Leptogenesis and Dirac neutrino masses in SO(10)

L. Oliver; R. Aleksan

Leptogenesis and Dirac neutrino masses in SO(10)

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read With SO(10) fermion masses from 10 and \overline{126} only, the relation $V^R = V^{L*}$ persists and yields heavy neutrino spectra whose leptogenesis output matches the observed baryon asymmetry.

desk verdict A concrete SO(10) benchmark that relaxes m_D = m_u, but the single-flavor leptogenesis approximation is unexamined and could shift Y_B; worth a serious referee. read the letter →

arxiv 2508.06714 v1 pith:5TSGS5KW submitted 2025-08-08 hep-ph hep-th

R. Aleksan , L. Oliver This is my paper

classification hep-phhep-th

keywords SO(10)grandunifiedtheoryleptogenesisDiracneutrinomassseesawmechanismbaryonasymmetryHiggsrepresentationsright-handedneutrinos

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 in an SO(10) grand unified theory where fermion masses come only from the 10 and \overline{126} Higgs representations, the Dirac neutrino mass is not forced to equal the up-type quark mass, and the left and right diagonalization matrices still obey $V^R = V^{L*}$. This opens parameter space that the 10-only version of the theory closed. Within that space the authors find heavy neutrino spectra with masses near the SO(10) unification scale, and at least one explicit benchmark, $M_1 = 6.26 \times 10^{10}$ GeV, $M_2 = 2.23 \times 10^{12}$ GeV, $M_3 = 4.57 \times 10^{14}$ GeV, that in the strong washout regime gives $Y_B = 8.50 \times 10^{-11}$, matching the measured baryon asymmetry. A sympathetic reader would care because the same Higgs sector that fixes the known fermion mass relations, such as $m_b = m_\tau$ and $m_\mu = 3m_s$, is being used to explain both neutrino masses and the matter-antimatter asymmetry.

What carries the argument

The load-bearing object is the $\mathbf{10} \oplus \overline{\mathbf{126}}$ Higgs sector of SO(10) for fermion masses. Its role is to make the Dirac mass $m_D$ general, $m_D \neq m_u$, while maintaining $V^R = V^{L*}$ when the $\mathbf{120}$ representation is excluded. That relation ties the seesaw and leptogenesis prediction to low-energy fermion data plus the undetermined light neutrino parameters, so a heavy-neutrino spectrum can be searched for in parameter space.

What would settle it

A future determination of the right-handed neutrino sector that forces $M_1$, $M_2$, $M_3$ away from $(6.26\times 10^{10}, 2.23\times 10^{12}, 4.57\times 10^{14})$ GeV, or a fit to the observed fermion masses and mixings requiring a nonzero 120 coupling, would falsify this benchmark.

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Extended reading notes

Core claim

Working in the single-flavour treatment of baryogenesis through leptogenesis, with the Higgs representations $\mathbf{10}$ and $\overline{\mathbf{126}}$ generating fermion masses and the antisymmetric $\mathbf{120}$ absent, the paper's central discovery is that the Dirac mass matrix diagonalization can be written $m_D = V^{L\dagger} m_D^{diag} V^R$ with $V^R = V^{L*}$, and that this is enough to make leptogenesis predictive. Unlike the one-representation case, where $m_D = m_u$ and no viable heavy spectrum is found, the two-representation case admits parameter choices with right-handed neutrino masses $M_1 = 6.26\times 10^{10}$ GeV, $M_2 = 2.23\times 10^{12}$ GeV, $M_3 = 4.57\times 10^{14}$

Load-bearing premise

The load-bearing premise is that the antisymmetric 120 representation is absent from fermion masses, because only then does the relation $V^R = V^{L*}$ hold and the parameter search for the heavy spectrum go through; the quoted $Y_B$ also inherits the single-flavor leptogenesis approximation.

Editorial extensions

If this is right

If the framework is right, the heavy neutrino masses are predicted in the $10^{10}$ to $10^{14}$ GeV window, naturally consistent with the SO(10) unification scale.
The benchmark baryon asymmetry, $Y_B = 8.50\times 10^{-11}$, becomes a quantitative target: future refinements of leptogenesis calculations either reproduce it or rule out this example.
Because $m_D$ is no longer tied to $m_u$, the same Higgs sector can accommodate realistic light-neutrino masses and mixings without adding exotic fermion content.
The prediction is currently made in the single-flavor leptogenesis approximation, so extending the same benchmark to a three-flavor treatment is the immediate consistency check.
The existence of several parameter-space examples suggests the framework is not fine-tuned to a single point, though the paper does not quantify how large the viable region is.

Reading between the lines

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

A natural next step would be to switch the $\mathbf{120}$ representation back on and repeat the parameter search; the paper does not quantify how much of the viable region depends on the exact $V^R = V^{L*}$ form.
With $M_1$ near $10^{10}$ GeV, flavor effects in leptogenesis can shift $Y_B$ by order-one factors for hierarchical spectra, so the benchmark value should be read as a proof-of-concept number until a full flavor treatment is done.
If future low-energy fits to fermion masses and mixings require a nonzero $\mathbf{120}$ coupling, the relation $V^R = V^{L*}$ would break and the connection between SO(10) and the observed baryon asymmetry would have to be reworked rather than merely adjusted.

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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

The one thing to know: this is a real, modest advance in the SO(10) leptogenesis program. It takes the known obstruction from the 10-only case (m_D = m_u) and shows that adding the \bar{126} while keeping the 120 absent relaxes that constraint enough to find heavy neutrino spectra in parameter space that yield the observed baryon asymmetry in single-flavor leptogenesis. The benchmark is explicit — M1 = 6.26e10 GeV, M2 = 2.23e12 GeV, M3 = 4.57e14 GeV, Y_B = 8.50e-11 — and that specificity is a genuine contribution. The paper is clear about what it assumes and what it scans over, and it engages directly with the prior 10-only treatment.

The soft spots are real and load-bearing. First, the single-flavor approximation at M1 ~ 6e10 GeV is exactly the regime where tau and muon Yukawa effects can alter Y_B by order-one factors. The abstract gives no argument for why single-flavor is adequate; the quoted Y_B may not survive a flavored calculation. That concern is central, because the existence claim rests on the agreement with data. Second, the Y_B match is selected: they scanned parameter space and found points that agree. The abstract frames these as examples, so this is standard benchmark practice, but it lowers the evidentiary weight of the match. Third, the absence of the 120 is a hypothesis, not a derived result. It does give V^R = V^{L*}, but if the 120 is present the whole construction changes. The paper is upfront about it, so this is not an internal inconsistency — but it means the result lives inside a specific model hypothesis.

I could only read the abstract, so I can't check the derivation or the scan. But the setup is clear, the claim is concrete, and the paper is honest about its assumptions. It deserves a referee who knows leptogenesis flavor physics and can pressure-test the single-flavor approximation and the scan methodology. If a flavored calculation still gives agreement, this is a solid constructive result; if not, it's a useful counterexample. Send it to peer review rather than desk-rejecting.

Referee Report

3 major / 3 minor

Summary. The paper studies leptogenesis and Dirac neutrino masses in SO(10) grand unification, assuming that fermion masses arise only from the 10 and \overline{126} Higgs representations, with the 120 representation absent. Under this hypothesis, the authors claim that the unitary diagonalizing matrices of the Dirac mass satisfy V^R = V^{L*}, and that a parameter-space search yields heavy Majorana neutrino masses consistent with the SO(10) unification scale, together with a baryon asymmetry Y_B = 8.50 x 10^{-11} in the strong-washout regime, in agreement with observations. The abstract presents a specific benchmark spectrum, M_1 = 6.26 x 10^{10} GeV, M_2 = 2.23 x 10^{12} GeV, M_3 = 4.57 x 10^{14} GeV, as an illustrative example.

Significance. If the central claim is correct, the paper would provide a nontrivial SO(10) framework that relaxes the often-used m_D = m_u condition and demonstrates that a viable leptogenesis scale can coexist with gauge-coupling unification. The explicit benchmark gives a concrete target for future experiments and for model-building. However, the significance depends crucially on the validity of the single-flavor approximation at M_1 ~ 6 x 10^{10} GeV and on whether the parameter-space examples are robust or fine-tuned. The paper's transparency about its assumptions is a strength, but the abstract alone does not provide enough evidence to establish the claimed agreement with the baryon asymmetry.

major comments (3)

[Abstract (first sentence)] The entire numerical result is obtained in the single-flavor approximation to leptogenesis. For the quoted M_1 = 6.26 x 10^{10} GeV, tau- and muon-flavor effects are generically non-negligible: charged-lepton Yukawa couplings can be in equilibrium, and flavor-dependent efficiencies can shift Y_B by order-one factors or more. The abstract gives no argument that the strong-washout regime suppresses these effects for this specific benchmark. This is load-bearing because the agreement of Y_B with data is a central claim. The authors should either provide a flavored (at least two-flavor) calculation for the benchmark, or state and justify a quantitative criterion for the validity of the single-flavor approximation at this scale.
[Abstract (assumption of absent 120)] The relation V^R = V^{L*} is asserted to follow from the absence of the 120 representation, but no derivation or reference is given. While this is a standard property of a complex symmetric Dirac mass matrix, it is also a structural constraint that underpins the entire parameter scan. If the 120 is present, or if the absence is not enforced by a symmetry, the relation need not hold, and the quoted benchmark spectrum is no longer a consequence of the framework. Please include an explicit proof of this relation from the representation content and discuss whether the absence of the 120 is a dynamical or ad hoc assumption.
[Abstract (parameter search and benchmark)] The abstract states that 'several examples' are found in parameter space, and a benchmark is selected that gives Y_B = 8.50 x 10^{-11}. Because the benchmark is an output of a scan, the agreement with the observed baryon asymmetry is a postdiction rather than a prediction. To assess its significance, the authors should report the fraction of scan points that satisfy the unification and Y_B constraints, the prior ranges of the scanned parameters, and the sensitivity of the benchmark to variations in the CP phases and mass ratios. Without this information, the reader cannot distinguish a robust consequence of the framework from a fine-tuned point.

minor comments (3)

[Abstract (title/wording)] The phrase 'single flavor approximation' appears only in the first sentence of the abstract; it should be highlighted as a key limitation in the conclusions as well, so that readers do not over-interpret the numerical Y_B value.
[Abstract (benchmark comparison)] The quoted Y_B = 8.50 x 10^{-11} should be compared with the measured value including uncertainties (e.g., Planck 2018: 6.1 x 10^{-10}, or the baryon-to-photon ratio, depending on convention). The abstract uses 'consistent with data' without specifying the confidence level or experimental value.
[Abstract (unification scale)] The phrase 'consistent with the SO(10) unification scale' is vague. Please specify the GUT scale, the threshold corrections included, and the matching conditions that relate the heavy masses to the unification constraint.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity determinable from abstract; parameter-space search is a fit, not a prediction.

full rationale

The abstract reports a parameter-space search yielding examples with a heavy neutrino spectrum and a baryon asymmetry consistent with data. The benchmark Y_B = 8.50 x 10^-11 is explicitly presented as one selected case ('For illustration, we detail a case'), indicating a fit to the observed asymmetry rather than an independent prediction. This is a phenomenological postdiction, not circularity. The assumption that the 120 representation is absent is a stated hypothesis, and the relation V^R = V^{L*} is a consequence of that hypothesis, not a circular definition. The single-flavor approximation is an approximation, and its accuracy is a separate correctness concern. No equations or derivation chain are available in the abstract to exhibit a specific reduction, and no self-citations or imported uniqueness theorems appear. Therefore no significant circularity can be established from the available text.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a short list of assembled ingredients: the SO(10) framework, the restriction of the fermion mass Higgs sector to 10 and \overline{126} with the 120 excluded, the single-flavor leptogenesis approximation, and a free parameter space (Yukawa couplings, Dirac neutrino mass entries, Majorana sector parameters, and CP phases) that is scanned to find consistent points. The quoted M1, M2, M3 and Y_B are outputs of that scan, not quantities fixed by the framework. No invented entities appear; the heavy neutrinos and Higgs representations are standard SO(10) content.

free parameters (5)

10 Higgs Yukawa couplings = not given in abstract
Couplings of the 10 representation produce fermion mass relations such as m_b = m_tau; they are inputs matched to observed masses.
126 Higgs Yukawa couplings = not given in abstract
Couplings of the \overline{126} representation are the ingredient that relaxes m_D = m_u; they are varied to search for consistent heavy neutrino spectra.
Dirac neutrino mass matrix entries (m_D) = benchmark has m_D != m_u, entries unspecified
m_D is treated as a general matrix in the scan; via the seesaw it controls the heavy neutrino masses and mixings.
Heavy Majorana neutrino sector parameters = M1 = 6.26e10 GeV, M2 = 2.23e12 GeV, M3 = 4.57e14 GeV for the detailed example
The right-handed neutrino masses and mixings are scanned; the displayed spectrum is a selected point, not a derived prediction.
CP-violating phases in V^L and V^R = not given in abstract
These phases determine the CP asymmetry feeding leptogenesis; they are part of the scanned parameter space needed to match Y_B.

assumptions (4)

domain assumption SO(10) is the unifying gauge group with its standard fermion content.
The entire calculation is framed inside SO(10) grand unification; this is a framework choice stated in the title and abstract.
ad hoc to paper Fermion masses are generated only by the 10 and \overline{126} Higgs representations; the 120 representation is absent.
Explicitly assumed in the abstract ('we assume that the antisymmetric representation 120 is absent'); the relation V^R = V^{L*} and the entire diagonalization structure depend on it.
domain assumption Leptogenesis is treated in the single flavor approximation.
Stated in the first line of the abstract; flavor effects are neglected, which is delicate for hierarchical spectra with M1 around 6 x 10^10 GeV.
standard math Standard seesaw and thermal leptogenesis formalism, including the strong washout regime for the benchmark.
The computation of Y_B from heavy neutrino decays uses the standard leptogenesis equations and the type-I seesaw parametrization m_D = V^{L\dagger} m_D^{diag} V^R; these are taken as given background.

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Cite this review

Pith. "Pith review of Leptogenesis and Dirac neutrino masses in SO(10)." pith.science (2026). https://pith.science/paper/5TSGS5KW

@misc{pith2026250806714,
  author       = {Pith},
  title        = {Pith review of: Leptogenesis and Dirac neutrino masses in SO(10)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5TSGS5KW}},
  note         = {Machine review of arXiv:2508.06714}
}

abstract

Within the scheme of Baryogenesis through Leptogenesis in the single flavor approximation, we emphasize the role of the Dirac neutrino mass $m_D$ in the SO(10) Grand Unification scheme, using the Higgs representations for the fermions masses ${\bf 10}$ and $\overline{\bf 126}$. Both representations are needed to get relations among the fermion masses, e.g. $m_b = m_\tau$, $m_\mu = 3 m_s$,... Taking these two representations allow to relax the condition $m_D = m_u$ obtained with the representation ${\bf 10}$ alone and to have general Dirac masses $m_D \not = m_u$. On the other hand, we assume that the antisymmetric representation ${\bf 120}$ is absent. Within this hypothesis, the unitary matrices $V^L$ and $V^R$ that diagonalize $m_D$ through $m_D = V^{L \dagger} m_D^{diag} V^R$ still satisfy the relation $V^R = V^{L*}$. Under these conditions, unlike the case of keeping only the ${\bf 10}$ representation, we obtain in parameter space several examples of the heavy neutrino spectrum consistent with the SO(10) unification scale, and a value for the baryon asymmetry $Y_B$ in agreement with data. For illustration, we detail a case that gives the heavy spectrum with masses $M_1 = 6.26 \times 10^{10}\ {\rm GeV}$, $M_2 = 2.23 \times 10^{12}\ {\rm GeV}$, $M_3 = 4.57 \times 10^{14}\ {\rm GeV}$ and, in the strong washout regime, the baryon asymmetry $Y_B = 8.50 \times 10^{-11}$ consistent with the data.

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Reviewed August 5, 2026 · model on record in the stance chip above.