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arxiv: 2605.24163 · v1 · pith:E5RWSHJ3new · submitted 2026-05-22 · ✦ hep-ph · astro-ph.CO

Leptogenesis without on-shell right-handed neutrinos

Simon Cl\'ery , Alejandro Ibarra , Onur Yonar This is my paper

Pith reviewed 2026-06-30 15:06 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords leptogenesisbaryon asymmetryright-handed neutrinosoff-shell decaysCP asymmetryfour-body decayscalar fieldreheating
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0 comments X

The pith

A lighter scalar generates the observed baryon asymmetry by decaying into leptons and Higgs bosons through off-shell right-handed neutrinos.

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

The paper proposes a leptogenesis mechanism in which right-handed neutrinos stay heavier than the universe's maximum temperature and never appear on-shell. A new scalar φ, lighter than the right-handed neutrinos, couples to them and decays into two lepton doublets and two Higgs doublets. The CP asymmetry generated by interference between tree-level and loop diagrams in this four-body decay is calculated, and the resulting baryon asymmetry is shown to match the observed value whether φ drives reheating or remains in thermal equilibrium with the plasma.

Core claim

We propose a novel mechanism for generating the baryon asymmetry of the Universe through leptogenesis in a scenario where the right-handed neutrinos are heavier than the maximal temperature of the Universe, and are never produced on-shell neither by thermal nor by non-thermal mechanisms. We introduce a new scalar field, φ, lighter than the right-handed neutrinos, that couples to the latter via a Yukawa coupling, so that it decays into two lepton doublets and two higgs doublets via off-shell right-handed neutrinos. Then, we derive the CP asymmetry arising from the interference between tree-level and loop diagrams in the four-body decay, and we show that the generated baryon asymmetry can repr

What carries the argument

The CP asymmetry arising from interference between tree-level and loop diagrams in the four-body decay φ → two lepton doublets + two Higgs doublets mediated by off-shell right-handed neutrinos.

If this is right

  • The generated baryon asymmetry reproduces the observed value when φ is the field responsible for reheating the universe.
  • The generated baryon asymmetry also reproduces the observed value when φ is a generic scalar that remains in thermal equilibrium with the plasma.
  • The right-handed neutrinos remain off-shell throughout the process and heavier than the maximum temperature.
  • The mechanism relies on the four-body decay channel to produce the necessary CP violation.

Where Pith is reading between the lines

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

  • This mechanism permits right-handed neutrino masses well above the reheating temperature, relaxing the usual mass bounds in standard leptogenesis.
  • Production and decay of the scalar φ at colliders could offer an indirect probe of the leptogenesis parameters.
  • The off-shell mediation approach might be adaptable to other baryogenesis scenarios that involve particles too heavy to be produced thermally.
  • The reheating temperature could be lower than typically required in on-shell leptogenesis models.

Load-bearing premise

Right-handed neutrinos are heavier than the maximal temperature of the Universe and are never produced on-shell by thermal or non-thermal mechanisms.

What would settle it

Detection of on-shell right-handed neutrinos with masses below the maximum temperature reached by the early universe, or a calculation showing that the four-body decay asymmetry cannot reach the observed baryon-to-photon ratio for any allowed values of the Yukawa couplings and masses.

Figures

Figures reproduced from arXiv: 2605.24163 by Alejandro Ibarra, Onur Yonar, Simon Cl\'ery.

Figure 1
Figure 1. Figure 1: Diagrams inducing the decay ϕ → LℓHLℓ ′H,LℓH†Lℓ ′H† at tree level (top panel) and at the one loop level (middle and bottom panels). Here, ℓ and ℓ ′ denote leptonic flavors. The CP conjugated diagrams, as well as diagrams crossing the external legs are not shown for simplicity, although they are included in the calculation. In the previous section we showed that the decay of a field ϕ into off-shell right-h… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution during reheating of the inflaton and radiation densities (left panel), as well as of the baryon asymmetry (right panel), for Mϕ = 3 × 1013 GeV, M1 = 3 × 1014 GeV and y ≃ 1, assuming that the upper bound on the CP asymmetry Eq. (2.6) is saturated. 4 Generic massive scalar in thermal equilibrium Let us now consider the scenario where the real scalar ϕ is not responsible for cosmic inflation, and is… view at source ↗
Figure 3
Figure 3. Figure 3: Numerical solutions of the thermal Boltzmann equations for a decaying massive scalar field. The baryon yield is frozen deeply in the non-relativistic regime as Γϕ ≪ Mϕ, and matches the observed one for Mϕ = 1013 GeV, M1 = 5 × 1013 GeV, y = 1, λϕH = 1. which is now expressed in terms of with z ≡ Mϕ/T, and where we have included the effect of the inverse reactions in the terms proportional to Y eq ϕ = 45 4π4… view at source ↗
Figure 4
Figure 4. Figure 4: Regions of the parameter space leading to the observed baryon asymmetry from the decay ϕ → LHLH, assuming radiation domination in the early Universe. The yellow and green areas limit respectively limit the regions where the Yukawa coupling y and the Higgs portal coupling λϕH remain perturbative, while the blue area limits the region where the scalar ϕ does not thermalize via scatterings with the Higgs (i.e… view at source ↗
read the original abstract

We propose a novel mechanism for generating the baryon asymmetry of the Universe through leptogenesis in a scenario where the right-handed neutrinos are heavier than the maximal temperature of the Universe, and are never produced on-shell neither by thermal nor by non-thermal mechanisms. We introduce a new scalar field, $\phi$, lighter than the right-handed neutrinos, that couples to the latter via a Yukawa coupling, so that it decays into two lepton doublets and two higgs doublets via off-shell right-handed neutrinos. Then, we derive the CP asymmetry arising from the interference between tree-level and loop diagrams in the four-body decay, and we show that the generated baryon asymmetry can reproduce the observed value both in a scenario where $\phi$ is responsible for the reheating of the Universe, and in a scenario where $\phi$ is a generic scalar that remains in thermal equilibrium with the plasma.

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

0 major / 2 minor

Summary. The paper proposes a leptogenesis mechanism in which right-handed neutrinos (RHNs) remain heavier than the maximum temperature of the Universe and are never produced on-shell. A lighter scalar φ couples to the RHNs via a Yukawa interaction and decays to two lepton doublets plus two Higgs doublets through off-shell RHNs. The CP asymmetry is obtained from interference between tree-level and one-loop diagrams in the four-body decay channel; the resulting baryon asymmetry is shown to match the observed value both when φ drives reheating and when φ remains in thermal equilibrium with the plasma.

Significance. If the explicit derivation of the four-body CP asymmetry is correct and the Yukawa couplings plus m_φ can be chosen to yield the observed asymmetry while strictly respecting the off-shell condition, the mechanism would enlarge the viable parameter space for leptogenesis by removing the usual requirement of on-shell RHN production. The paper's explicit treatment of two distinct cosmological histories for φ strengthens the claim.

minor comments (2)
  1. The abstract states that the asymmetry 'matches observations' but supplies neither the analytic expression for the CP asymmetry nor the benchmark values of the Yukawa coupling and m_φ that achieve the required magnitude; adding a short quantitative statement would improve readability.
  2. The four-body phase-space integration and the loop function that generates the imaginary part should be written explicitly (presumably in §3 or §4) so that the reader can verify the claimed non-vanishing asymmetry without reconstructing the diagrams from the text alone.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our manuscript and for recommending minor revision. The referee's description accurately reflects the proposed leptogenesis mechanism via off-shell RHNs in the four-body decay of φ. No major comments were provided in the report, so we have no specific points requiring response or clarification at this time.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives the CP asymmetry explicitly from tree-level versus one-loop interference diagrams in the four-body decay φ → ℓℓHH mediated by off-shell RHNs; this is a standard Feynman-diagram calculation whose result is not defined in terms of the final baryon asymmetry. The subsequent statement that the asymmetry can be made to match the observed value is achieved by varying free parameters (Yukawa couplings and m_φ), which is ordinary parameter tuning rather than a prediction that reduces to the input by construction. No self-citation chain, uniqueness theorem imported from the same authors, or ansatz smuggled via prior work is invoked as load-bearing. The derivation therefore remains self-contained and independent of the target observable.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The mechanism rests on the introduction of a new scalar, a strict mass hierarchy preventing on-shell production, and several unspecified couplings whose values are adjusted to match the observed asymmetry.

free parameters (2)
  • mass of scalar φ
    Must lie below the right-handed neutrino mass but above the electroweak scale to enable the four-body decay while satisfying cosmological constraints.
  • Yukawa coupling of φ to right-handed neutrinos
    Controls both the decay rate and the size of the CP asymmetry; its value is chosen to reproduce the observed baryon asymmetry.
axioms (2)
  • domain assumption Right-handed neutrinos are heavier than the maximal temperature reached by the Universe
    Ensures they are never produced on-shell, as stated in the abstract.
  • standard math Standard Model gauge interactions and particle content govern the final-state leptons and Higgs bosons
    Background assumption for the decay products and subsequent sphaleron conversion.
invented entities (1)
  • scalar field φ no independent evidence
    purpose: mediates four-body decays into two lepton doublets and two Higgs doublets via off-shell right-handed neutrinos
    New field introduced to realize the off-shell leptogenesis channel

pith-pipeline@v0.9.1-grok · 5678 in / 1471 out tokens · 49449 ms · 2026-06-30T15:06:16.280342+00:00 · methodology

discussion (0)

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Reference graph

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