mass scale while preserving their ratio. ... By scanning over r, we explore the parameter space and compute the resulting baryon asymmetry ηB for each model and mass ordering. ... For Model A in the NO scenario ... the observed baryon asymmetry is successfully reproduced when the scaling parameter lies in the range r∈(4.0,6.0)."

    Because n=(αDvh/Λ)^2 α_S is invariant under multiplying both αDvh and Λ by r, the entire neutrino-sector fit (mixing angles, phases, n) is r-independent. The baryon asymmetry is therefore matched only by choosing r intervals (Model A NO r∈(4.0,6.0); Model B NO r∈(4.6,6.0); Model C requires extending the scan beyond r=20). At the reference r=1 the quoted best-fit points are not in the reported success regions. The claimed 'TeV-scale leptogenesis consistent with observed baryon asymmetry' is thus a scan selection over an otherwise unconstrained scale, and the TeV heavy-neutrino masses in Table 5 are translations of that chosen r and the benchmark scales, not independent predictions.

full rationale

The neutrino-sector derivation is not circular: Eq. (3) gives Mν from the block mass matrix, the dimensionless couplings and τ are varied and fitted to external oscillation data, and the quoted CP phases, mass ordering and mββ ranges are outputs of that fit, not inputs. The overall scale n is fixed by the measured mass-squared differences, which is standard parameter determination rather than self-definition. Self-citations ([29]) are only used for kinetic terms and as a remark on correlations, not load-bearing. However, the combined central claim that the model 'realizes TeV-scale leptogenesis consistent with the observed baryon asymmetry' relies on a separate free scaling r that leaves the neutrino fit invariant and is scanned until ηB crosses 6.12×10^-10. That part of the claim is enforced by construction rather than predicted, so the overall circularity score is moderate, reflecting partial circularity in one central element while the neutrino-mixing predictions remain independent.

Axiom & Free-Parameter Ledger

8 free parameters · 8 axioms · 3 invented entities

The central claims rest on a set of fitted couplings, the modulus tau, and an ad hoc 'representation reduction' assumption, together with external modular-form tables. The leptogenesis result additionally depends on a scanned scaling parameter r and hand-set hierarchy ratios. These are not derived from the symmetry but are inputs chosen to match data.

free parameters (8)
  • beta_tilde_CL = beta_CL/alpha_CL = A NO: 1.2995; B NO: 0.7696; C NO: 2.2525, C IO: 3.4252
    Fitted to charged-lepton mass ratios and neutrino observables in the chi-squared scan.
  • gamma_tilde_CL = gamma_CL/alpha_CL = A NO: 0.0002; B NO: 0.000544; C NO: 159.15, C IO: 229.73
    Fitted in the charged-lepton mass matrix; some best-fit values are O(100), indicating a mild tuning.
  • beta_tilde_S = beta_S/alpha_S = A NO: 2.9998; B NO: 0.02242; C NO: 4.7687, C IO: 0.34199
    Fitted in the sterile Majorana mass matrix M_S.
  • beta_tilde_D = beta_D/alpha_D (Model C only) = C NO: 123.49; C IO: 31.611
    Fitted in the Model C Dirac mass matrix; large value contributes to the low chi2.
  • Re(tau) = A NO: 0.019; B NO: 0.03226; C NO: 0.36932, C IO: 0.49855
    Real part of the modulus, scanned over the fundamental domain; carries most of the flavor structure.
  • Im(tau) = A NO: 1.9268; B NO: 1.0416; C NO: 1.1714, C IO: 1.0775
    Imaginary part of the modulus, scanned; concentrates near fixed points or boundaries.
  • r (common scaling factor for alpha_D v_h and Lambda) = A NO: 4.0-6.0; A IO: 1.6-2.6; B NO: 4.6-6.0; B IO: 2.5-4.0; C: extended ranges in M1
    Introduced in Sec. 5.2 and scanned so that the baryon asymmetry matches eta_B = 6.12e-10; this is a fitted parameter for leptogenesis.
  • alpha_D v_h / Lambda = 1e-3 (Models A/B), 1e-4 (Model C)
    Hand-picked to enforce the inverse-seesaw hierarchy and keep heavy masses at the TeV scale; not derived from the symmetry.
axioms (8)
  • domain assumption The modular forms Y_r^(k)(tau) from Ref. 38 have the transformation properties and component values used in the mass matrices.
    All numerical results depend on these external tables; the paper does not reproduce or verify them.
  • ad hoc to paper Representation reduction: for fields marked 2-hat-prime plus 1, only the first two components are active low-energy degrees of freedom, with the remaining component decoupling or transforming as a singlet.
    Table 2 and Sec. 3 introduce this truncation without a dynamical mechanism; it is chosen to shape the mass matrices.
  • domain assumption A generalized CP symmetry is imposed so all coupling constants are real, leaving tau as the only CP-violating source.
    Reasonable in modular model building but not required; constrains the parameter space.
  • ad hoc to paper Modular weights are restricted to integers -4 <= k <= 3.
    Chosen to limit complexity and avoid proliferating free parameters; not derived from the symmetry.
  • domain assumption The inverse seesaw hierarchy O(M_S) << O(M_D) << O(M_SN) is required for Eq. (3).
    The hierarchy is enforced by hand via alpha_D v_h / Lambda and the r scan, not derived.
  • domain assumption Lepton-flavor equilibration reduces the Boltzmann equations to a single flavor-blind equation.
    Adopted from Refs. [55,56] and used to justify the leptogenesis calculation.
  • domain assumption The approximate analytic efficiency formulas in Eqs. (38)-(40) correctly capture washout in the inverse seesaw regime.
    Used instead of solving the Boltzmann equations; validity in this model is not demonstrated.
  • ad hoc to paper Scan priors are uniform in the ranges chosen: couplings in (0,10^3), Re(tau) in (0,0.5), Im(tau) > 0, |tau| >= 1.
    These ranges are broad but still prior choices that affect which regions are found viable.
invented entities (3)
  • Three right-handed neutrinos N_i no independent evidence
    purpose: Generate the Dirac mass term and drive leptogenesis through out-of-equilibrium decays.
    Heavy neutrino masses are predicted only after choosing the free scale r; no direct production or decay signature with rates is provided.
  • Three sterile singlet fermions S_i no independent evidence
    purpose: Implement the inverse seesaw and provide the small lepton-number-violating Majorana mass term.
    No independent experimental handle is given; their mass scale is tied to the fitted parameter alpha_S and r.
  • Scalar singlet phi no independent evidence
    purpose: Couple N and S through its VEV, v_phi, generating the N-S mixing term.
    No mass prediction, production mechanism, or collider signature is specified for phi.

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read the original abstract

A non-supersymmetric inverse seesaw model of neutrino mass based on the $A^{\prime}_5$ modular symmetry is presented. This framework provides a combined explanation for neutrino masses, mixing, and the cosmic baryon asymmetry through leptogenesis. Three concrete realizations are constructed, and their phenomenological predictions are analyzed. The results are not only compatible with the measured neutrino oscillation parameters within the current experimental 3$\sigma$ ranges, but also provide predictions for the neutrino mass ordering, Dirac and Majorana CP-violating phases, and the effective Majorana mass in neutrinoless double beta decay. The model further realizes TeV-scale leptogenesis consistent with the observed baryon asymmetry, rendering the scenario testable in both low-energy neutrino experiments and high-energy collider searches.

Figures

Figures reproduced from arXiv: 2603.19104 by Xianshuo Zhang, Yakefu Reyimuaji.

Figure 1
Figure 1. Figure 1: Results of the parameter scan for Model A in NO scenario. The panels show: (a) the allowed region of the modulus field τ ; correlations between Im(τ ) and (b) sin2 θ13, (c) sin2 θ23; correlations between Re(τ ) and (d) the total neutrino mass Pmi , (e) the Dirac CP phase δCP, (f) the effective electron neutrino mass mβ; correlations involving the CP-violating phases: (g) η2 vs. η1, (h) η2 vs. δCP, (i) η2 v… view at source ↗
Figure 2
Figure 2. Figure 2: Prediction of model A for the effective Majorana neutrino mass mββ as a function of the lightest neutrino mass m1 in NO scenario. The gray dashed area indicates param￾eter space favored by NO. Experimental constraints include the KamLAND-Zen exclusion limit (brown band, mββ < 0.028–0.122 eV [48]), the target sensitivities of next-generation 0νββ experiments LEGEND-1000 (green band, 0.009–0.021 eV [49]) and… view at source ↗
Figure 3
Figure 3. Figure 3: Results of the parameter scan for Model A in the IO scenario. The panels show: (a) the allowed region of the modulus field τ ; correlations between Im(τ ) and (b) sin2 θ13, (c) sin2 θ23; correlations between sin2 θ13 and (d) sin2 θ23, (e) sin2 θ12, (f) Re(τ ); and correlations involving the CP phases: (g) δCP vs. η1, (h) δCP vs. η2, (i) δCP vs. sin2 θ12. The color scale indicates the χ 2 value, with bright… view at source ↗
Figure 4
Figure 4. Figure 4: Prediction of Model A for the effective Majorana neutrino mass mββ as a function of the lightest neutrino mass m3 in the IO scenario. The gray dashed region indicates the entie parameter space, wherein the bold point-like colored area is the parameter space favored by the model. The vertical gray band shows the cosmological upper bound m3 ≲ 0.042 eV derived from Pmi < 0.12 eV [10, 51]. The predicted values… view at source ↗
Figure 5
Figure 5. Figure 5: Results of the parameter scan for Model B in the NO scenario. The panels show: (a) the allowed region of the modulus field τ ; correlations between Im(τ ) and (b) sin2 θ23, (c) δCP; correlations involving the Majorana phase η2 with (d) η1, (e) δCP, (f) sin2 θ23; correlations of the effective Majorana mass mββ with (g) δCP, (h) sin2 θ12, (i) sin2 θ23; and correlations among observables: (j) sin2 θ12 vs. sin… view at source ↗
Figure 6
Figure 6. Figure 6: Prediction of Model B for mββ as a function of the lightest neutrino mass m1 in NO scenario. The predicted range, mββ ≈ 0.95–1.20 meV, lies well below the sensitivity thresholds of next-generation 0νββ experiments: LEGEND-1000 (green band, 0.009–0.021 eV [49]) and nEXO (blue band, 0.0047–0.0203 eV [50]), as well as the current KamLAND-Zen exclusion limit (brown band, 0.028–0.122 eV [48]). The vertical gray… view at source ↗
Figure 7
Figure 7. Figure 7: Results of the parameter scan for Model B in the IO scenario. The panels show: (a) the allowed region of the modulus field τ ; correlations between Im(τ ) and (b) sin2 θ13, (c) sin2 θ23; correlations between Im(τ ) and (d) the total neutrino mass Pmi , (e) the effective electron neutrino mass mβ, (f) the effective Majorana mass mββ; and correlations involving the CP phases: (g) δCP vs. η1, (h) δCP vs. η2, … view at source ↗
Figure 8
Figure 8. Figure 8: Prediction of Model B for the effective Majorana neutrino mass mββ as a function of the lightest neutrino mass m3 in the IO scenario. The predicted range, mββ ≈ 0.045–0.048 eV, lies within the current KamLAND-Zen exclusion limit (brown band, 0.028–0.122 eV [48]) and partially overlaps with the projected sensitivities of next-generation experiments LEGEND￾1000 (green band, 0.009–0.021 eV [49]) and nEXO (blu… view at source ↗
Figure 9
Figure 9. Figure 9: Results of the parameter scan for Model C in the NO scenario. The panels show: (a) the allowed region of the modulus field τ ; correlations between Re(τ ) and (b) the effective Majorana mass mββ, (c) the solar mixing angle sin2 θ12; correlations involving the Dirac CP phase δCP with (d) the Majorana phase η2, (e) the atmospheric mixing angle sin2 θ23, (f) the Majorana phase η1; and correlations of the atmo… view at source ↗
Figure 10
Figure 10. Figure 10: Prediction of Model C for the effective Majorana neutrino mass mββ as a function of the lightest neutrino mass m1 in the NO scenario. The colored region indicates the parameter space favored by the model, with m1 ranging from approximately 0.0045 to 0.0065 eV and mββ ranging from 5.1 to 8.1 meV. Experimental and cosmological constraints are same as such plots in analyses of Model A and B. As shown, the en… view at source ↗
Figure 11
Figure 11. Figure 11: Results of the parameter scan for Model C in the IO scenario. The panels show: (a) the allowed region of the modulus field τ ; correlations between Im(τ ) and (b) the lightest neutrino mass m3, (c) the atmospheric mixing angle sin2 θ23; correlations between Re(τ ) and (d) the Majorana phase η1, (e) the Dirac CP phase δCP, (f) the solar mixing angle sin2 θ12; and correlations of the Majorana phase η1 with … view at source ↗
Figure 12
Figure 12. Figure 12: Prediction of Model C for the effective Majorana neutrino mass mββ as a function of the lightest neutrino mass m3 in the IO scenario. The almost point-like colored region, near the upper boundary of the dashed line, indicates the parameter space favored by the model. Experimental and cosmological constraints are same as the relevant figures in models A and B with IO case. KamLAND-Zen and next-generation 0… view at source ↗
Figure 13
Figure 13. Figure 13: Baryon asymmetry ηB as a function of the scaling parameter r for (a) Model A and (b) Model B. The blue points correspond to the NO scenario, while the red points denote the IO scenario. The horizontal dashed line indicates the experimentally observed value ηB = 6.12 × 10−10 [10, 11]. Both models successfully reproduce the observed asymmetry for specific ranges of r, with the corresponding heavy neutrino m… view at source ↗
Figure 14
Figure 14. Figure 14: ). 10 11 10 12 10 13 10 14 M1[eV] 10 29 10 25 10 21 10 17 10 13 10 9 10 5 10 1 B Model C (NO) Model C (IO) B =6.12×10 10 [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗

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Forward citations

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