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arxiv: 2604.06493 · v1 · submitted 2026-04-07 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Low-Scale Leptogenesis from Resonant Thermal Lepton Flavour Coherences

Shao-Ping Li , Apostolos Pilaftsis
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:26 UTC · model grok-4.3

classification ✦ hep-ph
keywords leptogenesisheavy neutrinosseesaw mechanismthermal effectsflavour coherencesKadanoff-Baym formalismbaryon asymmetrylow-scale
0
0 comments X

The pith

Resonant thermal lepton-flavour coherences enable low-scale leptogenesis down to GeV masses without degeneracy

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

The paper refines the flavour-covariant Kadanoff-Baym formalism to isolate a two-loop contribution from resonant thermal lepton-flavour coherences. This contribution greatly enhances lepton asymmetry generation in the early universe. The mechanism succeeds for both Dirac and Majorana singlet neutrinos and does not require their masses to be nearly degenerate. It therefore allows the type-I seesaw to produce the observed baryon asymmetry with heavy neutrino masses as low as a few GeV. A reader would care because this removes the usual need for fine-tuned mass degeneracy and opens the possibility of testing the scenario in laboratory experiments.

Core claim

After further developing the flavour-covariant Kadanoff-Baym formalism, we study in detail a novel dominant mechanism for low-scale leptogenesis which becomes greatly enhanced by resonant thermal lepton-flavour coherences at the two-loop level. This mechanism works successfully for both Dirac and Majorana singlet neutrinos, and it does not rely on whether these singlet neutrinos are quasi-degenerate or not. In particular, it implies that successful low-scale leptogenesis in the type-I seesaw framework can be naturally realised with heavy neutrino masses that could be as low as GeV.

What carries the argument

Resonant thermal lepton-flavour coherences at the two-loop level, isolated within the flavour-covariant Kadanoff-Baym equations

If this is right

  • Low-scale leptogenesis works for singlet neutrino masses as low as a few GeV in the type-I seesaw.
  • The asymmetry generation succeeds without quasi-degeneracy between the singlet neutrino masses.
  • The same mechanism applies to both Dirac and Majorana singlet neutrinos.
  • The observed baryon asymmetry can be explained naturally without additional parameter tuning beyond the seesaw.
  • Laboratory searches for GeV-scale heavy neutrinos become directly relevant to leptogenesis.

Where Pith is reading between the lines

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

  • Beam-dump or collider experiments searching for GeV-scale sterile neutrinos could simultaneously constrain or discover this leptogenesis channel.
  • Thermal coherence effects may need inclusion in other early-universe calculations involving neutrino mixing.
  • The mechanism could relax lower bounds on the seesaw scale in model-building exercises.
  • Numerical solutions of the full quantum transport equations could be used to map the viable parameter space for different CP phases.

Load-bearing premise

The further-developed flavour-covariant Kadanoff-Baym formalism correctly isolates the two-loop resonant thermal lepton-flavour coherences as the dominant contribution that is not overwhelmed by higher-order terms or other thermal effects.

What would settle it

A complete higher-order or non-perturbative calculation showing that the lepton asymmetry produced at GeV-scale non-degenerate singlet neutrino masses falls short of the observed baryon asymmetry by more than an order of magnitude.

Figures

Figures reproduced from arXiv: 2604.06493 by Apostolos Pilaftsis, Shao-Ping Li.

Figure 1
Figure 1. Figure 1: FIG. 1. Tree-level and one-loop diagrams for Higgs decay to leptons and relativistic singlet neutrinos. The [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The two-loop lepton-number conserving self-energy diagrams of relativistic singlet neutrinos con [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The lepton asymmetry yield [PITH_FULL_IMAGE:figures/full_fig_p031_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: as [iΣ>(kℓ)]αγ = y ′∗ αjy ′ γj Z d 4 kϕ (2π) 4 d 4 kN (2π) 4 (2π) 4 δ (4)(kℓ + kϕ − kN )PR[iS>(kN )]jPLiG<(kϕ), (D.1) [iΣ<(kℓ)]αγ = y ′∗ αjy ′ γj Z d 4 kϕ (2π) 4 d 4 kN (2π) 4 (2π) 4 δ (4)(kℓ + kϕ − kN )PR[iS<(kN )]jPLiG>(kϕ), (D.2) where we neglected flavour correlations for the nonthermal and non-degenerate singlet neutrinos, and simply used the free Wightman propagators iS<,> for neutrinos. However, we … view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. A two-loop diagram that contributes as a source to creating the off-diagonal correlation [PITH_FULL_IMAGE:figures/full_fig_p050_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The two-loop vertex diagrams of relativistic singlet neutrinos contributing to CP asymmetry, with [PITH_FULL_IMAGE:figures/full_fig_p052_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The two-loop self-energy diagrams of leptons contributing to CP asymmetry, with [PITH_FULL_IMAGE:figures/full_fig_p055_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Flavour-changing self-energy diagrams of singlet neutrinos as the inner loop in Fig. [PITH_FULL_IMAGE:figures/full_fig_p057_8.png] view at source ↗
read the original abstract

Resonant heavy-neutrino mixing and sterile neutrino oscillations are two prominent mechanisms to realize low-scale leptogenesis, with singlet neutrino masses below TeV energies that could be probed in current and future laboratory experiments. In their minimal settings, both mechanisms require a significant degree of degeneracy in the singlet neutrino masses to compensate for the suppression that results from the small neutrino Yukawa couplings. After further developing the flavour-covariant Kadanoff-Baym formalism, we study in detail a novel dominant mechanism for low-scale leptogenesis which becomes greatly enhanced by resonant thermal lepton-flavour coherences at the two-loop level. This mechanism works successfully for both Dirac and Majorana singlet neutrinos, and it does not rely on whether these singlet neutrinos are quasi-degenerate or not. In particular, it implies that successful low-scale leptogenesis in the type-I seesaw framework can be naturally realised with heavy neutrino masses that could be as low as GeV.

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

2 major / 2 minor

Summary. The manuscript develops the flavour-covariant Kadanoff-Baym formalism to isolate a two-loop contribution from resonant thermal lepton-flavour coherences as a novel source of CP asymmetry for low-scale leptogenesis. The central claim is that this mechanism generates sufficient asymmetry for successful baryogenesis in the type-I seesaw for both Dirac and Majorana singlet neutrinos, without requiring quasi-degeneracy, and remains viable down to singlet masses of order 1 GeV.

Significance. If the two-loop coherence term is shown to dominate parametrically, the result would meaningfully expand the viable parameter space for low-scale leptogenesis by removing the degeneracy requirement that typically suppresses the asymmetry when Yukawa couplings are small. The first-principles treatment via an extended Kadanoff-Baym approach is a methodological strength that could be applied more broadly to thermal leptogenesis calculations.

major comments (2)
  1. [Development of the flavour-covariant Kadanoff-Baym equations] The central claim that the two-loop resonant coherence contribution dominates over one-loop washout, three-loop corrections, and other thermal self-energies at GeV-scale masses without degeneracy is load-bearing. Explicit parametric estimates or numerical benchmarks comparing the magnitude of this term to higher-order contributions across the relevant temperature range (e.g., near the electroweak scale down to the GeV regime) are required to substantiate that it is not suppressed by the small Yukawa couplings.
  2. [Numerical results and parameter scans] The assertion that successful leptogenesis is achieved for non-degenerate singlets as light as ~1 GeV must be supported by concrete results. The manuscript should include explicit calculations or plots of the generated lepton asymmetry (and subsequent baryon asymmetry) as a function of singlet mass and temperature, with comparisons to the observed value and sensitivity checks to the truncation of the thermal expansion.
minor comments (2)
  1. [Abstract] The abstract states the mechanism 'works successfully' but does not specify the range of Yukawa couplings or temperatures over which the dominance holds; a brief qualification would improve clarity.
  2. [Formalism section] Notation for the coherence terms and the precise definition of the two-loop diagrams should be cross-referenced to earlier Kadanoff-Baym literature to aid readers familiar with the formalism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and positive evaluation of the significance of our work. We address each of the major comments below and have made revisions to the manuscript to incorporate the requested clarifications and additional results.

read point-by-point responses

  1. Referee: [Development of the flavour-covariant Kadanoff-Baym equations] The central claim that the two-loop resonant coherence contribution dominates over one-loop washout, three-loop corrections, and other thermal self-energies at GeV-scale masses without degeneracy is load-bearing. Explicit parametric estimates or numerical benchmarks comparing the magnitude of this term to higher-order contributions across the relevant temperature range (e.g., near the electroweak scale down to the GeV regime) are required to substantiate that it is not suppressed by the small Yukawa couplings.

    Authors: We agree that demonstrating the dominance of the two-loop resonant coherence term is crucial for the validity of our central claim. The manuscript develops the flavour-covariant Kadanoff-Baym formalism and derives the two-loop contribution analytically, showing its resonant enhancement due to thermal lepton-flavour coherences. However, to provide stronger substantiation, we have added explicit parametric estimates in the revised version, comparing the two-loop term to one-loop washout and three-loop corrections. These estimates confirm that for GeV-scale masses and small Yukawa couplings, the coherence term is not suppressed and dominates in the relevant temperature range from the electroweak scale down to GeV temperatures. We have also included numerical benchmarks for representative parameter points. revision: yes

  2. Referee: [Numerical results and parameter scans] The assertion that successful leptogenesis is achieved for non-degenerate singlets as light as ~1 GeV must be supported by concrete results. The manuscript should include explicit calculations or plots of the generated lepton asymmetry (and subsequent baryon asymmetry) as a function of singlet mass and temperature, with comparisons to the observed value and sensitivity checks to the truncation of the thermal expansion.

    Authors: We acknowledge that concrete numerical results are necessary to support the claim of successful leptogenesis down to ~1 GeV without degeneracy. In the original manuscript, we presented the analytical framework and argued for the viability based on the enhanced CP asymmetry from the two-loop term. To address this, we have now included explicit calculations and plots showing the evolution of the lepton asymmetry as a function of temperature for various singlet masses, demonstrating that the asymmetry reaches the required level for baryogenesis even for non-degenerate singlets at GeV scales. We also provide comparisons to the observed baryon asymmetry and sensitivity analyses to the truncation of the thermal expansion, confirming that the results are robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in formalism extension

full rationale

The paper's central result follows from further developing the flavour-covariant Kadanoff-Baym equations within this manuscript to isolate a two-loop resonant thermal lepton-flavour coherence term. This term is derived from the equations rather than presupposed, fitted to data, or reduced to a prior self-citation by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing uniqueness theorems imported from overlapping-author citations appear in the derivation chain. The mechanism's applicability to non-degenerate Dirac/Majorana cases at GeV scales is presented as a consequence of the developed equations, making the analysis self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard extensions of the Standard Model with singlet neutrinos plus thermal quantum field theory assumptions; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The flavour-covariant Kadanoff-Baym formalism remains valid and can be extended to capture two-loop resonant thermal lepton-flavour coherences in the early universe.
    Invoked to study the novel mechanism after further development of the formalism.
  • ad hoc to paper Two-loop contributions from resonant coherences dominate over higher-order effects in the relevant temperature regime.
    Required for the mechanism to be the dominant source of the asymmetry.

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Reference graph

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