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arxiv: 2605.00095 · v1 · submitted 2026-04-30 · ✦ hep-ph

Recognition: unknown

A Model of Annihilogenesis

Arvind Rajaraman , Alexander Stewart , Tim M.P. Tait
Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:24 UTC · model grok-4.3

classification ✦ hep-ph
keywords leptogenesisannihilogenesisfirst-order phase transitionright-handed neutrinosbaryon asymmetryelectroweak sphaleronsCP violationfalse vacuum pockets
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The pith

Right-handed neutrinos confined in shrinking false-vacuum pockets generate the observed baryon asymmetry through CP-violating 2-to-4 annihilations.

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

The paper constructs an explicit model in which two right-handed Majorana neutrinos acquire a large mass shift during a strong first-order phase transition driven by an additional scalar singlet. As bubbles of true vacuum expand, the neutrinos are reflected into shrinking pockets of false vacuum where their density rises sharply. There the dominant process is the 2-to-4 annihilation into lepton doublets and Higgs bosons; interference between tree-level gauge-boson exchange and one-loop diagrams involving the heavier neutrino produces a CP asymmetry of order 10^{-9} to 10^{-7} for order-one Yukawa couplings. Electroweak sphalerons convert the resulting lepton asymmetry into a baryon asymmetry that matches the observed value over wide ranges of parameters. Because the mass that sets the asymmetry is the residual value inside the pockets rather than the final vacuum value, the usual link to the light neutrino masses is broken and the lower bounds on the right-handed neutrino scale and reheating temperature are relaxed.

Core claim

In this annihilogenesis scenario two right-handed Majorana neutrinos χ1 and χ2 couple to Standard Model lepton doublets and the Higgs. During a strong first-order phase transition of a singlet scalar they experience a large mass shift. The lighter neutrino χ1 is reflected off expanding bubble walls and trapped in false-vacuum pockets whose volume shrinks, increasing its density. The dominant CP-violating reaction is the 2→4 annihilation χ1χ1 → L1L1Φ*Φ*. Interference between tree-level W/B exchange and one-loop diagrams containing χ2 yields a numerical CP asymmetry |ε| ∼ 10^{-9}–10^{-7} for O(1) Yukawas. Sphalerons then convert the lepton asymmetry into a baryon asymmetry Y_ΔB that reproduces

What carries the argument

The 2→4 annihilation χ1 χ1 → L1 L1 Φ* Φ* inside collapsing false-vacuum pockets, with CP asymmetry generated by interference between tree-level gauge exchange and one-loop diagrams involving the heavier χ2.

If this is right

  • The observed baryon asymmetry is reproduced across a broad region of parameter space with little dependence on bubble-wall velocity or initial pocket size.
  • The Majorana mass controlling the CP asymmetry is the residual value inside the pockets, decoupling it from the post-transition mass and from the light neutrino masses.
  • The upper bound on |ε| that arises in thermal leptogenesis from the largest light neutrino mass does not apply.
  • Lower limits on the right-handed neutrino mass scale and on the reheating temperature are relaxed relative to standard leptogenesis.
  • The mechanism works for O(1) Yukawa couplings and produces |ε| in the 10^{-9}–10^{-7} range.

Where Pith is reading between the lines

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

  • The model could be compatible with right-handed neutrino masses low enough to be probed at future colliders or in neutrino experiments.
  • Signatures of the required strong first-order phase transition might appear in gravitational-wave detectors or in precision Higgs studies.
  • Similar pocket-confinement dynamics could be applied to other asymmetry-generating processes that rely on out-of-equilibrium annihilations.

Load-bearing premise

That the 2-to-4 annihilation supplies the dominant source of CP violation and that the resulting lepton asymmetry survives without being erased by other processes inside the pockets before sphalerons act.

What would settle it

A detailed calculation showing that additional scatterings or decays inside the pockets wash out the asymmetry to far below the value needed for the observed baryon density, or a measurement of the light neutrino masses that forces the residual pocket mass of χ1 below the range where |ε| reaches 10^{-9}.

Figures

Figures reproduced from arXiv: 2605.00095 by Alexander Stewart, Arvind Rajaraman, Tim M.P. Tait.

Figure 1
Figure 1. Figure 1: Tree level cross section ⟨σv⟩tree in GeV−2 for the annihilation of two χ1 particles at rest as a function of the mass ratio mχ1 /mχ2 , for parameters: T = 107 GeV, mχ2 = 108 GeV, and A11 = 1/2. Using the fact that [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The CP-violation parameter ϵ as a function of mχ1 /mχ2 , for g ≈ 0.6, g ′ ≈ 0.3, |A12| = 1, and arg(A12) = π/4. Error bars indicate 1σ MC statistical uncertainties. 5 Lepton and Baryon Asymmetries A lepton asymmetry is produced at scales well above the EWSB scale, which is converted into a baryon asymmetry by the unsuppressed electroweak sphalerons. Following Ref. [57], to determine the total baryon asymme… view at source ↗
Figure 3
Figure 3. Figure 3: The computed baryon asymmetry Y∆B as a function of mχ1 /mχ2 , for T = 107 GeV and mχ2 = 5 × 107 GeV (left panel) and T = 107 GeV and mχ2 = 108 GeV (right panel). The dashed black line indicates the baryon asymmetry Y∆B ∼ 8 × 10−11 required for successful baryogenesis. The vertical blue dashed line marks the point where mχ1 = T and the non-relativistic approximation breaks down. Error bars indicate 1σ MC st… view at source ↗
read the original abstract

We present an explicit model of leptogenesis via annihilogenesis in which two right-handed Majorana neutrinos couple to the Standard Model lepton doublets and Higgs, and acquire a large mass shift during a strong first-order phase transition of an additional scalar singlet. As bubbles of true vacuum expand, the $\chi_a$ are reflected off the walls and confined to shrinking pockets of false vacuum, where the density grows and the dominant CP-violating process is the $2 \to 4$ annihilation $\chi_1 \chi_1 \to L_1 L_1 \Phi^* \Phi^*$. Interference between tree-level $W$ and $B$ exchange and one-loop diagrams containing the heavier $\chi_2$ produces a CP asymmetry $\epsilon$, which we evaluate numerically and find to lie in the range $|\epsilon| \sim 10^{-9}$--$10^{-7}$ for $\mathcal{O}(1)$ Yukawa couplings. Electroweak sphalerons convert the resulting lepton asymmetry into a baryon asymmetry $Y_{\Delta B}$ that reproduces the observed value across a broad region of parameter space, with little sensitivity to the bubble-wall velocity or initial pocket size. The Majorana mass that controls $\epsilon$ is the residual mass of $\chi_1$ inside the collapsing pockets rather than its post-transition value, so the usual relation between the singlet mass and the Standard Model active neutrino masses is relaxed. As a result, the upper bound on $|\epsilon|$ from the largest light-neutrino mass that constrains standard thermal leptogenesis does not apply, and the lower limits on the right-handed-neutrino scale and the reheating temperature are relaxed.

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 paper proposes an explicit model of leptogenesis via annihilogenesis. Two right-handed Majorana neutrinos χ1, χ2 couple to SM leptons and Higgs, acquiring a mass shift during a strong first-order phase transition of an additional scalar singlet. As true-vacuum bubbles expand, χ1 particles are confined to shrinking false-vacuum pockets where their density rises; the dominant CP-violating process is the 2→4 annihilation χ1 χ1 → L1 L1 Φ* Φ*. Interference between tree-level W/B exchange and one-loop diagrams with χ2 yields |ε| ∼ 10^{-9}–10^{-7} for O(1) Yukawas (evaluated numerically). Electroweak sphalerons convert the resulting lepton asymmetry into a baryon asymmetry Y_ΔB that matches observations across broad parameter space, with little sensitivity to bubble-wall velocity or initial pocket size. The controlling Majorana mass is the residual value inside the pockets, relaxing the usual link to active neutrino masses and associated bounds on the RH-neutrino scale.

Significance. If the numerical evaluation of ε and the survival of the asymmetry against washout are confirmed by explicit rate comparisons and Boltzmann evolution, the model offers a concrete realization of annihilogenesis that generates the observed Y_ΔB while relaxing the upper bound on |ε| from the largest light-neutrino mass that constrains standard thermal leptogenesis. This would provide a viable alternative pathway with lower requirements on the reheating temperature and RH-neutrino masses.

major comments (2)
  1. [§4] §4 (CP asymmetry and numerical evaluation): The manuscript states that ε is evaluated numerically and lies in the range 10^{-9}–10^{-7}, yet supplies neither the explicit expression for the interference term between the tree-level W/B diagrams and the one-loop χ2 diagrams, nor the definition of the residual mass shift inside the pockets, nor any error analysis or parameter scan details. This is load-bearing because the central claim that |ε| falls in the required window for broad parameter space rests on this unverified numerical result.
  2. [§5] §5 (Baryon asymmetry and sphaleron conversion): The claim that sphalerons convert the lepton asymmetry to the observed Y_ΔB with little sensitivity to wall velocity or pocket size assumes the CP asymmetry survives without significant washout. No comparison of the 2→4 annihilation rate to inverse 4→2 processes, 2→2 lepton-number-violating scatterings, or other channels inside the pockets is presented, nor is the Boltzmann equation for the asymmetry evolution solved. This is load-bearing for the reproduction of Y_ΔB across broad parameter space.
minor comments (2)
  1. [§2] The Lagrangian for the additional scalar singlet and its coupling to the phase transition is introduced without an explicit potential or vacuum expectation value expression; adding these would improve clarity of the mass-shift mechanism.
  2. [§3] Notation for the Yukawa couplings and the two Majorana neutrinos (χ1 vs. χ2) is used consistently but would benefit from a summary table of all free parameters and their ranges.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and will incorporate revisions to provide the requested details and strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§4] §4 (CP asymmetry and numerical evaluation): The manuscript states that ε is evaluated numerically and lies in the range 10^{-9}–10^{-7}, yet supplies neither the explicit expression for the interference term between the tree-level W/B diagrams and the one-loop χ2 diagrams, nor the definition of the residual mass shift inside the pockets, nor any error analysis or parameter scan details. This is load-bearing because the central claim that |ε| falls in the required window for broad parameter space rests on this unverified numerical result.

    Authors: We agree that the explicit details of the numerical evaluation are necessary to support the central claim. The manuscript reports the range |ε| ∼ 10^{-9}–10^{-7} obtained from the interference between tree-level W/B exchange and one-loop χ2 diagrams but does not display the full analytic expression or the scan methodology. In the revised manuscript we will add the explicit formula for the CP-violating interference term in §4, define the residual mass shift inside the false-vacuum pockets as the effective Majorana mass of χ1 in the unbroken phase (distinct from its post-transition value), and include a new appendix with the numerical integration procedure, convergence checks, error estimates, and the full parameter scan over O(1) Yukawa couplings that produces the quoted range. revision: yes

  2. Referee: [§5] §5 (Baryon asymmetry and sphaleron conversion): The claim that sphalerons convert the lepton asymmetry to the observed Y_ΔB with little sensitivity to wall velocity or pocket size assumes the CP asymmetry survives without significant washout. No comparison of the 2→4 annihilation rate to inverse 4→2 processes, 2→2 lepton-number-violating scatterings, or other channels inside the pockets is presented, nor is the Boltzmann equation for the asymmetry evolution solved. This is load-bearing for the reproduction of Y_ΔB across broad parameter space.

    Authors: We acknowledge that explicit verification of washout suppression is required to substantiate the robustness of Y_ΔB. The manuscript argues that the 2→4 process dominates inside the high-density pockets and that the asymmetry survives with little sensitivity to wall velocity or pocket size, but does not present rate comparisons or a Boltzmann solution. In the revision we will add to §5 a direct comparison of the 2→4 annihilation rate against the inverse 4→2 and 2→2 lepton-number-violating channels inside the pockets, together with a numerical solution of the Boltzmann equation for the asymmetry evolution. This will demonstrate that washout remains negligible and that the observed Y_ΔB is reproduced across the broad parameter space with the stated insensitivity. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit diagram calculation and parameter-independent conversion claim

full rationale

The paper computes the CP asymmetry ε numerically from interference between tree-level W/B exchange and one-loop χ2 diagrams, treating Yukawa couplings and the residual Majorana mass inside pockets as independent inputs; the resulting |ε| range is an output, not a fit. Sphaleron conversion to Y_ΔB matching observation is asserted across broad parameter space with stated insensitivity to wall velocity and pocket size, but this follows from the model dynamics rather than reducing to a definitional equivalence or self-citation. No load-bearing self-citations, ansatze smuggled via prior work, or uniqueness theorems appear in the provided text. The skeptic concern about missing Boltzmann washout equations addresses verification and completeness, not circularity in the derivation chain itself.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 2 invented entities

The central claim rests on the existence of a strong first-order phase transition driven by an extra scalar, the dominance of a specific 2-to-4 annihilation inside pockets, and standard sphaleron conversion; several O(1) parameters are chosen by hand to place ε in the observed range.

free parameters (3)
  • Yukawa couplings
    Assumed O(1) to obtain |ε| in 10^{-9}–10^{-7}
  • bubble-wall velocity
    Scanned but claimed to have little effect
  • initial pocket size
    Scanned but claimed to have little effect
axioms (3)
  • domain assumption A strong first-order phase transition occurs for the additional scalar singlet
    Required for bubble expansion and neutrino confinement
  • domain assumption Electroweak sphalerons efficiently convert lepton asymmetry to baryon asymmetry
    Standard assumption in leptogenesis models
  • ad hoc to paper No other washout processes dominate inside the false-vacuum pockets
    Implicit in the claim that the generated asymmetry survives
invented entities (2)
  • Additional scalar singlet no independent evidence
    purpose: Drives the first-order phase transition and induces the mass shift for the right-handed neutrinos
    Postulated new field not present in the Standard Model
  • Two right-handed Majorana neutrinos χ1 and χ2 no independent evidence
    purpose: Provide the CP-violating annihilation channel and the loop interference
    Extension of standard seesaw leptogenesis

pith-pipeline@v0.9.0 · 5602 in / 2018 out tokens · 71110 ms · 2026-05-09T20:24:02.164189+00:00 · methodology

discussion (0)

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