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REVIEW 3 major objections 4 minor 26 references

Thermal leptogenesis in minimal unified models

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

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Pith's one-line read Requiring thermal leptogenesis to make all baryons fixes the lightest neutrino below 0.03 eV and the B-L scale near $10^{12.5}$ GeV.

desk verdict Proceedings-grade review of flipped SU(5) leptogenesis plus a promising but underdocumented preview of SO(10) fits; the B-L scale inference should not be treated as established yet. read the letter →

arxiv 2506.23117 v1 pith:V7FS6G7R submitted 2025-06-29 hep-ph

Michal Malinský This is my paper
classification hep-ph
keywords thermalleptogenesisbaryonasymmetryflippedSU(5)SO(10)grandunificationMajorananeutrinomassesB-Lbreakingscaleprotondecaymassbound
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 argues that the baryon asymmetry of the Universe can act as a sharp extra constraint on the flavour structure of two minimal grand unified models, not just as a number to be checked afterwards. Assuming thermal leptogenesis—CP-asymmetric out-of-equilibrium decays of heavy Majorana neutrinos, with the resulting lepton number reprocessed by sphalerons into baryons—is the only source of the asymmetry, two concrete consequences follow. In the minimal flipped SU(5) model, matching the observed asymmetry forces the lightest active neutrino below about 0.03 eV. In the minimal SO(10) model, the same requirement places the B-L breaking scale near $10^{12.5}$ GeV, close to the region independently favoured by gauge coupling unification, and leans the leptonic Dirac CP phase toward the third or fourth quadrant.

What carries the argument

The load-bearing object is a rigid seesaw-stabilised Yukawa sector. In flipped SU(5), the Dirac neutrino mass matrix is fixed to $M_D^\nu = M_u^T$ and the right-handed Majorana mass arises at two loops, leaving one unitary matrix $U_\nu$ to control light-neutrino masses, heavy-neutrino decays, and proton-decay flavour ratios. In minimal SO(10), a highly constrained renormalisable Yukawa sector must simultaneously fit all quark and lepton masses and mixings. Thermal leptogenesis supplies the extra equation: out-of-equilibrium decays of the heavy Majorana neutrinos generate a CP-asymmetric lepton number that sphalerons convert into baryons, and the observed $\eta_B \simeq 6\times10^{-10}$ filters the remaining parameter space, turning one cosmological number into geometric constraints such as the $0.03$ eV neutrino ceiling and the $10^{12.5}$ GeV $B-L$ scale.

What would settle it

Measure the absolute neutrino mass scale: a lightest neutrino shown to be heavier than about $0.03$ eV, whether from beta-decay kinematics or from cosmological limits on the summed neutrino masses, would rule out the flipped-SU(5) leptogenesis solution. Assigning a comparable baryon asymmetry to another mechanism would likewise make the whole constraint inapplicable.

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Extended reading notes

Core claim

The central claim is that adding the requirement $\eta_B \simeq 6\times10^{-10}$ to already tightly constrained Yukawa sectors does more than check consistency; it localises parameters that low-energy flavour data alone leave free. In the flipped SU(5) model, the seesaw structure fixes the Dirac neutrino mass matrix to the transposed up-quark matrix and generates right-handed Majorana masses radiatively, so the entire neutrino and proton-decay flavour pattern is controlled by a single unitary matrix; the reported scan finds no point with the observed asymmetry once the lightest active neutrino exceeds about $0.03$ eV. In the minimal SO(10) model, a global flavour fit augmented by $\eta_B$ yields a $B-L$ breaking scale in the $10^{12.5}$ GeV ballpark, independently reproducing the scale singled out by gauge coupling unification, and prefers a negative leptonic Dirac CP phase, i.e. the third or fourth quadrant.

Load-bearing premise

The load-bearing premise is that thermal leptogenesis is the only significant source of the baryon asymmetry; if grand-unification-scale B-violating decays or any other mechanism produced a comparable share, the derived neutrino-mass and $B-L$ scale bounds would no longer follow.

Editorial extensions

If this is right

  • If the flipped-SU(5) bound is correct, the absolute neutrino mass scale sits inside the reach of beta-decay and cosmological surveys, and quasi-degenerate neutrino spectra are excluded.
  • Proton decay branching ratios in flipped SU(5) become calculable in terms of the same unitary matrix that leptogenesis constrains, so a proton decay signal would directly test the flavour link.
  • In minimal SO(10), the baryon-asymmetry condition independently fixes the $B-L$ breaking scale near $10^{12.5}$ GeV, reinforcing the gauge-coupling unification picture and setting the mass scale of the heavy right-handed neutrinos.
  • The preferred third/fourth-quadrant value of the leptonic Dirac CP phase is a concrete prediction that long-baseline oscillation experiments can confront.
  • Treating baryogenesis as a flavour observable turns one cosmological number into several correlated low-energy predictions, making both models more falsifiable.

Reading between the lines

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

  • An implication left implicit in the proceedings text: the $0.03$ eV bound comes from scans aimed at promising parameter patches, so if an exhaustive scan confirms it, quasi-degenerate neutrino spectra would be excluded while both mass orderings with a hierarchical spectrum remain open.
  • The same machinery could be applied to non-minimal variants of these models to test whether the recovered $B-L$ scale is a genuine consequence of minimality or an artifact of the restricted Yukawa sector.
  • A future proton decay signal in a channel controlled by the same unitary matrix would effectively measure an entry of the matrix that also governs the leptogenesis yield, making baryogenesis and proton decay two views of one observable.
  • If cosmological surveys fix the sum of neutrino masses, combining that value with the leptogenesis constraint could sharpen predictions for leptonic CP violation beyond the quadrant preference the paper reports.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This proceedings-style paper reviews thermal leptogenesis in two minimal unified models under the explicit assumption that the baryon asymmetry of the Universe is generated primarily by the out-of-equilibrium decays of heavy Majorana neutrinos (i.e., direct GUT-scale baryon-number violation is neglected). In the minimal flipped SU(5) model, the paper reports, based on the published study [9], that the requirement of sufficient leptogenesis forces the lightest active neutrino mass below roughly 0.03 eV, a result testable at KATRIN. In the minimal SO(10) GUT, the paper presents preliminary results from an in-preparation study [24]: with roughly 20 fitted Yukawa parameters, the fitter achieves global chi-squared values below 10, the leptonic Dirac CP phase falls preferentially in the third or fourth quadrant, and the B-L breaking scale is localized to about 10^12.5 GeV from low-energy flavour data plus the observed baryon asymmetry. The paper claims that this scale coincides with the region preferred by an independent gauge-coupling-unification analysis [16].

Significance. If the SO(10) result holds, it would constitute a non-trivial connection between low-energy flavour physics, thermal leptogenesis, and gauge-coupling unification, and the preferred range of the Dirac CP phase is testable at upcoming long-baseline experiments. The flipped SU(5) bound on the lightest neutrino mass is a clean, falsifiable prediction grounded in a peer-reviewed analysis, and the paper is explicit about the leptogenesis-only assumption. These strengths are genuine. However, the SO(10) results are explicitly preliminary and lack the statistical documentation needed to assess whether the claimed localization is a robust model prediction or an artifact of the fitting procedure. At present, the significance of the central new claim is therefore limited.

major comments (3)
  1. [Section 3 and Fig. 3] The central new result, the localization of the B-L breaking scale to approximately 10^12.5 GeV, rests entirely on a 'small subset of preliminary results' of the in-preparation study [24]. The manuscript gives no definition of the chi-squared function, no list of the low-energy observables used with their uncertainties or covariance, no description of the scan priors, and no convergence or robustness diagnostics. Consequently, the reader cannot distinguish a genuine model prediction from an artifact of the sampling procedure or prior choices. The statement that neglected high-scale thresholds and the simplified unified-gauge-coupling estimate are 'under reasonable control' is made without any quantitative estimate. This issue is load-bearing because the B-L scale claim is the main new physics content of the paper.
  2. [Section 3, global chi-squared discussion] The observation that the fitter can reach global chi-squared values below 10 with almost 20 fitted parameters demonstrates compatibility of the model with low-energy data, but it does not by itself demonstrate that the model predicts a narrow range for the B-L scale. To support the claim that the eta_B constraint pins the B-L VEV, the paper should show the distribution of the fitted B-L scale over the accepted parameter space (for example, a histogram or density plot) and, crucially, a control fit performed without the eta_B constraint. Without such a control, the causal attribution of the localization to the leptogenesis constraint is not established.
  3. [Section 3, comparison with gauge-coupling unification] The comparison of the fitted B-L scale with the gauge-coupling-unification analysis [16] is only qualitative. The text says that 10^12.5 GeV is 'in the ballpark' and 'not far from' the region favoured by the omega_BL -> 0 scenario, but it does not quantify the overlap, e.g., whether the value lies within the 1-sigma or 2-sigma region of [16]. A quantitative comparison is needed to support the claimed concordance, especially because the apparent agreement with an independent constraint is a key part of the paper's appeal.
minor comments (4)
  1. [Section 3] The symbol omega_BL is used without definition; please define it when first introduced.
  2. [Figure 2 caption] The abbreviation 'NH' (or 'normal hierarchy') is used in the caption without spelling out at first use; please expand it.
  3. [Sections 2-3] The ULYSSES package [12] is mentioned but not described; a single sentence on its role (e.g., computing the baryon asymmetry from the model parameters) would help readers.
  4. [Section 3] The text refers to 'the B-L breaking VEV of the relevant SU(2)_R scalar triplet'; please clarify how this VEV is related to the heavy Majorana neutrino masses used in the leptogenesis calculation.

Circularity Check

0 steps flagged · score 2.0 of 10

No substantive circularity: ηB is an external input to the fits; the B-L scale, neutrino-mass bound, and CP-phase preference are fitted outputs, not rearrangements of the input. The caveats are about verifiability and same-group preliminary results, not circular derivation.

full rationale

The paper uses the measured baryon-to-photon ratio ηB as a fixed external constraint in global fits of the Yukawa sectors of flipped SU(5) and minimal SO(10). The outputs — an upper limit on the lightest neutrino mass (Section 2), and the localization of the B−L breaking scale around 10^12.5 GeV together with a preference for δCP in the 3rd/4th quadrant (Section 3, Fig. 3) — are not defined in terms of ηB. They follow from model dynamics (heavy-neutrino decays, washout, two-loop seesaw, or the SO(10) Yukawa structure), so imposing the measured ηB is a legitimate consistency constraint rather than a self-fulfilling prediction. The Fig. 3 comparison with the gauge-coupling preferred region uses Ref. [16] only after the fit; no gauge-unification information is fed into the fit, and the text explicitly says no other constraints were used. Thus no equation reduces to an input by construction. The main caveats are non-circular: the SO(10) result is explicitly preliminary, drawn from an unpublished same-author study [24] with no χ² definition, scan priors, or threshold-error quantification, and the statement that neglected uncertainties are 'under reasonable control' is unquantified. These are verifiability and reproducibility issues, not circularity defects. The self-citations to [16] and [24] do not substitute for the argument; the model predictions are tested against low-energy fermion data and ηB, which are external benchmarks.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central constraints are obtained from numerical fits and scans in two specific minimal GUTs. The flipped SU(5) results come from a full published scan [9]; the SO(10) results are preliminary fits from an unpublished study [24]. In both cases, the heavy lifting is done by the assumed minimal Yukawa structures and by numerical optimization, with of order 20 fitted parameters in SO(10). The 'predictions' are outputs of fits that use eta_B as an input, so they are not parameter-free. No new particles or forces are introduced.

free parameters (2)
  • SO(10) Yukawa-sector fitted parameters (about 20) = Not specified; global chi2 < 10 reported
    The SO(10) fits use a stochastic differential evolution algorithm to adjust roughly 20 couplings and phases in the minimal renormalizable SO(10) Yukawa sector; the inferred B-L scale and CP phase are outputs of this fit.
  • Flipped SU(5) seesaw parameters (U_nu elements, heavy neutrino masses) = Not specified; scans reported
    The flipped SU(5) results come from a full parameter scan in Ref. [9] that varies U_nu and heavy neutrino properties; the m0 < 0.03 eV bound emerges from this scan.
assumptions (4)
  • domain assumption Leptogenesis is the sole source of baryon asymmetry
    Section 1 states 'we shall for simplicity assume that leptogenesis is the primary source of the asymmetry, i.e. we shall neglect the direct net B production at the unification scale.' If this is violated, the derived constraints do not follow.
  • domain assumption Minimal flipped SU(5) model with radiatively generated seesaw
    The analysis is embedded in the specific model of Ref. [3]; the constraint results depend on the assumed Yukawa structure and the two-loop Majorana mass generation.
  • domain assumption Minimal renormalizable SO(10) model is consistent at one loop
    The SO(10) analysis assumes the model of Refs. [4,5] is viable at one loop as argued in [6]; the parameter space and flavour predictions rely on this consistency.
  • domain assumption ULYSSES leptogenesis package correctly computes the asymmetry
    Both analyses use the ULYSSES package [12] to compute the final baryon asymmetry; the results inherit any approximations or bugs in that package.

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Cite this review

Pith. "Pith review of Thermal leptogenesis in minimal unified models." pith.science (2026). https://pith.science/paper/V7FS6G7R

@misc{pith2026250623117,
  author       = {Pith},
  title        = {Pith review of: Thermal leptogenesis in minimal unified models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V7FS6G7R}},
  note         = {Machine review of arXiv:2506.23117}
}
abstract

We review the status of thermal leptogenesis in the minimal $SU(5)\times U(1)$ and $SO(10)$ unified models under the assumption that the leptonic asymmetry generated in the out-of-equilibrium decays of heavy Majorana neutrinos (and its subsequent conversion into baryons via sphalerons) constitutes the primary source of baryon asymmetry of the Universe. In both cases, leptogenesis is shown to provide a strong extra constraint on the flavour structure of the model under consideration, leading to interesting and potentially testable phenomenological effects.

Figures

Figures reproduced from arXiv: 2506.23117 by the authors.

Figure 1
Figure 1. Two-loop Feynman diagrams giving rise to a radiatively generated Majorana [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Maximum levels of attainable baryon asymmetry displayed along two differ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The B − L breaking scale in the minimal SO(10) GUT determined solely from the requirement of the compatibility of the flavor structure of the model with the measured value of the baryon asymmetry (assumed to be dominated by thermal leptogenesis); no other constraints have been used in producing the plot. Remarkably enough, the scale of the U(1)B−L breaking VEV automatically falls into the vicinity of the region favo… view at source ↗

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