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arxiv: 2604.19434 · v2 · submitted 2026-04-21 · ✦ hep-ph

Recognition: unknown

SO(10)-inspired leptogenesis

Pasquale Di Bari

Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:37 UTC · model grok-4.3

classification ✦ hep-ph
keywords SO(10) leptogenesisN2 leptogenesisneutrino mass orderingbaryon asymmetryflavour couplingneutrinoless double beta decayJUNO experiment
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0 comments X

The pith

SO(10)-inspired leptogenesis excludes inverted neutrino mass ordering under strict conditions

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

The paper reviews how the assumption that the neutrino Dirac mass matrix resembles the up-quark mass matrix in SO(10) models forces leptogenesis to proceed via decays of the next-to-lightest right-handed neutrino. This N2-leptogenesis mechanism generates concrete predictions for the neutrino mass spectrum and mixing parameters. Inverted mass ordering is incompatible with these strict conditions and is therefore ruled out. A subset of viable solutions achieves strong thermal leptogenesis, rendering the final asymmetry independent of initial conditions and potentially detectable in future neutrinoless double beta decay searches. Recent extensions examine how flavour coupling modifies the allowed parameter space.

Core claim

Under the assumption that the neutrino Dirac mass matrix is not too different from the up-quark mass matrix, SO(10)-inspired leptogenesis necessarily produces the baryon asymmetry through N2 decays, which imposes strong constraints on low-energy neutrino parameters and excludes inverted ordering while permitting strong thermal leptogenesis in a subset of cases.

What carries the argument

The similarity between the neutrino Dirac mass matrix and the up-quark mass matrix, which enforces production of the asymmetry by next-to-lightest right-handed neutrino decays and thereby constrains the neutrino mass ordering and mixing angles.

If this is right

  • Inverted neutrino mass ordering is excluded.
  • Strong thermal leptogenesis is realized in a subset of solutions, making the final asymmetry independent of initial conditions.
  • A signal from these solutions could be discovered by next-generation neutrinoless double beta decay experiments.
  • Flavour coupling effects further refine the allowed parameter space in recent calculations.

Where Pith is reading between the lines

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

  • Confirmation of normal ordering by JUNO would lend support to the viability of SO(10)-inspired leptogenesis.
  • Relaxing the strict mass-matrix similarity assumption could open additional viable regions while preserving some of the predictive power.
  • The strong thermal solutions provide a concrete link between high-scale leptogenesis and low-scale 0 uetaeta decay searches that can be tested independently of the full GUT framework.

Load-bearing premise

The neutrino Dirac mass matrix is not too different from the up quark mass matrix.

What would settle it

Observation of inverted neutrino mass ordering by the JUNO experiment would falsify the strict SO(10)-inspired leptogenesis scenario.

Figures

Figures reproduced from arXiv: 2604.19434 by Pasquale Di Bari.

Figure 1
Figure 1. Figure 1: Scatter plot of the solutions obtained imposing successful SO10INLEP neglecting (left) and including (right) flavour coupling (from [1]). The three grey areas correspond to the excluded regions by the three upper bounds on the absolute neutrino mass scale, in particular, Eq. (1) from cosmological observations and then from 0𝜈𝛽𝛽 and from tritium beta decay. The three planes in light blue simply help underst… view at source ↗
Figure 2
Figure 2. Figure 2: Iso-contour lines of the value of the lower bound on 𝑚1 in the 𝜃23 − 𝛿 plane (from [1]) without flavour coupling (left) and with flavour coupling (right). The white dashed lines are the 1𝜎, 2𝜎and 3𝜎 experimental constraints from [7]. The orange area is the area excluded by the cosmological upper bound (1) [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Two-dimensional projection on the plane 𝑚1-𝜃23 of the scatter plot of the solutions obtained imposing successful SO10INLEP (from [1]), neglecting flavour coupling effects (left panel) and accounting for flavour coupling effects (right panel). Colour code as in [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: Two-dimensional projection on the plane 𝜎-𝜌 of the scatter plot of the solutions obtained imposing successful SO10INLEP. Right: Solutions in the plane 𝑚𝑒𝑒 versus 𝑚1 [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: In these three panels, one can see how strong thermal 𝑆𝑂(10)-inspired leptogenesis: (i) it requires a non-vanishing 𝜃13 (left); (ii) it makes a sharp prediction on 𝑚1 and implies a stringent upper bound on 𝜃23 (centre and right); (iii) it strongly favours 𝛿 in the fourth quadrant (right). these conditions to be satisfied, necessarily 𝑚1 ≳ 10 meV for 𝑁 p,i 𝐵−𝐿 ∼ 10−3 (there is a logarithmic dependence of th… view at source ↗
Figure 6
Figure 6. Figure 6: Left: determination of the upper bound on 𝜃23 as a function of 𝛿. Right: Value of the asymmetry for fixed 𝛿 = −75◦ and for the four indicated values of 𝜃23 as a function of 𝑚1 (from [56]). predicted a non-vanishing 𝜃13. Indeed, first results were presented in September 2011 at the DESY theory workshop [53] before the DayaBay discovery in January 2012 [55]. This is a remarkable success for this scenario of … view at source ↗
Figure 7
Figure 7. Figure 7: Strong thermal 𝑆𝑂(10)-inspired leptogenesis allowed region in the plane 𝛿 versus 𝜃23. The red line delimits the region when flavour coupling is neglected, the coloured region is the result in the case when flavour coupling is taken into account. The colour code denotes point density: lighter blue means higher density of solutions. The thin dashed lines are 1𝜎, 2𝜎 and 3𝜎 experimental constraints from [7] (f… view at source ↗
read the original abstract

In the first part of the talk, I review general properties of $SO(10)$-inspired leptogenesis. This high-scale leptogenesis scenario is based on the simple assumption that the neutrino Dirac mass matrix is not too different from the up quark mass matrix. After showing how this necessarily implies a production of the asymmetry from the next-to-lightest right handed neutrino decays, so-called $N_2$-leptogenesis, I discuss how this results into important testable constraints on low energy neutrino parameters. In particular inverted ordering is not viable if strict $SO(10)$-inspired conditions are assumed. This is an important test in view of the expected results from the JUNO experiment. I also discuss how a subset of the $SO(10)$-inspired leptogenesis solutions realises strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions. In this case a signal might be discovered by next generation $0\nu\beta\beta$ decay experiments. In the second part, I present some new results from \cite{DiBari:2025zlv}, where the impact of flavour coupling on $SO(10)$-inspired leptogenesis has been studied in detail.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reviews general properties of SO(10)-inspired leptogenesis based on the assumption that the neutrino Dirac mass matrix is not too different from the up-quark mass matrix. This leads to N2-leptogenesis and imposes testable constraints on low-energy neutrino parameters, in particular excluding inverted mass ordering under strict conditions. It further discusses a subset of solutions realizing strong thermal leptogenesis and presents new results on the impact of flavour coupling from a referenced 2025 work.

Significance. If the core assumption holds with sufficient robustness, the exclusion of inverted ordering constitutes a clear, falsifiable prediction for the JUNO experiment, while strong-thermal solutions offer potential signals in next-generation 0νββ searches. The flavour-coupling analysis adds a useful layer to the scenario. The overall significance is reduced by the absence of quantitative bounds on the similarity assumption and the lack of explicit derivations or scans that would allow independent verification of the ordering constraint.

major comments (3)
  1. The central claim that inverted ordering is excluded under strict SO(10)-inspired conditions rests on the unquantified statement that m_D is 'not too different' from m_u. No explicit matrix forms, deviation parameters, or numerical scans are supplied to show how deviations affect the CP asymmetry or washout factors, preventing confirmation that the exclusion holds for all viable cases.
  2. The transition to N2-leptogenesis dominance is asserted as a necessary consequence of the similarity assumption, yet the manuscript contains no Boltzmann equations, flavour-coupling terms, or parameter ranges demonstrating why N1 decays cannot generate the observed asymmetry while N2 decays can.
  3. Strong-thermal leptogenesis solutions are stated to exist as a subset, but no concrete conditions (e.g., specific ranges for the right-handed neutrino masses or Yukawa couplings) are given that would allow a reader to identify which solutions are independent of initial conditions.
minor comments (2)
  1. The new flavour-coupling results are referenced only to the unpublished work DiBari:2025zlv without even a brief summary of the key equations or numerical outcomes; including a short self-contained description would improve readability.
  2. The distinction between 'strict SO(10)-inspired conditions' and the more general similarity assumption should be clarified with at least one illustrative example to delineate the scope of the inverted-ordering exclusion.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential significance of the SO(10)-inspired leptogenesis scenario. We address each major point below and will revise the manuscript to improve clarity and self-containment while preserving its character as a review of established results.

read point-by-point responses

  1. Referee: The central claim that inverted ordering is excluded under strict SO(10)-inspired conditions rests on the unquantified statement that m_D is 'not too different' from m_u. No explicit matrix forms, deviation parameters, or numerical scans are supplied to show how deviations affect the CP asymmetry or washout factors, preventing confirmation that the exclusion holds for all viable cases.

    Authors: The quantitative bounds on the similarity between m_D and m_u, including explicit parameterization of deviations and their impact on the CP asymmetry and washout, are established in the prior literature on which this review is based. The manuscript does not introduce new scans, as it summarizes those results. To address the concern, we will add a concise summary of the deviation parameterization and the resulting exclusion of inverted ordering, with direct references to the relevant calculations. revision: partial

  2. Referee: The transition to N2-leptogenesis dominance is asserted as a necessary consequence of the similarity assumption, yet the manuscript contains no Boltzmann equations, flavour-coupling terms, or parameter ranges demonstrating why N1 decays cannot generate the observed asymmetry while N2 decays can.

    Authors: The N2 dominance arises because the SO(10)-inspired hierarchy implies strong washout for N1 decays while allowing N2 to produce the asymmetry. The full Boltzmann equations and flavour-coupling terms appear in the cited works. We will insert a brief explanatory paragraph in the revised manuscript outlining the key dynamical reasons and indicative mass and coupling ranges that enforce N2 dominance. revision: yes

  3. Referee: Strong-thermal leptogenesis solutions are stated to exist as a subset, but no concrete conditions (e.g., specific ranges for the right-handed neutrino masses or Yukawa couplings) are given that would allow a reader to identify which solutions are independent of initial conditions.

    Authors: The concrete conditions for the strong-thermal subset, including specific ranges for right-handed neutrino masses and Yukawa couplings, are derived in the referenced work DiBari:2025zlv. We will expand the relevant section to quote these ranges explicitly so that readers can identify the initial-condition-independent solutions. revision: yes

Circularity Check

0 steps flagged

No significant circularity: claims follow from explicit assumption with external testability

full rationale

The paper opens by stating its central premise as a 'simple assumption' that the neutrino Dirac mass matrix is not too different from the up-quark mass matrix. It then derives consequences including N2-leptogenesis and the exclusion of inverted ordering under strict conditions. These are presented as logical implications of the input assumption rather than inputs themselves. The self-citation to DiBari:2025zlv covers supplementary flavour-coupling results and is not required to establish the core exclusion. No equations or steps in the text reduce any prediction to a self-definition, fitted parameter, or self-citation chain by construction. The resulting constraints are framed as testable by JUNO and 0νββ experiments, satisfying the criterion for self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The scenario rests primarily on the qualitative similarity assumption between neutrino Dirac and up-quark mass matrices, which is introduced without first-principles derivation and directly generates the N2-leptogenesis and ordering constraints.

free parameters (1)
  • Degree of similarity between neutrino Dirac and up-quark mass matrices
    The assumption that the matrices are 'not too different' functions as an effective tunable closeness that selects N2 dominance and the resulting low-energy constraints.
axioms (1)
  • domain assumption Neutrino Dirac mass matrix is similar to the up-quark mass matrix
    This is the foundational assumption explicitly stated in the abstract as the basis for the entire SO(10)-inspired leptogenesis scenario.
invented entities (1)
  • Right-handed neutrinos N1, N2, N3 no independent evidence
    purpose: Generate the lepton asymmetry through their out-of-equilibrium decays
    Standard ingredients of leptogenesis models; no new independent evidence is supplied in the abstract.

pith-pipeline@v0.9.0 · 5499 in / 1488 out tokens · 40283 ms · 2026-05-10T02:37:01.300274+00:00 · methodology

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Reference graph

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