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arxiv: 2503.10366 · v2 · submitted 2025-03-13 · ✦ hep-ph · astro-ph.CO· hep-th

Does thermal leptogenesis in a canonical seesaw rely on initial memory?

Partha Kumar Paul , Narendra Sahu , Shashwat Sharma This is my paper

Pith reviewed 2026-05-23 00:14 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th
keywords thermal leptogenesistype-I seesawright-handed neutrinosflavor effectsdensity matrix equationsB-L asymmetryneutrinoless double beta decay
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The pith

Asymmetries from heavier right-handed neutrinos survive N1 washout due to flavor misalignment in the seesaw model.

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

In the standard picture of thermal leptogenesis with hierarchical right-handed neutrinos, only the lightest one (N1) is expected to set the final B-L asymmetry because its washout erases contributions from heavier states. Solving the full density-matrix equations that track flavor projections from the Yukawa couplings shows that misaligned components in the asymmetries produced by N2 and N3 escape complete erasure. This memory effect persists even while N1 remains active and leads to four distinct dynamical regimes once low-energy neutrino data are imposed. The resulting modification to the asymmetry can push viable parameters into the range probed by neutrinoless double beta decay experiments.

Core claim

Asymmetries generated by the heavier RHNs (N2 and N3) generally possess components that are misaligned in flavor space with respect to N1, resulting in a partially protected contribution that survives the N1 washout. This memory effect arises even when N1 remains dynamically relevant and cannot be captured within the classical Boltzmann framework.

What carries the argument

Density-matrix equations that include decay, inverse decay, scattering processes and Yukawa-induced flavor projections.

If this is right

  • At most one right-handed neutrino can lie in the weak washout regime once neutrino mass and mixing constraints are applied.
  • The parameter space divides into four distinct dynamical regimes whose final asymmetries must be calculated separately.
  • Including projection effects can extend viable leptogenesis points into the sensitivity range of neutrinoless double beta decay experiments.
  • The memory contribution modifies the final B-L asymmetry by an amount that depends on the specific regime.

Where Pith is reading between the lines

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

  • Leptogenesis calculations that rely only on Boltzmann equations may systematically under- or over-estimate the asymmetry in parts of parameter space.
  • The same misalignment mechanism could affect other early-universe processes that depend on flavor-specific washout rates.
  • Future precision measurements of the baryon asymmetry combined with neutrino data could distinguish the density-matrix regimes from classical ones.

Load-bearing premise

The density-matrix equations with the included decay, inverse decay, scattering and Yukawa flavor projections accurately represent the early-universe dynamics without omitted channels or approximations that would alter the misalignment survival.

What would settle it

A measured baryon asymmetry that matches the density-matrix prediction but deviates from the classical Boltzmann result for a hierarchical seesaw point consistent with neutrino oscillation data.

Figures

Figures reproduced from arXiv: 2503.10366 by Narendra Sahu, Partha Kumar Paul, Shashwat Sharma.

Figure 1
Figure 1. Figure 1: FIG. 1. Feynman diagrams for tree and one-loop level decays [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Plot illustrating the constraints between [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (top) Allowed parameter space in the plane [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. A summary plot illustrating the impact of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (top) Allowed parameter space in the plane [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. A summary plot illustrating the impact of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (top) Allowed parameter space in the plane [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. A summary plot illustrating the impact of [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (top) Allowed parameter space in the plane [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

It is a common lore that in thermal leptogenesis within the type-I seesaw framework and a hierarchical spectrum of heavy right-handed neutrinos (RHNs), the CP-violating, out-of-equilibrium decay of the lightest RHN ($N_1$) is the only relevant source of the final $B-L$ asymmetry, since any asymmetry produced by the heavier RHNs is expected to be erased by subsequent $N_1$-mediated washout processes. In this work, we revisit this assumption by solving the density-matrix equations, including decay, inverse decay, and relevant scattering processes, and by fully accounting for flavor-projection effects induced by the Yukawa coupling structure. We show that the asymmetries generated by the heavier RHNs ($N_2$ and $N_3$) generally possess components that are misaligned in flavor space with respect to $N_1$, resulting in a partially protected contribution that survives the $N_1$ washout. Unlike the conventional picture of $N_2$-dominated leptogenesis, this memory effect arises even when $N_1$ remains dynamically relevant and cannot be captured within the classical Boltzmann framework. Furthermore, imposing consistency with low-energy neutrino mass and mixing data, we find that at most one RHN can lie in the weak washout regime, which naturally divides the parameter space into four distinct dynamical regimes. We systematically quantify the memory effect in each regime and demonstrate that it can significantly modify the final $B-L$ asymmetry. We find that including projection effects can indeed extend the viable parameter space into the sensitivity range of neutrinoless double beta decay experiments.

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 / 1 minor

Summary. The paper claims that in thermal leptogenesis with a hierarchical type-I seesaw, the final B-L asymmetry is not determined solely by N1 decays; instead, flavor-misaligned components of the asymmetry generated by N2 and N3 survive N1 washout when the full density-matrix equations (including decays, inverse decays, scatterings, and Yukawa-induced projectors) are solved. This 'memory effect' persists even when N1 is dynamically relevant and cannot be reproduced in the classical Boltzmann framework. Under neutrino-data constraints the authors divide the parameter space into four regimes (at most one RHN in weak washout) and show that the effect can substantially modify the final asymmetry, extending viable regions into the sensitivity of neutrinoless double-beta-decay experiments.

Significance. If the numerical results hold, the work would revise a long-standing assumption in leptogenesis model building by demonstrating that initial-state memory from heavier RHNs can contribute to the observable asymmetry even in the presence of active N1 washout. This would enlarge the viable parameter space and strengthen the link between high-scale leptogenesis and low-energy observables such as 0νββ, while highlighting the necessity of the density-matrix treatment over Boltzmann equations.

major comments (2)
  1. [density-matrix equations (as described in the abstract and methods)] The central claim that a misaligned component survives N1 washout rests on the completeness of the density-matrix equations. The manuscript states that decay, inverse decay, and 'relevant scattering processes' plus Yukawa projectors are included, but does not demonstrate that omitted channels (additional 2↔2 scatterings, gauge-mediated flavor mixing, or off-diagonal coherence damping) cannot erase the protected component while N1 remains active. This is load-bearing for the memory-effect claim and for the regime classification.
  2. [regime classification and numerical results] The division of parameter space into four dynamical regimes and the quantitative statement that the memory effect 'can significantly modify' the final asymmetry rely on numerical solutions whose implementation details, validation against known limits (e.g., strong-washout or N2-dominated cases), and error analysis are not provided. Without these, the regime boundaries and the size of the reported effect cannot be assessed.
minor comments (1)
  1. Notation for the flavor projectors and the precise definition of the 'misaligned component' should be stated explicitly with equation numbers to allow direct comparison with the Boltzmann limit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these important points regarding the density-matrix treatment and numerical validation. We address each major comment below.

read point-by-point responses

  1. Referee: [density-matrix equations (as described in the abstract and methods)] The central claim that a misaligned component survives N1 washout rests on the completeness of the density-matrix equations. The manuscript states that decay, inverse decay, and 'relevant scattering processes' plus Yukawa projectors are included, but does not demonstrate that omitted channels (additional 2↔2 scatterings, gauge-mediated flavor mixing, or off-diagonal coherence damping) cannot erase the protected component while N1 remains active. This is load-bearing for the memory-effect claim and for the regime classification.

    Authors: We agree that an explicit justification for the set of included processes would strengthen the presentation. The equations solved are the standard density-matrix formulation used in the leptogenesis literature, with the Yukawa projectors providing the flavor misalignment that protects part of the N2/N3 asymmetry. In the hierarchical limit, additional gauge-mediated flavor mixing and higher-order scatterings are parametrically suppressed relative to the included decay, inverse-decay, and ΔL=1,2 processes at the temperatures where N1 washout operates. Nevertheless, to address the concern directly we will add a short subsection discussing the expected size of the omitted channels and why they do not erase the protected component in the regimes under study. revision: partial

  2. Referee: [regime classification and numerical results] The division of parameter space into four dynamical regimes and the quantitative statement that the memory effect 'can significantly modify' the final asymmetry rely on numerical solutions whose implementation details, validation against known limits (e.g., strong-washout or N2-dominated cases), and error analysis are not provided. Without these, the regime boundaries and the size of the reported effect cannot be assessed.

    Authors: We accept that the numerical implementation requires more documentation. In the revised version we will add an appendix that (i) lists the full set of density-matrix equations and the scattering processes retained, (ii) shows validation against the strong-washout limit (where the final asymmetry becomes independent of initial conditions) and against the N2-dominated analytic approximation, and (iii) reports convergence tests with respect to integration step size and parameter sampling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows from solving stated density-matrix equations

full rationale

The paper obtains the memory effect and regime division by numerically solving the density-matrix equations that incorporate decay, inverse decay, scattering, and Yukawa flavor projections, then applying external neutrino oscillation data constraints. This produces the claimed misalignment survival as an output of the dynamics rather than by redefinition, fitting, or self-citation chain. No load-bearing step reduces to an input by construction, and the framework is self-contained against the stated equations without invoking prior author results as uniqueness theorems.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Analysis rests on the type-I seesaw framework and the completeness of the listed processes in the density-matrix equations. No new particles or forces are introduced. Free parameters are the RHN masses and Yukawa couplings adjusted to low-energy neutrino data. Since only the abstract is available, the ledger is necessarily incomplete.

free parameters (1)
  • RHN masses and Yukawa couplings
    Adjusted to reproduce observed neutrino masses and mixings; at most one RHN allowed in weak washout regime.
axioms (2)
  • domain assumption Type-I seesaw with hierarchical RHN spectrum
    Standard framework invoked for thermal leptogenesis.
  • domain assumption Density-matrix equations capture all relevant decay, inverse decay, and scattering processes plus flavor projections
    Central to the claim that misalignment survives N1 washout.

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