Throwing away antimatter via neutrino oscillations during the reheating era

Ryuichiro Kitano; Shintaro Eijima; Wen Yin

REVIEW 3 major objections 5 minor 1 cited by

Throwing away antimatter via neutrino oscillations during the reheating era

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read During reheating, CP-violating neutrino flavor oscillations can leave a net lepton asymmetry that becomes the observed baryon asymmetry, at reheating temperatures as low as 10 TeV (or 100 GeV) and without fine-tuned right-handed neutrino…

desk verdict A genuinely new low-scale baryogenesis mechanism with a robust neutrino-mass prediction; the assumed CP source in the inflaton decay is the main soft spot. read the letter →

arxiv 1908.11864 v2 pith:OPNPHTDX submitted 2019-08-30 hep-ph astro-ph.COgr-qchep-ex

Shintaro Eijima , Ryuichiro Kitano , Wen Yin This is my paper · ORCID

classification hep-phastro-ph.COgr-qchep-ex PACS 14.60.Pq98.80.Cq

keywords baryogenesisleptogenesisneutrinooscillationsreheatingright-handedneutrinosleptonasymmetrysphaleronseesawmechanism

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

During the reheating era, the inflaton decays into a coherent mixture of the three left-handed lepton flavors. As these leptons traverse the hot plasma, CP-violating flavor oscillations develop: the total lepton number stays zero, but part of the antilepton number is moved into right-handed neutrinos (neutrinos with no weak interactions). The paper argues that if those right-handed neutrinos later decay in a lepton-number-violating way, the visible sector is left with a net lepton asymmetry that the sphaleron process — the nonperturbative weak-interaction transition that converts lepton number into baryon number — turns into the observed baryon asymmetry. This works without tuning the right-handed neutrino masses and lowers the required reheating temperature to about 10 TeV for perturbative inflaton decay and about 100 GeV for dissipative reheating.

What carries the argument

The engine is the CP-violating oscillation probability \[ P_{L_\phi\to L_N}-P_{\bar L_\phi\to \bar L_N} \simeq \sum_{i>j}4\,\Im[c_i c_j^*]\, \sin\!\left(\frac{$y_i^{2}$-$y_j^{2}$}{16\$alpha_2^{2}$}\right)\frac{y_{Ni}y_{Nj}}{y_\$tau^{2}$}, \] together with the asymmetry formula $\Delta_N/s\simeq 10^{-10}(T_R/m_\phi)B\,\xi_{CP}(|y_N|/10^{-6})^2$. The ingredients are the complex coefficients $c_i$ defining the coherent flavor state from inflaton decay, the thermal-potential phase differences $y_i^2 T^2/(16|p|)$ that make the oscillation flavor-dependent, the CP-even "strong phases" $y_i^2/(16\alpha_2^2)$ accumulated before the lepton pair-annihilates, and the $O(|y_N|^2/y_\tau^2)$ probability that the flavor is observed by the neutrino Yukawa interaction rather than by the tau Yukawa. The right-handed neutrino thermalization rate $\Gamma_N^{\rm th}\simeq\gamma_N|y_N|^2 T$ with $\gamma_N\simeq 0.01$ then sets the lower bound on the reheating temperature and the mass window for $N$.

What would settle it

A decisive check is to compute the inflaton decay amplitude in a concrete model and test whether $\xi_{CP}\propto\Im[c_i c_j^*]$ is nonzero; if it vanishes, Eq. (15) gives no asymmetry. Observationally, if cosmological data force the lightest active neutrino mass above $\sim 4\times10^{-3}$ eV or the sum of neutrino masses above $\sim 0.12$ eV, the perturbative-reheating version's condition (23) is violated and the scenario fails.

Watch

Extended reading notes

Core claim

The central claim is that baryogenesis can happen by "throwing away" antilepton number during reheating rather than by creating net lepton number at high temperature. Inflaton decays inject a coherent lepton state $|L_\phi\rangle=\sum_i c_i|i\rangle$ at time $t_R$; the plasma's flavor-dependent thermal potentials give the electron, muon, and tau components different phases, and the small neutrino Yukawa coupling acts as a flavor "measurement" with probability $O(|y_N|^2/y_\tau^2)$. The resulting asymmetry stored in the right-handed neutrino sector is $\Delta_N/s\simeq 10^{-10}(T_R/m_\phi)B\,\xi_{CP}(|y_N|/10^{-6})^2$, while the visible sector gets the opposite asymmetry. If the right-handed neutrinos are heavy enough not to re-enter equilibrium before the sphaleron freezes out, the visible asymmetry matches the required $-(2.45\pm 0.01)\times10^{-10}$, producing the observed baryon asymmetry. The mechanism requires no degenerate right-handed neutrino masses and works with a single right-handed neutrino.

Load-bearing premise

The mechanism's load-bearing assumption is that a specific inflaton model produces a coherent superposition of lepton flavors with complex, non-aligned coefficients; if those coefficients are real or aligned with the neutrino Yukawa couplings, the CP-violating phase combination $\xi_{CP}$ vanishes and no baryon asymmetry is generated.

Editorial extensions

If this is right

Reheating temperatures as low as $\sim$10 TeV (perturbative inflaton decay) or $\sim$100 GeV (dissipative reheating) can produce the observed baryon asymmetry, far below the usual thermal-leptogenesis bound.
No degeneracy among right-handed neutrino masses is needed; a single right-handed neutrino with $M_N\gtrsim 7\,{\rm TeV}(|y_N|/10^{-6})^2$ in the perturbative case is enough.
The seesaw contribution of that neutrino to the lightest active neutrino mass is at most $4\times10^{-3}$ eV, so the scenario predicts a normal or inverted hierarchy with $\sum m_\nu\simeq 0.06$ or $0.10$ eV and restricts neutrinoless double beta decay through $|m_{ee}|$ as in Eq. (26).
The remaining two right-handed neutrinos must avoid washing out the asymmetry, which restricts them to one of four mass patterns; the sub-100 GeV options are testable in beam-dump and collider searches, and a $\sim$6 GeV right-handed neutrino is predicted in the ALP-inflation dissipative-reheating case.

Reading between the lines

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

A complete particle-physics model would have to supply the phases $c_i$ from the inflaton–lepton coupling; computing $\Im[c_i c_j^*]$ in such a model would turn Eq. (15) from an estimate into a sharp prediction for the baryon asymmetry.
The mechanism is a template for separating any conserved charge: any out-of-equilibrium source that injects a coherent flavor state with complex phases could split matter and antimatter into different sectors, making asymmetric dark matter a natural further application.
If dissipative reheating is realized, the predicted $M_N\sim 6$ GeV right-handed neutrino would be kinematically accessible to fixed-target and short-baseline experiments, and its decay length would be fixed by the same coupling $|y_N|$ that sets the baryon asymmetry, making the signal rate predictable.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this is a plausible new route to low-scale baryogenesis, and the most important part—the neutrino-mass prediction—holds up even though the CP source in the perturbative case is assumed rather than derived.

What's new: Refs [3,4] showed oscillation-induced baryogenesis with only the LLHH operator; here they add a seesaw right-handed neutrino N, let CP-violating oscillations put a lepton asymmetry into N (and the opposite asymmetry into visible leptons), then use lepton-number-violating decays of N to erase the N-sector asymmetry. That trick is what decouples the final asymmetry from washout and allows TR as low as ~10 TeV perturbatively and ~100 GeV with dissipative reheating. Eq. (16) gives a clean analytic scaling, Fig. 1 checks it numerically, and Eq. (25) converts the thermalization condition into δmν ≲ 4 meV independent of yN. That last step is the best part: it makes a sharp, falsifiable statement about the lightest neutrino mass and neutrinoless double beta decay, and it does not depend on fixing yN to the observed asymmetry.

Soft spots, in order of importance. First, ξ_CP is an input, not an output. The authors argue "in general" the inflaton decay coefficients ce, cμ are complex, and the numerical example just sets them to (e^i, e^2i, 1)/√3. For the perturbative case no explicit inflaton-lepton Lagrangian is given, so nobody has shown that a UV completion with O(1) ξ_CP and the required reheating actually exists. If ξ_CP ends up much smaller than one, the allowed TR range shrinks and the 10 TeV claim would need a model. This is a genuine gap, but I would not call it fatal: the mechanism's logic does not depend on any specific value, and the dissipative ALP section shows a concrete setup where complex coefficients do arise. The stress-test note is right about the gap but overstates it as a load-bearing flaw rather than a model-building caveat.

Second, the washout analysis for the other two right-handed neutrinos is schematic—four mass patterns are listed, but no detailed rate calculation is shown. That matters for whether the visible asymmetry survives, and it deserves more work, but it does not undermine the core mechanism.

Third, the sign convention for anti-lepton oscillations and some thermal rates are inherited from earlier work. If the convention were wrong you would get the wrong sign, but a wrong sign is not a wrong mechanism; a referee should ask them to state the convention explicitly.

The reader's conditional verdict is fair. I do not see a load-bearing internal contradiction, and the circularity worry is misplaced: fixing yN to reproduce the observed asymmetry and then deriving the neutrino-mass bound is normal model building.

Who this is for: people working on low-scale baryogenesis, seesaw models, and testable neutrino-mass predictions. It deserves a serious referee. I would engage with it and would cite it in my own work on low-scale leptogenesis.

Referee Report

3 major / 5 minor

Summary. This paper proposes a baryogenesis mechanism based on CP-violating flavor oscillations of left-handed leptons produced by inflaton decays during reheating. The inflaton is assumed to decay with branching fraction B into a coherent superposition of active lepton flavors; in the presence of a thermal plasma, flavor-dependent potentials induce phases, and a small probability η ~ |y_N|^2/y_τ^2 projects the oscillating state onto a right-handed neutrino N. The resulting N asymmetry is equal and opposite to the visible-sector asymmetry. If N's asymmetry is subsequently washed out by lepton-number-violating processes before being transferred back, the visible asymmetry survives and is reprocessed by sphalerons into the baryon asymmetry. The central analytic result is Eq. (16), ΔN/s ≃ 10^{-10} (T_R/m_φ) B ξ_CP (|y_N|/10^{-6})^2, and the main phenomenological condition is Eq. (23), T_R ≳ M_N ≳ T_N^th ≃ 7 TeV (|y_N|/10^{-6})^2, leading to T_R ~ O(10) TeV for perturbative reheating and T_R ~ O(100) GeV for dissipative reheating. The paper also derives a robust prediction δm_ν ≲ 4×10^{-3} eV for the lightest active neutrino mass and discusses testable implications for neutrinoless double beta decay and heavy neutral lepton searches. A numerical solution of the density-matrix equations (Fig. 1) confirms the order of magnitude and sign of the asymmetry for one parameter point with an uncertainty band from the O(1) factors C and C'.

Significance. If the mechanism is realized, the paper is significant: it lowers the required reheating temperature for baryogenesis by several orders of magnitude relative to vanilla thermal leptogenesis, avoids fine-tuning in the right-handed neutrino mass spectrum, and connects the mechanism to low-energy neutrino observables. Eq. (25) is a genuine prediction in which the unknown |y_N| cancels between the seesaw relation and the thermalization bound. The analytic scaling in Eq. (16) is transparent, and the numerical check in Fig. 1 is a useful consistency test with the claimed O(1) uncertainty bands. The two load-bearing weaknesses are the assumed CP-violating source in the perturbative case and the asserted, rather than derived, conversion of ΔN into a net visible asymmetry; both are addressable but need to be strengthened.

major comments (3)

[Sec. 2.1, Eqs. (5)-(16), (38)] The entire asymmetry in the perturbative reheating scenario is proportional to the combination ξ_CP defined after Eq. (16), which involves Im[c_i c_j*] and is therefore nonzero only if the inflaton decay coefficients c_i are complex and flavor-nonaligned after all allowed field redefinitions. The paper assumes 'in general' such O(1) complex c_i after Eq. (6) and uses the ad hoc choice c_i = (e^i, e^{2i}, 1)/√3 in Fig. 1, but it provides no explicit inflaton-lepton Lagrangian or invariant argument for the perturbative decay that would show the physical CP-violating phases survive. Since ξ_CP is a multiplicative factor in Eq. (16), this is not a cosmetic issue: it controls whether the mechanism can match the observed asymmetry at all. I request either a concrete perturbative UV example with an estimate of ξ_CP, or a clear statement that the claim is conditional on ξ_CP being of order unity.
[Sec. 2.1, Eqs. (16), (18), (23)] The quantitative impact of the unquantified ξ_CP is severe for the central T_R ~ O(10) TeV claim. Matching the required asymmetry Eq. (18) at T_R/m_φ ~ 1 with B ~ 1 requires |y_N| ≈ 10^{-6} ξ_CP^{-1/2}. Substituting into Eq. (20) gives T_N^th ≈ 7 TeV / ξ_CP, so for ξ_CP = 0.01 the thermalization bound becomes about 700 TeV and Eq. (23) is violated for T_R ~ 10 TeV. Thus the advertised low-reheating window is established only for ξ_CP sufficiently close to unity; a scan over the inflaton decay coefficients or a model computation is needed to show that such values are generic rather than fine-tuned.
[Sec. 2.1, Eqs. (22)-(23); Sec. 1, abstract] The step in which the N asymmetry becomes a net visible asymmetry is asserted rather than derived. The text says that for M_N ≳ T_N^th the N becomes non-relativistic and ΔN is 'washed out' while Δvis remains untouched, but no LNV washout rate is given and no comparison with the Hubble rate at the relevant temperature is made. The mechanism also requires that this washout occurs without transferring ΔN back into the SM sector before T_sph ~ 100 GeV. Please provide the relevant rate (for example the Majorana-mass-induced helicity/lepton-number mixing rate, or the appropriate ΔL = 2 scattering rate) and demonstrate the ordering of rates explicitly; otherwise the central claim that the baryon asymmetry survives is not supported by the equations given.

minor comments (5)

[Eqs. (10) and (14)] The phase in the overlap in Eq. (14) is written with the opposite sign relative to the state in Eq. (10); the final CP asymmetry is likely insensitive to this convention, but the intermediate expressions should be made consistent.
[Eq. (38)] The initial condition for the antilepton density matrix is printed with the same symbol ρ_k as the lepton one; the bar on the second ρ_k appears to have been lost in typesetting, and should be restored.
[Eq. (7) and around Eq. (1)] The use of y_i for the charged-lepton Yukawa couplings in Eq. (7) while y_Ni denotes the neutrino Yukawa couplings may confuse readers; a different symbol such as y_{\ell,i} would help.
[Sec. 3, paragraph after Eq. (45)] For the ALP model the statement that c_i is 'an eigenvector of c_{ij}' is terse; since this is the main explicit example with complex phases, it would help to state explicitly which c_{ij} entries are complex and why the resulting ξ_CP is of order unity.
[Sec. 2.2, Eq. (26)] The range 0.01 eV ≲ |m_eff| ≲ 0.05 eV for the inverted hierarchy should be accompanied by a reference to the underlying oscillation fit or a one-line derivation, since the bounding of m_eff from below by about 0.01 eV is not self-evident from Eq. (25) alone.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the asymmetry formula is derived from stated oscillation inputs, and the low-T_R and neutrino-mass claims do not reduce to fitted parameters.

full rationale

The central derivation, Eq. (16), follows from the assumed coherent decay state Eq. (6), the thermal-potential phases Eqs. (7) and (10), and the projection probability Eq. (12); the paper does not define y_N or xi_CP in terms of the baryon asymmetry. The observed baryon asymmetry Eq. (18) is used only to fix the free Yukawa coupling y_N, which is standard model building rather than a prediction masquerading as derivational output. The advertised low-reheating-temperature window is conditional on O(1) complex decay coefficients c_i; this CP structure is explicitly assumed (Eq. (6) and the statement that 'ce and c_mu are in general complex numbers') and is not passed off as derived, so its plausibility is a UV-completion/correctness concern, not circularity. The numerical check uses kinetic equations quoted in Eqs. (33)-(37) and cites the authors' earlier work [4] for details, but the analytic result and the y_N-independent estimate delta m_nu <= 4 x 10^-3 eV (Eq. (25)) stand on their own. No fitted parameter is renamed as a prediction, no central premise is justified solely by a self-citation, and no uniqueness claim is imported from the authors' prior papers.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the oscillation formalism, the CP-conjugate sign convention, the out-of-equilibrium initial state, the production and decoupling of the right-handed neutrino, the seesaw relation, and the sphaleron conversion. None of these are derived in this paper; they are imported from standard results or the authors' earlier work. The only truly ad hoc input is the flavor-coherent initial state with undetermined CP phases.

free parameters (6)

yN = ~10^-6 (perturbative), ~10^-8..10^-7 (dissipative)
Set by matching the observed baryon asymmetry in Eqs. (16)-(18); not predicted from first principles. The seesaw contribution to active neutrino mass is then bounded by Eq. (25).
ξ_CP = O(1), model-dependent
Product of CP-violating phases in the inflaton decay amplitudes and yNi phases, defined below Eq. (16). The baryon asymmetry is linear in ξ_CP; the paper assumes O(1) values, e.g., c_i = (e^i, e^{2i}, 1)/√3 in Fig. 1.
B = 1 assumed in numerics
Branching fraction of inflaton into leptons in Eq. (2); scales the asymmetry linearly in Eq. (16).
TR/mφ = ~1 (perturbative), 10^2..10^3 (dissipative)
Ratio of reheating temperature to inflaton mass; controls the amount of asymmetry in Eq. (16). In perturbative reheating TR ≤ mφ; dissipative reheating allows TR ≫ mφ.
C, C' = 1 (varied 1/3 to 3)
Order-one calibration constants for LPM and pair-annihilation rates in Eqs. (35)-(36); Fig. 1 shows the asymmetry band for their variation.
MN = ≥ ~7 TeV (perturbative case); ~6 GeV for yN=1e-7 (dissipative)
Right-handed neutrino mass chosen in the window of Eq. (23) so that N is not thermalized before sphaleron freeze-out and is kinematically accessible. Together with yN it fixes the active neutrino mass via seesaw.

assumptions (6)

domain assumption Flavor evolution in the thermal plasma follows the Sigl-Raffelt density-matrix kinetic equations with thermal potentials Ei ~ y_i^2 T^2/(16|p|) (Eq. (7)).
The entire asymmetry estimate depends on this evolution; the equations are imported from Refs [37] and [4] rather than re-derived.
domain assumption Anti-lepton kinetic equations are obtained by reversing the sign of the oscillation matrix Ω (Sec. 2.3).
Stated without derivation. The CP asymmetry in Eq. (15) relies on this sign convention for the CP-conjugate sector.
domain assumption N is produced only through the Yukawa interaction (1) with probability η ~ |yN|^2/yτ^2 and is not thermalized until after sphaleron freeze-out, enforced by MN > T_Nth (Eqs. (19)-(23)).
If N is thermalized or transfers its asymmetry back before freeze-out, the produced baryon asymmetry is washed out.
ad hoc to paper At t_R the preexisting plasma is exactly thermal with no flavor deviation or lepton asymmetry; only the inflaton decay products are out of equilibrium (Eq. (38)).
This initial condition is chosen so that the whole asymmetry comes from the oscillation; it is not derived from an explicit reheating model.
domain assumption Type-I seesaw relation δmν = |yN|^2 <H>^2/MN (Eq. (24)) connects the baryogenesis condition to active neutrino masses.
Standard seesaw mechanism, assumed to govern the neutrino mass generated by N.
domain assumption The sphaleron process converts the surviving visible lepton asymmetry into the observed baryon asymmetry for T > Tsph ~ 100 GeV.
Standard electroweak physics; the paper uses the standard conversion and freeze-out temperature.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Throwing away antimatter via neutrino oscillations during the reheating era." pith.science (2026). https://pith.science/paper/OPNPHTDX

@misc{pith2026190811864,
  author       = {Pith},
  title        = {Pith review of: Throwing away antimatter via neutrino oscillations during the reheating era},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPNPHTDX}},
  note         = {Machine review of arXiv:1908.11864}
}

abstract

The simplest possibility to explain the baryon asymmetry of the Universe is to assume that radiation is created asymmetrically between baryons and anti-baryons after the inflation. We propose a new mechanism of this kind where CP-violating flavor oscillations of left-handed leptons in the reheating era distribute the lepton asymmetries partially into the right-handed neutrinos while net asymmetry is not created. The asymmetry stored in the right-handed neutrinos is later washed out by the lepton number violating decays, and it ends up with the net lepton asymmetry in the Standard Model particles, which is converted into the baryon asymmetry by the sphaleron process. This scenario works for a range of masses of the right-handed neutrinos while no fine-tuning among the masses is required. The reheating temperature of the Universe can be as low as $O(10)$~TeV if we assume that the decays of inflatons in the perturbative regime are responsible for the reheating. For the case of the reheating via the dissipation effects, the reheating temperature can be as low as $O(100)$~GeV.

Figures

Figures reproduced from arXiv: 1908.11864 by the authors.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Leptogenesis with sub-electroweak-scale reheating temperature
hep-ph 2026-07 conditional novelty 6.0 of 10

Leptogenesis remains viable for reheating temperatures below sphaleron freeze-out in three perturbative monomial-inflaton scenarios, with blue-tilted primordial GWs as a potential probe.

Reference graph

Works this paper leans on

55 extracted references · 6 canonical work pages · cited by 1 Pith paper

[2]

A. D. Sakharov, Pisma Zh. Eksp. Teor. Fiz. 5, 32 (1967) [JETP Lett. 5, 24 (1967)] [Sov. Phys. Usp. 34, no. 5, 392 (1991)] [Usp. Fiz. Nauk 161, no. 5, 61 (1991)]. doi:10.1070/PU1991v034n05ABEH002497

doi:10.1070/pu1991v034n05abeh002497 1967
[3]

Hamada and R

Y. Hamada and R. Kitano, JHEP 1611, 010 (2016) doi:10.1007/JHEP11(2016)010 [arXiv:1609.05028 [hep-ph]]

arXiv 2016
[4]

Hamada, R

Y. Hamada, R. Kitano and W. Yin, JHEP 1810, 178 (2018) doi:10.1007/JHEP10(2018)178 [arXiv:1807.06582 [hep-ph]]

arXiv 2018
[5]

Hamada and K

Y. Hamada and K. Kawana, Phys. Lett. B 763, 388 (2016) doi:10.1016/j.physletb.2016.10.067 [arXiv:1510.05186 [hep-ph]]

arXiv 2016
[6]

The reheating era leptogenesis in models with seesaw mechanism

Y. Hamada, K. Tsumura and D. Yasuhara, Phys. Rev. D 95, no. 10, 103505 (2017) doi:10.1103/PhysRevD.95.103505 [arXiv:1608.05256 [hep-ph]]

work page Pith review arXiv 2017
[7]

Lazarides and Q

G. Lazarides and Q. Shaﬁ, Phys. Lett. B 258, 305 (1991). doi:10.1016/0370- 2693(91)91090-I

doi:10.1016/0370- 1991
[8]

Asaka, K

T. Asaka, K. Hamaguchi, M. Kawasaki and T. Yanagida, Phys. Lett. B 464, 12 (1999) doi:10.1016/S0370-2693(99)01020-5 [hep-ph/9906366]

arXiv 1999
[9]

Hamaguchi, H

K. Hamaguchi, H. Murayama and T. Yanagida, Phys. Rev. D 65, 043512 (2002) doi:10.1103/PhysRevD.65.043512 [hep-ph/0109030]

arXiv 2002

Show all 55 references

[10]

Yanagida, Conf

T. Yanagida, Conf. Proc. C 7902131, 95 (1979)

1979
[11]

Gell-Mann, P

M. Gell-Mann, P. Ramond and R. Slansky, Conf. Proc. C 790927, 315 (1979) [arXiv:1306.4669 [hep-th]]

1979 arXiv
[12]

Yanagida, Prog

T. Yanagida, Prog. Theor. Phys. 64, 1103 (1980). doi:10.1143/PTP.64.1103 16

1980 doi
[13]

Schechter and J

J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980). doi:10.1103/PhysRevD.22.2227

1980 doi
[14]

Schechter and J

J. Schechter and J. W. F. Valle, Phys. Rev. D 25, 774 (1982). doi:10.1103/PhysRevD.25.774

1982 doi
[15]

Minkowski, Phys

P. Minkowski, Phys. Lett. 67B, 421 (1977). doi:10.1016/0370-2693(77)90435-X

1977 doi
[16]

R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980). doi:10.1103/PhysRevLett.44.912

1980 doi
[17]

Buchmuller, R

W. Buchmuller, R. D. Peccei and T. Yanagida, Ann. Rev. Nucl. Part. Sci. 55, 311 (2005) doi:10.1146/annurev.nucl.55.090704.151558 [hep-ph/0502169]

2005
[18]

Davidson, E

S. Davidson, E. Nardi and Y. Nir, Phys. Rept. 466, 105 (2008) doi:10.1016/j.physrep.2008.06.002 [arXiv:0802.2962 [hep-ph]]

2008 arXiv
[19]

Pilaftsis, Nucl

A. Pilaftsis, Nucl. Phys. B 504, 61 (1997) doi:10.1016/S0550-3213(97)00469-0 [hep-ph/9702393]

1997 arXiv
[20]

Buchmuller and M

W. Buchmuller and M. Plumacher, Phys. Lett. B 431, 354 (1998) doi:10.1016/S0370-2693(97)01548-7 [hep-ph/9710460]

1998 arXiv
[21]

E. K. Akhmedov, V. A. Rubakov and A. Y. Smirnov, Phys. Rev. Lett. 81, 1359 (1998) doi:10.1103/PhysRevLett.81.1359 [hep-ph/9803255]

1998 arXiv
[22]

Asaka and M

T. Asaka and M. Shaposhnikov, Phys. Lett. B 620, 17 (2005) doi:10.1016/j.physletb.2005.06.020 [hep-ph/0505013]

2005 arXiv
[23]

K. Dick, M. Lindner, M. Ratz and D. Wright, Phys. Rev. Lett. 84, 4039 (2000) doi:10.1103/PhysRevLett.84.4039 [hep-ph/9907562]

2000 arXiv
[24]

L. D. Landau and I. Pomeranchuk, Dokl. Akad. Nauk Ser. Fiz. 92, 535 (1953)

1953
[25]

A. B. Migdal, Phys. Rev. 103, 1811 (1956). doi:10.1103/PhysRev.103.1811

1956 doi
[26]

P. A. R. Ade et al. [Planck Collaboration], Astron. Astrophys. 594, A13 (2016) doi:10.1051/0004-6361/201525830 [arXiv:1502.01589 [astro-ph.CO]]

2016 arXiv
[27]

F. R. Klinkhamer and N. S. Manton, Phys. Rev. D 30, 2212 (1984). doi:10.1103/PhysRevD.30.2212

1984 doi
[28]

V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. 155B, 36 (1985). doi:10.1016/0370-2693(85)91028-7

1985 doi
[29]

Besak and D

D. Besak and D. Bodeker, JCAP 1203, 029 (2012) doi:10.1088/1475- 7516/2012/03/029 [arXiv:1202.1288 [hep-ph]]. 17

2012 arXiv
[30]

Hern´ andez, M

P. Hern´ andez, M. Kekic, J. L´ opez-Pav´ on, J. Racker and J. Salvado, JHEP1608, 157 (2016) doi:10.1007/JHEP08(2016)157 [arXiv:1606.06719 [hep-ph]]

2016 arXiv
[31]

Ghiglieri and M

J. Ghiglieri and M. Laine, JHEP 1705, 132 (2017) doi:10.1007/JHEP05(2017)132 [arXiv:1703.06087 [hep-ph]]

2017 arXiv
[32]

Esteban, M

I. Esteban, M. C. Gonzalez-Garcia, A. Hernandez-Cabezudo, M. Maltoni and T. Schwetz, JHEP 1901, 106 (2019) doi:10.1007/JHEP01(2019)106 [arXiv:1811.05487 [hep-ph]]

2019 arXiv
[33]

Aghanim et al

N. Aghanim et al. [Planck Collaboration], arXiv:1807.06209 [astro-ph.CO]

arXiv
[34]

Alekhin et al., Rept

S. Alekhin et al., Rept. Prog. Phys. 79, no. 12, 124201 (2016) doi:10.1088/0034- 4885/79/12/124201 [arXiv:1504.04855 [hep-ph]]

2016 arXiv
[35]

Benes, A

P. Benes, A. Faessler, F. Simkovic and S. Kovalenko, Phys. Rev. D 71, 077901 (2005) doi:10.1103/PhysRevD.71.077901 [hep-ph/0501295]

2005 arXiv
[36]

Asaka, S

T. Asaka, S. Eijima and H. Ishida, JHEP 1104, 011 (2011) doi:10.1007/JHEP04(2011)011 [arXiv:1101.1382 [hep-ph]]

2011 arXiv
[37]

Sigl and G

G. Sigl and G. Raﬀelt, Nucl. Phys. B 406, 423 (1993). doi:10.1016/0550- 3213(93)90175-O

1993 doi
[38]

Yokoyama, Phys

J. Yokoyama, Phys. Lett. B 635, 66 (2006) doi:10.1016/j.physletb.2006.02.039 [hep-ph/0510091]

2006 arXiv
[39]

Anisimov, W

A. Anisimov, W. Buchmuller, M. Drewes and S. Mendizabal, Annals Phys. 324, 1234 (2009) doi:10.1016/j.aop.2009.01.001 [arXiv:0812.1934 [hep-th]]

2009 arXiv
[40]

Drewes, arXiv:1012.5380 [hep-th]

M. Drewes, arXiv:1012.5380 [hep-th]

arXiv
[41]

Mukaida and K

K. Mukaida and K. Nakayama, JCAP 1301, 017 (2013) doi:10.1088/1475- 7516/2013/01/017 [arXiv:1208.3399 [hep-ph]]

2013 arXiv
[42]

Drewes and J

M. Drewes and J. U. Kang, Nucl. Phys. B 875, 315 (2013) Erra- tum: [Nucl. Phys. B 888, 284 (2014)] doi:10.1016/j.nuclphysb.2013.07.009, 10.1016/j.nuclphysb.2014.09.008 [arXiv:1305.0267 [hep-ph]]

2013 arXiv
[43]

Mukaida and K

K. Mukaida and K. Nakayama, JCAP 1303, 002 (2013) doi:10.1088/1475- 7516/2013/03/002 [arXiv:1212.4985 [hep-ph]]

2013 arXiv
[44]

Daido, F

R. Daido, F. Takahashi and W. Yin, JCAP 1705, 044 (2017) doi:10.1088/1475- 7516/2017/05/044 [arXiv:1702.03284 [hep-ph]]

2017 arXiv
[45]

Daido, F

R. Daido, F. Takahashi and W. Yin, JHEP 1802, 104 (2018) doi:10.1007/JHEP02(2018)104 [arXiv:1710.11107 [hep-ph]]. 18

2018 arXiv
[46]

Takahashi and W

F. Takahashi and W. Yin, JHEP 1907, 095 (2019) doi:10.1007/JHEP07(2019)095 [arXiv:1903.00462 [hep-ph]]

2019 arXiv
[47]

P. W. Graham and A. Scherlis, Phys. Rev. D 98, no. 3, 035017 (2018) doi:10.1103/PhysRevD.98.035017 [arXiv:1805.07362 [hep-ph]]

2018 arXiv
[48]

Takahashi, W

F. Takahashi, W. Yin and A. H. Guth, Phys. Rev. D 98, no. 1, 015042 (2018) doi:10.1103/PhysRevD.98.015042 [arXiv:1805.08763 [hep-ph]]

2018 arXiv
[49]

S. Y. Ho, F. Takahashi and W. Yin, JHEP 1904, 149 (2019) doi:10.1007/JHEP04(2019)149 [arXiv:1901.01240 [hep-ph]]

2019 arXiv
[50]

Takahashi and W

F. Takahashi and W. Yin, arXiv:1908.06071 [hep-ph]

1908 arXiv
[51]

I. G. Irastorza et al. , JCAP 1106, 013 (2011) doi:10.1088/1475- 7516/2011/06/013 [arXiv:1103.5334 [hep-ex]]

2011 arXiv
[52]

Armengaud et al

E. Armengaud et al. , JINST 9, T05002 (2014) doi:10.1088/1748- 0221/9/05/T05002 [arXiv:1401.3233 [physics.ins-det]]

2014 arXiv
[53]

Armengaud et al

E. Armengaud et al. [IAXO Collaboration], JCAP 1906, 047 (2019) doi:10.1088/1475-7516/2019/06/047 [arXiv:1904.09155 [hep-ph]]

2019 arXiv
[54]

S. M. Barr, R. S. Chivukula and E. Farhi, Phys. Lett. B 241, 387 (1990). doi:10.1016/0370-2693(90)91661-T

1990 doi
[55]

D. B. Kaplan, Phys. Rev. Lett. 68, 741 (1992). doi:10.1103/PhysRevLett.68.741

1992 doi
[56]

Kitano and I

R. Kitano and I. Low, Phys. Rev. D 71, 023510 (2005) doi:10.1103/PhysRevD.71.023510 [hep-ph/0411133]. 19

2005 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [2]

A. D. Sakharov, Pisma Zh. Eksp. Teor. Fiz. 5, 32 (1967) [JETP Lett. 5, 24 (1967)] [Sov. Phys. Usp. 34, no. 5, 392 (1991)] [Usp. Fiz. Nauk 161, no. 5, 61 (1991)]. doi:10.1070/PU1991v034n05ABEH002497

doi:10.1070/pu1991v034n05abeh002497 1967

[2] [3]

Hamada and R

Y. Hamada and R. Kitano, JHEP 1611, 010 (2016) doi:10.1007/JHEP11(2016)010 [arXiv:1609.05028 [hep-ph]]

arXiv 2016

[3] [4]

Hamada, R

Y. Hamada, R. Kitano and W. Yin, JHEP 1810, 178 (2018) doi:10.1007/JHEP10(2018)178 [arXiv:1807.06582 [hep-ph]]

arXiv 2018

[4] [5]

Hamada and K

Y. Hamada and K. Kawana, Phys. Lett. B 763, 388 (2016) doi:10.1016/j.physletb.2016.10.067 [arXiv:1510.05186 [hep-ph]]

arXiv 2016

[5] [6]

The reheating era leptogenesis in models with seesaw mechanism

Y. Hamada, K. Tsumura and D. Yasuhara, Phys. Rev. D 95, no. 10, 103505 (2017) doi:10.1103/PhysRevD.95.103505 [arXiv:1608.05256 [hep-ph]]

work page Pith review arXiv 2017

[6] [7]

Lazarides and Q

G. Lazarides and Q. Shaﬁ, Phys. Lett. B 258, 305 (1991). doi:10.1016/0370- 2693(91)91090-I

doi:10.1016/0370- 1991

[7] [8]

Asaka, K

T. Asaka, K. Hamaguchi, M. Kawasaki and T. Yanagida, Phys. Lett. B 464, 12 (1999) doi:10.1016/S0370-2693(99)01020-5 [hep-ph/9906366]

arXiv 1999

[8] [9]

Hamaguchi, H

K. Hamaguchi, H. Murayama and T. Yanagida, Phys. Rev. D 65, 043512 (2002) doi:10.1103/PhysRevD.65.043512 [hep-ph/0109030]

arXiv 2002