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The Neutrino Mass Bound from Leptogenesis Revisited

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Pith's one-line read Improved leptogenesis rates push the lightest-neutrino mass bound from 0.12 eV to about 0.15 eV.

desk verdict A careful, incremental update that relaxes the leptogenesis mass bound from 0.12 to 0.15 eV via spectator protection, but the headline number still depends on an uncomputed N2,N3 contribution to ΔL=2 washout. read the letter →

arxiv 2411.09765 v2 pith:22WW6R5T submitted 2024-11-14 hep-ph astro-ph.COhep-ex

Björn Garbrecht , Edward Wang This is my paper · ORCID
classification hep-phastro-ph.COhep-ex MSC 81V1583F05 PACS 98.80.Cq14.60.Pq
keywords leptogenesistype-IseesawneutrinomassboundbaryonasymmetryCTPformalismspectatoreffectsΔL=2washout
topics Matter-Antimatter Asymmetry
open problems Matter-Antimatter Asymmetry
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper revisits a long-standing connection between the baryon asymmetry of the Universe and neutrino masses: in the simplest unflavored leptogenesis setup, the lightest active neutrino cannot be too heavy, or the asymmetry is washed out. Using improved closed-time-path rates, spectator dynamics, and a newly derived $\Delta L=2$ washout, it claims the bound is $m_\text{lightest} \lesssim 0.15\,\text{eV}$, slightly above the earlier $0.12\,\text{eV}$ limit. The relaxation is not because washout is weaker; the new $\Delta L=2$ rates are stronger. It comes from partially equilibrated spectator fields that hide part of the early asymmetry from lepton-number-violating reactions. The parameter scan shows viable baryogenesis up to this mass scale and suggests the same methods apply to other leptogenesis models.

What carries the argument

The load-bearing objects are the even/odd helicity combinations of the lightest sterile neutrino and two sets of rates: the $\Delta L=1$ rates from the CTP formalism and the new $\Delta L=2$ washout rate $W_2$, derived from the off-shell part of the N1 spectral self-energy. This off-shell term produces $\Delta L=2$ scattering processes that need no real-intermediate-state subtraction and decay as $z^{-2}$, so they keep erasing asymmetry after inverse decays freeze out. Against that, the partially equilibrated bottom-Yukawa and weak sphaleron reactions move part of the asymmetry into a down-type quark combination, $Y_{\Delta_{\text{down}}}$, which N1-mediated interactions cannot efficiently erase. The balance between these two mechanisms sets the final baryon asymmetry.

What would settle it

Compute the $\Delta L=2$ washout including N2 and N3 without flavour averaging; if the net rate is much smaller than the N1-only rate used here, the bound $m_\text{lightest}\lesssim0.15\,\text{eV}$ would no longer follow. A concrete alternative check: find a point in the full seesaw parameter space with $m_\text{lightest}>0.15\,\text{eV}$ that produces the observed baryon asymmetry under the same equations.

Watch

Extended reading notes

Core claim

The central result is that in a strongly hierarchical type-I seesaw with $M_2, M_3 \gg M_1$, unflavored leptogenesis remains viable for lightest neutrino masses up to $m_\text{lightest} \approx 0.15\,\text{eV}$. The paper solves momentum-averaged CTP fluid equations from $z = 0.01$ to $z = 1000$, varying $K$ between $10^{-2}$ and $10^{3}$ and $M_1$ between $10^{10}\,\text{GeV}$ and $10^{16}\,\text{GeV}$. With fully equilibrated spectators the improved $\Delta L=2$ washout tightens the old bound to $0.08\,\text{eV}$; with partially equilibrated bottom-Yukawa and weak sphaleron interactions, part of the early asymmetry is protected, and the bound relaxes to $0.15\,\text{eV}$. The scan also yields a lower bound $M_1 \gtrsim 10^{10}\,\text{GeV}$, slightly stronger than the Davidson-Ibarra bound. For $m_\text{lightest} \approx 0.14\,\text{eV}$, viable points require $M_1 \gtrsim 5\times10^{12}\,\text{GeV}$, which keeps the scenario unflavored.

Load-bearing premise

The calculation assumes the $\Delta L=2$ washout is dominated by the lightest sterile neutrino, so contributions from N2 and N3 are dropped; if those contributions largely cancel the N1 term, the central bound would weaken.

Editorial extensions

If this is right

  • With fully equilibrated spectators, the improved $\Delta L=2$ washout would tighten the bound to $m_\text{lightest} \lesssim 0.08\,\text{eV}$; partial spectator equilibration is what brings the final bound back up to $0.15\,\text{eV}$.
  • Partially equilibrated spectator fields can change the freeze-out asymmetry by several orders of magnitude and can flip its sign across much of the parameter space.
  • The calculation strengthens the lower bound on $M_1$ to about $10^{10}\,\text{GeV}$, slightly above the Davidson-Ibarra bound.
  • For $m_\text{lightest} \approx 0.14\,\text{eV}$, viable leptogenesis requires $M_1 \gtrsim 5\times10^{12}\,\text{GeV}$, safely in the unflavored regime.
  • The same method can be applied to flavored leptogenesis and to scenarios with the next-to-lightest sterile neutrino, where spectator protection is expected to open additional viable parameter space.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the heavier sterile neutrinos N2 and N3 were included and their $\Delta L=2$ contributions cancelled part of the N1 rate, the $0.15\,\text{eV}$ bound could loosen further; the paper itself does not compute that cancellation.
  • The same competition between stronger $\Delta L=2$ washout and spectator protection could shift allowed regions in flavored leptogenesis; a direct extension of this scan would show whether the qualitative conclusion survives.
  • The spectator-induced sign change means that simplified fully-equilibrated treatments can mislabel which parameter combinations produce the observed baryon asymmetry; future scans should treat spectator equilibration as part of the dynamical system rather than a fixed boundary condition.
  • Should terrestrial experiments push the lightest neutrino mass above $0.15\,\text{eV}$, it would not disprove leptogenesis in general, but it would rule out this minimal unflavored hierarchical scenario unless additional contributions restore the asymmetry.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper revisits the upper bound on the lightest neutrino mass from unflavoured thermal leptogenesis in a hierarchical type-I seesaw model. The authors combine the CTP-derived rates of Ref. [14] with a new ΔL=2 washout rate W2 derived from the off-shell N1 propagator, and they include partially equilibrated spectator fields. After a parameter scan over K and M1 for vanishing and thermal initial conditions, they find m_lightest ≲ 0.15 eV, which is slightly less stringent than the earlier 0.12 eV bound because spectator protection of the early asymmetry overcompensates the stronger ΔL=2 washout.

Significance. The paper is a careful application of modern CTP methods to a classic leptogenesis question, and it is transparent about its approximations. The technical contributions include a CTP derivation of ΔL=2 washout that avoids real-intermediate-state subtraction, the use of momentum-dependent rates from Ref. [14], and the treatment of partially equilibrated spectator fields. If the result is robust, it updates the standard bound and shows that spectator dynamics can change the final asymmetry by orders of magnitude. However, the headline bound currently rests on an unquantified assumption about the N2,N3 contributions to ΔL=2 washout; since the earlier flavour-averaged calculation in Ref. [37] exhibits a cancellation among heavy-neutrino contributions, this is a genuine correctness risk for the central numeric claim.

major comments (2)
  1. [Section IV, Eqs. (40)–(41)] The washout rate W2 is computed only from the off-shell N1 propagator, and the contributions from N2 and N3 are dropped with the expectation that they are subdominant 'due to their large masses'. This expectation is not derived. In the flavour-averaged treatment of Ref. [37], summing over all heavy Majorana fermions cancels the large-K terms and leaves a rate that depends only on light neutrino masses. The authors argue that because N1 decays populate a single linear combination ℓ∥, this cancellation does not occur for ℓ∥ washout; however, the ΔL=2 process ℓ∥ φ → ℓ̄β φ̄ receives contributions from all Ni, and the combination Σ_i h_{i∥} h_{iβ}/M_i is fixed by the seesaw neutrino mass matrix. The relative size of N2,N3 is therefore not determined by M1 ≪ M2 ≪ M3 alone, and unless the omitted terms are computed or bounded, the central numeric claim m_lightest ≲ 0.15 eV is not established.
  2. [Section III (first paragraph) and Section V] The momentum-averaged fluid equations carry an order-one uncertainty in the final asymmetry [27,28], which the authors acknowledge and argue is mild in the strong washout regime. However, the final bound m_lightest ≲ 0.15 eV is reported without an uncertainty estimate, and the difference from the previous 0.12 eV bound is only about 25%. Since the bound is obtained by scanning a grid in K and M1 (Section V), the precise location of the excluded region could shift by more than this difference under the momentum-averaging uncertainty. The authors should either propagate this uncertainty into the bound or explain why it does not affect the comparison with previous results.
minor comments (6)
  1. [Section II] The text 'pushes M1 ≳ 5 × 10^12 eV' should read GeV, not eV.
  2. [Sections III and VI] There are several typos: 'tratment' should be 'treatment', 'sourse' should be 'source', 'Yuakwa' should be 'Yukawa' in Section III, and 'sigificant' should be 'significant' and 'equlibration' should be 'equilibration' in Section VI.
  3. [Section IV and figure captions] The symbol formed by M1 with a tilde is used without definition; please define it and state its relation to the physical mass M1.
  4. [References] The reference entries for [14], [27], [28], and [30] are missing publication years; please complete them.
  5. [Equation (25)] The notation α5_2 is ambiguous; please write α2^5 or define it explicitly.
  6. [Section IV, around Eq. (37)] The statement that the first term in the propagator is 'more strongly peaked around the pole' and does not depend on chemical potentials to leading order would benefit from a more quantitative justification, since it underlies the neglect of an off-shell contribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the new ΔL=2 washout rate is derived in the CTP formalism, and the m_lightest bound emerges from a parameter scan over independently computed rates, not from a fitted or self-referential input.

full rationale

The paper's central input rates γLNC and γLNV are taken from Ref. [14] (Garbrecht, Klose, and Tamarit), a prior same-group calculation; the paper states: 'We take the numerical data points for γLNC and γLNV obtained in Ref. [14] and interpolate between them to compute our rates' (Sec. III). This is load-bearing but not circular: those rates were derived in the CTP formalism in a separate paper, are not adjusted to reproduce the final baryon asymmetry, and enter as known functions of z for given K and M1. The new ΔL=2 washout rate W2 is derived inside the present paper (Sec. IV, Eqs. (36)–(41)) from the off-shell N1 spectral self-energy, and the final bound m_lightest ≲ 0.15 eV is obtained by scanning K and M1 and testing whether the freeze-out asymmetry is sufficient (Sec. V); no fitted parameter is renamed as a prediction. The use of the literature upper bound ϵmax (Eq. (4)) is conservative rather than circular. The paper explicitly acknowledges an incompleteness rather than a circularity when it drops N2, N3 contributions to ΔL=2 washout: 'Since we expect these interactions to be subdominant with respect to the interactions with N1 due to their large masses, we only keep the latter ones' (Sec. IV). That is a model assumption that could affect the numerical value of the bound, and the Appendix also warns that the KMS relation cannot be applied to the on-shell N1 propagator; but neither statement makes any prediction equivalent by construction to its input. No self-citation chain forces the central claim; Ref. [14] is independent support because it does not include the target bound as an assumption and is not fitted to the present paper's result.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

No parameters are fitted to data; the scan varies K and M1, and the maximal asymmetry from Ref [20] is used as an upper bound. The main assumptions are the model structure, kinetic equilibrium, momentum-averaged equations, and the off-shell KMS approximation.

assumptions (7)
  • domain assumption Type-I seesaw with three heavy Majorana neutrinos and strongly hierarchical masses M1 << M2 << M3.
    Defines the model; stated in Section II, Eq. (1).
  • domain assumption Unflavored leptogenesis: lepton flavor is conserved and only the N1-induced asymmetry is relevant.
    Authors state this in Section II and Introduction; neglects flavor effects.
  • domain assumption Momentum-averaged (fluid) Boltzmann equations are accurate enough for the strong washout regime.
    Section III; authors note order-one uncertainty, citing Refs [27-30].
  • domain assumption Standard Model particles are in kinetic equilibrium, parametrized by chemical potentials.
    Section II, Eq. (11).
  • ad hoc to paper The KMS relation applied to the off-shell part of the N1 propagator yields the ΔL=2 washout rate.
    Section IV and Appendix; authors emphasize it does not apply to the on-shell part, but assume it is valid for the off-shell self-energy.
  • ad hoc to paper ΔL=2 washout is dominated by N1-mediated processes; N2 and N3 contributions are neglected.
    Section IV; authors argue subdominance and non-exact cancellation, but do not compute it.
  • domain assumption The maximal CP asymmetry ϵmax can be used as the asymmetry parameter for the scan.
    Section II, Eq. (4) from Ref [20]; conservative for an upper bound on m_lightest.

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Cite this review

Pith. "Pith review of The Neutrino Mass Bound from Leptogenesis Revisited." pith.science (2026). https://pith.science/paper/22WW6R5T

@misc{pith2026241109765,
  author       = {Pith},
  title        = {Pith review of: The Neutrino Mass Bound from Leptogenesis Revisited},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/22WW6R5T}},
  note         = {Machine review of arXiv:2411.09765}
}
abstract

Recent years have seen a great improvement in the computation of $CP$-conserving and $CP$-violating equilibration rates for leptogenesis. These are relevant for the relativistic regime of the sterile Majorana fermions and the dynamics of the Standard Model particles acting as spectator processes. In order to probe the regime of large $({\cal O}(10^2))$ washout parameters, we add $\Delta L = 2$ washout processes, which we derive in the CTP-formalism. To demonstrate their significance, we apply state-of-the-art computational techniques to a simple yet well-motivated phenomenological scenario: unflavored leptogenesis in a hierarchical type-I seesaw model. We then perform a parameter scan of the final baryon asymmetry and find a constraint $m_\text{lightest} \lesssim 0.15 \, \text{eV}$ on the absolute neutrino mass scale, which is slightly less stringent than previously reported bounds obtained without the aforementioned improvements. The relaxation of the bounds is mainly due to partially equilibrated spectator fields, which protect part of the asymmetry from washout and lead to larger final asymmetries. While this might seem like a minor correction, the actual dynamics of the fields is substantially altered by these effects. Even though we focused on a particularly simple scenario for leptogenesis, the methods employed here can and should be extended to other models, thus giving us a more accurate picture of the different leptogenesis scenarios.

Figures

Figures reproduced from arXiv: 2411.09765 by the authors.

Figure 1
Figure 1. Comparison of washout rates for M˜1 = 1013 GeV for K = 100 (a) and K = 500 (b). which, to first order in the chemical potentials, is gw d dz Yℓ∥ = − 16g 2 w(h †h) 2 11 M˜ 1s µℓ + µϕ T Z d 4k (2π) 4 (1 − fF (k0))fF (k0) 1 k 2 − M2 1 [Σˆ A N1,R µ(k)ΣˆµA N1,L(k)]µℓ=µϕ=0. (39) From this we can extract the new contribution to the washout rate W2 = − 24K2 T3 M˜ 1 T  Yl∥ + 1 2 Yϕ  Z d 4 k (2π) 4 (1 − fF (k0))fF (k0) γ∆L=… view at source ↗
Figure 2
Figure 2. Numerical solutions of Boltzmann equations with fully equilibrated spectators with (solid lines) and without [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Numerical solutions of Boltzmann equations with partially (solid lines) and fully equilibrated (dashed lines) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Allowed regions for vanishing (a) and thermal (b) initial conditions and different choices of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

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