Baryogenesis through leptogenesis in the minimal flipped $SU(5)$ with radiative seesaw

Martin Zdr\'ahal; Michal Malinsk\'y; Renato Fonseca; V\'aclav Mi\v{r}\'atsk\'y

REVIEW 3 major objections 3 minor 18 references

Baryogenesis through leptogenesis in the minimal flipped $SU(5)$ with radiative seesaw

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

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Pith's one-line read The paper claims that in the minimal flipped $SU(5)$ model, reproducing the cosmic baryon asymmetry by thermal leptogenesis requires the lightest neutrino mass below about $3\times10^{-2}$ eV, making the model testable in beta-decay and…

desk verdict Useful proceedings summary of the authors' own PRD scan; the m1 bound is real but conditional on an unquantified thermal-leptogenesis-dominance assumption, and the abstract overstates it. read the letter →

arxiv 2506.23113 v1 pith:N2SER6XM submitted 2025-06-29 hep-ph

Michal Malinský , Renato Fonseca , Václav Miřátský , Martin Zdráhal This is my paper

classification hep-ph PACS 12.10.Dm14.60.Pq98.80.Cq

keywords baryogenesisleptogenesisflippedSU(5)radiativeseesawneutrinomassprotondecayKATRINgrandunifiedtheories

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 examines whether the minimal flipped $SU(5)$ grand unified theory with radiatively generated right-handed neutrino masses can explain the observed matter-antimatter asymmetry of the Universe through thermal leptogenesis. It reports that imposing successful leptogenesis as an extra condition on the model's already tightly constrained flavour structure forces the lightest active neutrino mass below about $3\times10^{-2}$ eV, regardless of which of the three viable production regimes is at work. If correct, this is a testable prediction: the bound translates into an effective neutrino mass within reach of the KATRIN $\beta$-decay experiment, and into a universal upper bound of $30\%$ on the $p\to\pi^0\mu^+$ proton decay branching ratio. The paper therefore turns the baryon asymmetry from a given into a sharp constraint that can distinguish the model.

What carries the argument

The load-bearing structure is the correlation between the Dirac neutrino Yukawa matrix and the up-quark mass matrix, $M_D^\nu = M_u^T$, combined with the two-loop radiative generation of the right-handed neutrino Majorana masses. Because the model has no tree-level source of those masses, the heavy spectrum is tied to the charged-fermion sector and to perturbativity and non-tachyonicity bounds. The mass relation $m_1 m_2 m_3 M_1 M_2 M_3 = m_u^2 m_c^2 m_t^2 \sim 1.3\ \mathrm{GeV}^6$ links the light and heavy neutrino spectra, and a numerical evaluation of the baryon-to-photon ratio $\eta_B$ over the parameter space shows that $\eta_B \approx 6\times10^{-10}$ is attainable only for $m_1 \lesssim 3\times10^{-2}$ eV. The same scan fixes the unitary matrix $U_\nu$ connecting neutrino and quark sectors, which enters the two-body proton decay amplitudes such as $\Gamma(p\to\pi^0\mu^+) \propto |(V_{\mathrm{PMNS}}U_\nu)_{21}|^2$.

What would settle it

Measure the effective electron-neutrino mass $m_\beta$ in $\beta$ decay or the sum of neutrino masses $\sum m_\nu$ in cosmology. If the data require the lightest active neutrino mass to be above $3\times10^{-2}$ eV, the model cannot produce the observed baryon asymmetry, given the stated assumption that thermal leptogenesis is the primary source of $B-L$. Alternatively, observe proton decay with $\mathrm{BR}(p\to\pi^0\mu^+) > 30\%$, which no point in the $\eta_B$-compatible region allows.

Watch

Extended reading notes

Core claim

The paper's central claim is that in the minimal flipped $SU(5)$ theory, where the right-handed neutrino Majorana masses arise at two loops and the Dirac neutrino Yukawa matrix is tied to the up-quark mass matrix, the observed baryon-to-photon ratio $\eta_B \approx 6\times10^{-10}$ is reproduced only when the lightest active neutrino mass $m_1$ lies below about $3\times10^{-2}$ eV. This holds across all three leptogenesis regimes the authors distinguish: lightest right-handed neutrino ($N_1$)-dominated production, $N_2$-dominated production protected from washout, and hierarchical spectra kept alive by suppressed decoherence. The constraint follows from the mass relation $m_1 m_2 m_3 M_1 M_2 M_3 = m_u^2 m_c^2 m_t^2 \sim 1.3\ \mathrm{GeV}^6$ and the two-loop suppression which together push the heavy spectrum toward the lower bound on the lightest right-handed neutrino mass required for successful leptogenesis. As a result, the effective neutrino mass in $\beta$ decay is bounded at a level relevant for KATRIN, and the proton decay branching ratio into $\pi^0\mu^+$ never exceeds $30\%$ in the $\eta_B$-compatible region.

Load-bearing premise

The paper assumes that no comparable baryon-minus-lepton asymmetry is generated at or above the unification scale — for instance by decays of heavy colour triplets — so that thermal leptogenesis is the primary source of the net $B-L$ asymmetry; if an earlier source dominates, the computed $\eta_B$ values and the $m_1 < 3\times10^{-2}$ eV conclusion need not hold.

Editorial extensions

If this is right

The observed baryon asymmetry can be reproduced in three distinct regimes — decays of the lightest right-handed neutrino, decays of the next-to-lightest one with suppressed washout, and hierarchical spectra with strongly suppressed decoherence — so the model is not excluded by generic lower bounds on the heavy neutrino mass.
The absolute neutrino mass scale is bounded by $m_1 < 3\times10^{-2}$ eV, which translates into an upper limit on the effective beta-decay mass $m_\beta$ at a level that ongoing experiments such as KATRIN can probe.
In the baryogenesis-compatible region, the proton decay branching ratio satisfies $\mathrm{BR}(p\to\pi^0\mu^+) < 30\%$, and the bound tightens to about $10\%$ when $m_1$ drops near $10^{-3}$ eV.
The heavy neutrino spectrum in the compatible region is at least mildly degenerate, with masses peaking near $10^{8.8}$ GeV, which distinguishes the scenario from generic hierarchical seesaw models.
If the prediction survives experimental scrutiny, the minimal flipped $SU(5)$ with radiative seesaw would simultaneously account for neutrino masses, proton decay patterns, and baryogenesis.

Reading between the lines

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

If future cosmology (for instance, CMB measurements of $\sum m_\nu$) settles the lightest neutrino mass above $3\times10^{-2}$ eV, the paper's assumption of thermal leptogenesis dominance would be pressed, and the model would need an additional source of $B-L$ above the seesaw scale.
The same logic could be applied to other grand unified models with strong correlations between heavy right-handed neutrino and fermion mass matrices; those models may inherit analogous upper bounds on the absolute neutrino mass once baryogenesis is imposed.
The boundary at $m_1\sim3\times10^{-2}$ eV is a fine-tuned corner: a future positive signal near that value in a KATRIN-like experiment would force the model into a narrow, strongly constrained parameter region, making nearby observables like lepton-flavour-violating decays sharper tests.
A combined measurement strategy could pair beta-decay and proton-decay searches: finding muon-channel proton decay with a branching ratio above $30\%$ would falsify the region that reproduces the baryon asymmetry under the paper's assumptions, whereas a low $m_\beta$ together with absence of such a signal would support it.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a conference proceedings that repackages the authors' own PRD 110, 015030 numerical scan. Nothing numerically new is computed here; the paper explicitly says the result 'is exactly what has been observed in a dedicated analysis of Ref. [12]'. What is new is the packaging: the claim that requiring thermal leptogenesis forces m1 < 3e-2 eV, the KATRIN testability angle, and the proton decay branching ratio bound BR(p -> pi0 mu+) < 30% in the compatible region. As a summary, it is clear and honest about where things come from.

The paper does a good job at laying out the model, the radiative seesaw structure, and the three distinct parameter domains (A, B, C) where the observed baryon asymmetry can be reproduced. The citation to their own prior work is appropriate — the heavy lifting is in Ref. [12] — and they are explicit that the result comes from a ULYSSES scan. That is real, reproducible work, even if it is not reproduced here.

Now the soft spots. The biggest one is the assumption that thermal leptogenesis is the primary source of B-L. They acknowledge it in Sec. 2.1 but do not quantify it. The stress-test concern is fair: U(1)_X breaking at M_GUT can generate a net B-L before the seesaw scale, and with the seesaw scale radiatively generated around 1e8 GeV there is a large window where such an asymmetry can survive, especially in Domain A where washout is suppressed. The escape clauses — strong washout or suppressed CP asymmetry in heavy triplet decays — are not demonstrated for the parameter regions that give the quoted bound. So the m1 limit is a model prediction only under an additional, untested assumption. The paper says this, but the abstract and conclusions state the limit more baldly than the text justifies.

A second, smaller issue: the abstract and Sec. 2.4 present the limit as an absolute neutrino mass bound, but Fig. 2 and the surrounding text specify a compressed, normally ordered spectrum with m1 around 3e-2 eV. The normally-ordered-only caveat should be carried through the summary. That is an overclaim, though easy to fix.

Who is this for? GUT phenomenologists and neutrino model builders who want a quick pointer to what the flipped SU(5) radiative seesaw can do, and KATRIN watchers. It is not a standalone research paper; if it were submitted as one, I would desk reject it because the content is a summary. As a proceedings contribution, it is acceptable once the caveats above are added. For your own reading, cite the PRD, not this proceedings.

Referee Report

3 major / 3 minor

Summary. The manuscript studies baryogenesis via thermal leptogenesis in the minimal flipped SU(5) model where the right-handed neutrino Majorana mass scale is generated radiatively at two loops. It claims that imposing the observed baryon asymmetry eta_B ~ 6e-10 as a requirement selects parameter regions in which the lightest active neutrino mass m1 is bounded above by about 3e-2 eV, that this bound translates into a prediction for the effective neutrino mass m_beta testable by KATRIN, and that the compatible parameter region also implies BR(p -> pi0 mu+) < 30%. The paper explicitly assumes that thermal leptogenesis is the primary source of net B-L, acknowledging that high-scale B-L generation may occur at U(1)_X breaking. The numerical results are taken from a previous paper [12] that used the ULYSSES package, and Fig. 2 shows a sample scan cut.

Significance. If the central claim is correct, the paper offers a concrete connection between cosmological baryogenesis and low-energy neutrino observables, with a falsifiable upper bound on the absolute neutrino mass scale and a characteristic proton decay branching ratio pattern. The strength of the paper is its explicit model context and the use of a dedicated leptogenesis solver (ULYSSES) in the companion work [12]; the manuscript also honestly states its central assumption. However, the upper limit is not a theorem of the model alone; it depends on an unquantified assumption about the absence of competing high-scale B-L sources and on numerical details that are not reported here. The significance is therefore conditional: it would be high if the assumption can be justified or quantified, but as it stands the robustness of the claimed bound is not established.

major comments (3)

[Sec. 2.2, Fig. 2] The manuscript assumes that thermal leptogenesis is the primary source of net B-L, but it explicitly acknowledges that in the genuine flipped SU(5) the (10,+1) scalar breaks U(1)_X at the unification scale and that 'a net B-L may be first produced well above the seesaw scale'. This is a load-bearing assumption for the central m1 < 3e-2 eV bound: if any comparable B-L is generated at M_GUT through CP-violating decays of the heavy fields, the required thermal yield is reduced and the upper limit on m1 does not follow. The paper does not estimate the high-scale asymmetry or demonstrate that it is washed out. Moreover, the parameter region that yields the quoted bound (Domain A in Sec. 2.2) is characterized by 'relatively suppressed washout', which would also preserve a pre-existing asymmetry. The escape clause 'strong washout precedes' is thus in tension with the very domain used to obtain the bound. Please either quantify the high-scale B-L yield and washout or state explicitly that the bound holds only under an additional, unverified assumption.
[Sec. 2.2, Fig. 2] The numerical results supporting the upper limit m1 < 3e-2 eV are not described in sufficient detail. The paper refers to a 'sample scan' and to Ref. [12] for the ULYSSES computation, but the present manuscript presents no information on scan ranges, number of points, convergence criteria, or sensitivity to input quantities such as quark masses, phases, and renormalization-group uncertainties. Since the upper limit is the main new physical statement of this paper (as opposed to Ref. [12], which may have different scope), the reader cannot assess whether the limit is robust or an artifact of a particular parameter cut. Please provide these details or explicitly defer the full analysis to Ref. [12] and describe which parts of the result are new here.
[Sec. 2.3] The claimed universal bound BR(p -> pi0 mu+) < 30% in the eta_B-compatible region is stated without showing the scan that leads to it. The proton decay branching ratio depends on the U_nu matrix (Eq. (2)), which in turn depends on the same high-scale parameters and on the assumption about thermal leptogenesis dominance. It is not clear from the text whether this bound is a hard constraint across all of the eta_B-compatible parameter space or a feature of the sampled points. Please clarify the provenance of this bound and its dependence on the assumptions in Sec. 2.1.

minor comments (3)

[Abstract / Sec. 2.2] There are several typographical errors, e.g., 'neturino' in Sec. 2.2 and 'theoris' in the Introduction; the manuscript would benefit from a careful proofreading pass.
[Fig. 2] The caption of Fig. 2 mentions a log-log plane but does not label the axes in the figure; please add axis labels and units so the reader can understand the 'triangular shape' without referring to Ref. [12].
[Sec. 2.1] The phrase 'the current scenario' is used multiple times with differing referents; please clarify whether it denotes the minimal flipped SU(5) model with radiative seesaw, the thermal-leptogenesis scenario, or the specific parameter scan of Fig. 2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the m1 upper limit is a numerical exclusion bound obtained from an external benchmark, not a fitted input or self-referential derivation.

full rationale

The central claim is an exclusion bound, not a fit: the observed baryon asymmetry η_B ≈ 6×10^-10 is used as an external benchmark, while m1 and the heavy-neutrino parameters are scanned and η_B is computed with the ULYSSES package. No parameter is adjusted to reproduce η_B and then renamed a prediction; the bound m1 < 3×10^-2 eV is the point at which the computed maximum η_B falls below the observed value. Equation (3) is a determinant relation following from M_D^ν = M_u^T and the seesaw relation, not an identity that assumes the m1 bound. The same-author citations [3,9,12] supply the model construction and the numerical scan; [12] uses a public code (ULYSSES) and external data, so it is independent support rather than a self-referential uniqueness argument. The explicit assumption that thermal leptogenesis is the primary B-L source (Sec. 2.1) is a stated caveat about initial conditions, not a definitional or fitted circular step. The KATRIN and proton-decay statements are translations of the scanned constraints into observables. No equation in the paper reduces, by construction, to its own input.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central bound is extracted from a numerical scan over model parameters; the scan itself is not described in this proceedings. The thermal-leptogenesis-dominance assumption is the main extra postulate beyond the established model framework, and the two-loop seesaw mechanism and Dirac mass relation are model-defining inputs.

free parameters (3)

lightest active neutrino mass m1 = constrained to be below about 3e-2 eV
Scanned in the parameter space; the central claim is an upper limit on this quantity, not a fitted value.
right-handed neutrino masses M1, M2, M3 = scanned, subject to relation (3) and perturbativity
These are free model parameters in the scan, constrained by the determinant relation and by the requirement of reaching the observed baryon asymmetry.
additional high-scale phases and mixing parameters = scanned in Ref. [12]
The paper mentions additional high-scale parameters and phases beyond the RHN masses, but does not specify their ranges or values.

assumptions (5)

domain assumption Thermal leptogenesis is the primary source of the net B-L asymmetry.
Explicitly assumed in Sec. 2.1; the paper acknowledges that a net B-L may be produced above the seesaw scale and assumes it is washed out or subdominant.
domain assumption The two-loop radiative mechanism generates the right-handed neutrino Majorana mass matrix.
This mechanism, from Refs. [3,9], is the defining feature of the model and underlies the relation between the seesaw scale and the RHN spectrum.
domain assumption The Dirac neutrino mass matrix equals the up-quark mass matrix, M_D^nu = M_u^T.
This flipped SU(5) relation, Eq. (1), leads to the determinant relation (3) used throughout the leptogenesis analysis.
domain assumption Perturbativity and non-tachyonicity constraints restrict the scalar parameter space as derived in earlier work.
The paper relies on these bounds from Refs. [3,12] to define the allowed flavour patterns and the scanned parameter space.
domain assumption The ULYSSES package correctly solves the Boltzmann equations for the lepton asymmetry.
The numerical results are obtained with ULYSSES [18]; the present paper gives no independent check of the solver's accuracy or convergence.

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Cite this review

Pith. "Pith review of Baryogenesis through leptogenesis in the minimal flipped $SU(5)$ with radiative seesaw." pith.science (2026). https://pith.science/paper/N2SER6XM

@misc{pith2026250623113,
  author       = {Pith},
  title        = {Pith review of: Baryogenesis through leptogenesis in the minimal flipped $SU(5)$ with radiative seesaw},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N2SER6XM}},
  note         = {Machine review of arXiv:2506.23113}
}

abstract

The minimal flipped $SU(5)$ unification with the right-handed neutrino Majorana mass scale generated as a two-loop effect is arguably one of the most constrained models of perturbative baryon and lepton number violation currently on the market. This is namely due to its very simple scalar sector structure which, subject to perturbativity and non-tachyonicity bounds, leads to the emergence of characteristic flavour patterns providing interesting insights into proton decay phenomenology, neutrino physics etc. In this contribution, we discuss the potential impact of the baryon asymmetry of the Universe as an additional requirement imposed onto the already strongly constrained flavour structure of the model, focusing on thermal leptogenesis as its hypothetical primary source in this framework. Remarkably, this single extra condition leads, among other things, to a very interesting upper limit on the absolute neutrino mass scale which, in turn, renders the model potentially testable in the existing beta-decay experiments such as KATRIN.

Figures

Figures reproduced from arXiv: 2506.23113 by the authors.

**Figure 1.** Radiative generation of RHN Majorana mass in the minimal flipped 𝑆𝑈(5) model [3]. 𝑋 and Δ𝑖 denote the high-scale vector bosons and scalar 𝑆𝑈(3) triplets, respectively. generation of their Majorana masses requires an appropriate irreducible representation from the symmetric product of two 10’s of 𝑆𝑈(5), namely, a (50, −2) scalar multiplet. This option, however, makes the model suffer from similar drawbacks as its “st… view at source ↗

**Figure 2.** The maximum 𝜂𝐵 attainable in a sample scan of the minimal flipped 𝑆𝑈(5) model parameter space for a relatively compressed normally ordered active neutrino spectrum with 𝑚1 around 3 × 10−2 eV. Due to the constraint (3) the relevant domain has a triangular shape in the log − log plane, with the rightmost apex corresponding to all 𝑀𝑖’s around 108.8 GeV. It is worth noting that the plot represents a two-dimensional cut … view at source ↗

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [12]

Leptogenesis in the minimal flipped $SU(5)$ unification

R. Fonseca, M. Malinský, V. Miřátský, and M. Zdráhal, Phys. Rev. D110, 015030 (2024), arXiv:2312.08357

work page Pith review arXiv 2024

[2] [1]

S. M. Barr, Phys. Lett. B112, 219 (1982)

work page 1982

[3] [2]

J. P. Derendinger, J. E. Kim, and D. V. Nanopoulos, Phys. Lett. B139, 170 (1984)

work page 1984

[4] [3]

Arbeláez Rodríguez, H

C. Arbeláez Rodríguez, H. Kolešová, and M. Malinský, Phys. Rev. D89, 055003 (2014), arXiv:1309.6743

arXiv 2014

[5] [4]

Georgi and S

H. Georgi and S. L. Glashow, Phys. Rev. Lett.32, 438 (1974)

1974

[6] [5]

S.Bertolini,L.DiLuzio,andM.Malinský, Phys.Rev.D 81,035015(2010),arXiv:0912.1796

arXiv 2010

[7] [6]

Jarkovská, M

K. Jarkovská, M. Malinský, T. Mede, and V. Susič, Phys. Rev. D105, 095003 (2022), arXiv:2109.06784. 6 Baryogenesis through leptogenesis in the minimal flipped𝑆𝑈(5) with radiative seesaw Michal Malinský

arXiv 2022

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Could we rotate proton decay away?

I. Doršner and P. Fileviez Perez, Phys.Lett.B606, 367 (2005), arXiv:hep-ph/0409190

work page Pith review arXiv 2005