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Baryogenesis via the CKM Matrix with Minimal Flavor Violation

T0 review · 1 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A leptoquark decay chain can turn the CKM phase into the observed baryon asymmetry.

desk verdict A solid proof-of-principle that an MFV leptoquark can source the baryon asymmetry with the CKM phase as the only CP violation; the low-reheat branch holds up, but the high-reheat branch has an unproven assumption about right-handed neutrino CP phases. read the letter →

arxiv 2608.05269 v1 pith:SSYPNPFY submitted 2026-08-05 hep-ph

Innes Bigaran , Gordan Krnjaic , Kevin Langhoff , Huangyu Xiao This is my paper · ORCID
classification hep-ph PACS 12.15.Ff13.30.Eg98.80.Cq
keywords baryogenesisCKMmatrixCPviolationminimalflavorleptoquarkJarlskoginvariantprotondecaysphaleron
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

This paper claims that the observed baryon asymmetry of the universe can arise entirely from Standard Model CP violation, specifically the phase of the CKM quark-mixing matrix, without any new source of CP violation and without time-varying model parameters. The vehicle is a scalar leptoquark whose interactions obey minimal flavor violation, so all flavor- and CP-violating structures come from the SM Yukawa couplings. If correct, the paper would overturn the widespread expectation that SM CP violation is hopelessly insufficient for baryogenesis. The proof-of-principle model can reach a per-decay asymmetry of order 0.1, and the authors show two cosmological histories that convert it into Y_B = 8.7e-11.

What carries the argument

The machinery is the combination of minimal flavor violation (MFV), in which the Yukawa matrices Y_u and Y_d are the only flavor spurions, with the Jarlskog invariant J = Im(V_ud V_cs V_us^* V_cd^*) as the only CP-odd phase. The leptoquark S has three flavor components S_i which get slightly non-degenerate masses through the spurion Delta_i^j = gamma (Y_d^dag Y_d)_i^j. The baryon asymmetry per decay comes from the interference of tree-level and one-loop propagator diagrams in Fig. 1; the unitarity of the CKM matrix makes the vertex diagrams cancel, leaving only the propagator loop, and the MFV flavor structure conspires so that all imaginary parts collapse to products of J times a real kinematic function of the S_i masses.

What would settle it

A state-of-the-art lattice calculation or a future precision experiment could measure proton decay to K0bar e+ or pi+ nu-bar with couplings at the MFV-predicted strength; a decay rate above the predicted bound would falsify the model. Alternatively, if a future collider or flavor experiment showed that the leptoquark couplings required for baryogenesis have a non-MFV complex phase, the claim that J is the only CP-violating source would be falsified.

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Extended reading notes

Core claim

The central claim is that a scalar leptoquark S charged as (3,1)_{1/3} under the SM gauge group and as a 3_bar_d under the flavor group, with couplings built only from the SM Yukawa spurions (A_ija = $\alpha$ epsilon_ABC (Y_d)_Ai (Y_d)_Bj (Y_u)_Ca, B_i_a = $\beta$ epsilon_ABC epsilon_abc (Y_d^dag)_iA (Y_u^dag)_bB (Y_u^dag)_cC with real $\alpha$ and $\beta$), produces a baryon asymmetry per decay epsilon_i whose CP-violating part is proportional to the Jarlskog invariant J. The one-loop propagator diagrams interfere with the tree diagrams, and the key identity is Im(C^i_{T,ud} $C^{{ik*}}$_{P,ud}) = -8 |$\alpha$|^2 |$\beta$|^2 $y_d^{2}$ $y_s^{2}$ $y_b^{2}$ $y_c^{2}$ $y_t^{4}$ J, up to Levi-Civita factors. Near resonance the kinematic function f_P^ik = $m_i^{2}$ ($m_k^{2}$ - $m_i^{2}$) / (($m_k^{2}$ - $m_i^{2}$)^2 + $m_k^{2}$ $Gamma_k^{2}$) can be of order 8 pi / D_k, giving epsilon_1^max ~ 0.15. The decays preserve B - L, so two cosmological scenarios are needed: either reheating below 130 GeV so sphalerons have decoupled, or adding right-handed neutrinos whose $\Delta$ L = 2 washout converts a B+L asymmetry into a B-L asymmetry before sphalerons turn on.

Load-bearing premise

The paper's central claim that all CP violation comes from the CKM matrix relies on the leptoquark couplings being exactly MFV, namely the specific forms in Eqs. (8)-(9) with real coefficients and the mass matrix Delta_i^j = gamma (Y_d^dag Y_d)_i^j with real gamma; if any other complex flavor spurion enters, new CP phases could appear.

Editorial extensions

If this is right

  • If the central claim is correct, the standard lore that SM CP violation is insufficient for baryogenesis is shown to be false: a new flavor-charged particle built purely from MFV can amplify the CKM phase into an order-one CP asymmetry.
  • The baryogenesis mechanism does not require any time variation of parameters, unlike Mesogenesis, so it can be probed with ordinary particle physics constraints such as proton decay searches.
  • In the low-reheat scenario, the observed Y_B requires m_S roughly 10^11 GeV with T_RH < 130 GeV, and in the high-reheat scenario the required efficiency is only epsilon_i > 10^-7, which is comfortably available in the model.
  • The model is constrained by proton decay: coupling to electrons forces M > 10^14 GeV sqrt(r_alpha r_beta), but coupling dominantly to tau relaxes this to M > 6e9 GeV sqrt(r_alpha r_beta).
  • The baryon asymmetry vanishes if the S_i masses are degenerate (gamma -> 0), providing a new flavor-invariant structure analogous to X_CP in the SM.

Reading between the lines

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

  • The calculation suggests a broader principle: any MFV-preserving extension with flavor-charged heavy particles whose CP-violating couplings are functions of the Yukawa spurious can, in principle, convert J into an asymmetry without an additional source of CP violation, as long as the heavy masses are non-degenerate.
  • If this mechanism is right, the numerical value of Y_B might be viewed as a prediction of the CKM phase combined with whatever MFV-flavored particles exist, rather than a coincidence requiring new CP phases; one could scan the space of representations for the largest achievable emission asymmetry.
  • A natural extension would be to promote S to a full family of leptoquarks in a GUT-like representation, where the flavor structure of the proton decay modes would be correlated with the baryogenesis yield and could be tested by proton lifetime measurements.
  • The high-reheat branch relies on right-handed neutrinos whose Majorana masses erase L; a careful derivation of the full Boltzmann system, including inverse decays and scattering, would be the next step toward a quantitative prediction of Y_B across the parameter space.
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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

1 major / 6 minor

Summary. The paper proposes a baryogenesis mechanism based on a scalar leptoquark S whose MFV-preserving couplings are built entirely from the SM Yukawa spurions, so that the CKM Jarlskog invariant J is the only CP-violating source. The authors compute the one-loop CP asymmetry for S_i decays in App. II, where the vertex contribution vanishes by CKM unitarity and the propagator contribution is proportional to J; near resonance the per-decay asymmetry can reach epsilon_1^max ~ 0.15 with unitarity-saturated couplings. Two cosmological histories are presented: a low-reheat branch in which a long-lived scalar Phi produces S_i after sphaleron decoupling, and a high-reheat branch in which right-handed-neutrino Delta L=2 processes convert an initial B+L asymmetry into B-L before sphalerons equilibrate. Proton-decay constraints are estimated and used to identify viable parameter regions.

Significance. This is a serious proof-of-principle. The calculation in App. II cleanly factorizes kinematic and flavor contributions, explicitly shows the vanishing of the vertex contribution, and reduces the propagator contribution to the Jarlskog invariant. The two cosmological branches are clearly formulated, and the paper includes explicit proton-decay bounds with numerical benchmarks. If the CKM-only CP claim can be fully established in both branches, the model is a genuine counterexample to the common expectation that SM CP violation cannot generate the observed baryon asymmetry without time-varying parameters. The low-reheat branch is the most solid part of the paper and can stand on its own as a demonstration of the mechanism.

major comments (1)
  1. [Sec. IV B and App. III, conditions 1 and 2 after Eq. (31)] The high-reheat branch introduces right-handed neutrinos with Majorana masses to wash out lepton number, but the paper does not demonstrate that this sector can be made CP-conserving while preserving the required Delta L=2 washout. The model explicitly does not impose lepton flavor symmetries (Sec. II after Eq. (7)), and MFV does not constrain the lepton sector. A generic complex right-handed-neutrino Yukawa matrix will produce its own out-of-equilibrium CP asymmetry epsilon_N, which can be comparable to or larger than the value ~10^-7 needed from the leptoquark decays here. Conditions 1 and 2 are asserted, not derived: the text states that the B-L asymmetry from right-handed-neutrino decays is 'negligible' and that lepton-number washout is 'efficient', but no concrete choice of the right-handed-neutrino mass matrix and Yukawa couplings is shown to satisfy both requirements. Without such a demonstration, the abstract's unqualified claim that all CP violation arises from the CKM matrix is not established for this branch. The authors should either prove that a CP-conserving right-handed-neutrino sector with adequate Delta L=2 washout exists, or explicitly frame the high-reheat branch as requiring an additional no-CP assumption and qualify the abstract accordingly.
minor comments (6)
  1. [Eq. (15) and App. II, Eq. (A38)] The baryon-number-weighting convention should be clarified. With the standard SM assignment B(bar-u)=B(bar-d)=-1/3, the difference B_{bar-u^dagger bar-d^dagger} - B_{bar-u bar-e} is -2/3, not 1 as stated in the text near Eq. (27). This rescales all epsilon values by 2/3, which does not change the qualitative conclusions but should be stated explicitly.
  2. [Eq. (10)] The 'unitarity' bounds on alpha and beta should be derived explicitly: the maximal elements of A_ija and B_i^a that saturate max(A)=max(B)=sqrt(4 pi) should be identified, since this fixes the normalization of r_alpha and r_beta used in Fig. 2 and in the proton-decay bounds of Sec. V.
  3. [Sec. IV A] The low-reheat branch relies on a long-lived scalar Phi that dominates the early universe and decays via Phi -> S_i S_i^dagger, but the Phi-S coupling, the Phi mass, its lifetime, and the conditions for Phi domination before BBN are not specified. This is acceptable for a proof of principle, but a minimal Lagrangian for this sector and a check that Phi decays before BBN without introducing new CP phases would strengthen the presentation.
  4. [Eqs. (26)-(27) and Fig. 2] The numerical value epsilon_1^max ~ 0.15 is quoted without propagated uncertainties in J, the CKM elements, and the Yukawa ratios, and without stating whether Fig. 2 is computed with the full D_i or with the approximation D_1 D_k ~ 9 pi^2 r_alpha^4 used in Eq. (27). Please state the input values used and provide at least a rough error estimate, or explicitly label 0.15 as an order-of-magnitude upper bound.
  5. [Sec. V] The proton-decay bounds assume that RG running of the baryon-number-violating Wilson coefficients from M to m_p contributes at most O(1). This is a reasonable simplification for a proof-of-principle, but it should be stated as an assumption rather than a demonstrated result, especially because the low-reheat scenario operates at M values close to the tau-channel bound in Eq. (40).
  6. [Fig. 2] The color scale and the grey proton-decay curves are difficult to read in the low-r, low-gamma region where the viable low-reheat parameter space lies. Consider using contour labels and a logarithmic color scale with explicit epsilon values.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the CKM-induced asymmetry is computed from measured J and Yukawas, and the observed baryon yield is used only as a target for free model parameters.

full rationale

The derivation chain is self-contained against external inputs. The CP asymmetry is built from Eq. (8)-(9) with real α, β and Eq. (13) with real γ, so the only physical CP phase entering the loop is the CKM Jarlskog invariant; App. II derives the interference term proportional to J (Eq. A34) and the vertex loop vanishes by CKM unitarity (Eq. A30). The observed Y_B from Eq. (1) is not inserted into any definition of the model parameters; r_α, r_β, γ, M, and T_RH are free parameters scanned for consistency with the observed yield, which is standard model-building existence argument, not fitting-then-predicting. The high-reheat branch's conditions 1 and 2 are asserted rather than derived, and MFV does not constrain the right-handed-neutrino sector, so the claim that RH-neutrino CP violation is negligible is an unproven assumption; this is a completeness or correctness risk, not circularity. Self-citations ([2], [17], [27], [41], [42]) are contextual or technical; in particular, the [42] subtraction scheme affects only the vertex correction, which contributes zero to the final asymmetry, so the self-citation is not load-bearing. No circular step meets the evidentiary bar of Eq. X = Eq. Y by construction.

Assumptions & free parameters 7 free parameters · 6 assumptions · 3 invented entities

The model introduces one new scalar leptoquark plus, depending on branch, a spectator Phi or right-handed neutrinos. The central asymmetry calculation depends on measured CKM and Yukawa inputs and on the free parameters r_alpha, r_beta, gamma, and M; Y_B is matched by scanning these parameters, so the paper is an existence proof rather than a parameter-free prediction. The MFV postulate, the absence of additional flavor or CP structures, and the assumptions about washout and reheating are assumed, not derived.

free parameters (7)
  • alpha (or r_alpha) = free; scanned in Fig. 2 up to unitarity
    Overall strength of the A_ija MFV coupling in Eq. (8); sets decay widths, proton-decay rates, and the normalization of epsilon_i.
  • beta (or r_beta) = free; scanned in Fig. 2 up to unitarity
    Overall strength of the B_ia coupling in Eq. (9); enters the asymmetry numerator and the width denominator.
  • gamma = free; scanned from about 1e-5 to 1e7
    Mass-splitting parameter in Eq. (13); controls the resonant denominator f_P and must be tuned near resonance to obtain large epsilon_i.
  • M = low-reheat branch M ≲ 1e11 GeV; high-reheat branch M ~ 3e14 GeV
    Common leptoquark mass scale in Eq. (14); bounded from below by proton decay and from above by the need to reproduce Y_B.
  • Phi mass and branching ratios Br_i = 2 m_S < m_Phi; Br_i unspecified
    Low-reheat branch: Phi dominates the early universe and decays to S_i S_i^dagger, Eq. (28)-(29); its Lagrangian and decay properties are not specified.
  • right-handed neutrino mass m_N and Tr(m_nu^dagger m_nu) = m_N ≳ T_S; Tr(m_nu^dagger m_nu) ≲ (0.8 eV)^2
    High-reheat branch: sets the Delta L=2 washout temperature in Eq. (A48) and is chosen so that T_S > T_dec > T_sph.
  • lepton flavor of ebar = e, mu, or tau
    Discrete choice: coupling to tau weakens the proton-decay bound by about four orders of magnitude, Eq. (38)-(40).
assumptions (6)
  • domain assumption Minimal flavor violation: Yu and Yd are the only sources of flavor violation, and all S couplings are G_F singlets built from spurions.
    Invoked in Sec. II around Eq. (6); guarantees no new CP phases, but is a model-building postulate not derived from the SM.
  • ad hoc to paper The S_i mass matrix is diagonal in the down-aligned basis, with splitting Delta_i^j = gamma (Yd_dagger Yd)_i^j and real gamma.
    Eqs. (12)-(14); needed for nonzero and resonant f_P. If other spurions contribute, new phases or flavor structures could enter.
  • domain assumption SM fermions can be treated as massless in the loop calculation, so the amplitudes factorize into flavor coefficients C and kinematic factors A.
    Stated before Eq. (16) and used throughout App. II; breaks down near T ~ m_t, although the decays are at higher scales.
  • domain assumption Right-handed neutrino Majorana masses can provide efficient Delta L=2 washout without generating a competing B-L asymmetry.
    High-reheat branch, condition 1 in Sec. IV B; requires suppressing CP phases in the neutrino sector, which is imposed rather than shown.
  • ad hoc to paper RG running of baryon-number-violating Wilson coefficients from M to m_p contributes at most O(1).
    Stated in Sec. V before Eq. (34); if running is large, the proton-decay mass bounds shift correspondingly.
  • domain assumption The instantaneous-decay approximation describes the Phi-dominated reheating and entropy production in the low-reheat branch.
    Used in Eq. (28) and Eq. (29); a full reheating calculation could change the yield by O(1) factors.
invented entities (3)
  • Scalar leptoquark S with SM charges (3,1)_1/3 and flavor triplet under SU(3)_dbar
    purpose: Carries baryon- and lepton-number-violating MFV interactions whose decays generate the CKM-sourced CP asymmetry.
    No existing experimental evidence for such a leptoquark; predicted proton decay is used as a constraint, not as independent evidence.
  • Long-lived scalar Phi
    purpose: Matter-dominated early universe decays to S_i S_i^dagger in the low-reheat branch, producing a non-thermal S population.
    Introduced in Sec. IV A without a Lagrangian, mass specification, or phenomenological handle.
  • Right-handed neutrinos with Majorana masses
    purpose: High-reheat branch: Delta L=2 washout converts B+L into B-L before sphalerons equilibrate.
    Neutrino masses motivate such states, but the paper adds them ad hoc and assumes negligible CP phases and negligible B-L from their decays.

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Cite this review

Pith. "Pith review of Baryogenesis via the CKM Matrix with Minimal Flavor Violation." pith.science (2026). https://pith.science/paper/SSYPNPFY

@misc{pith2026260805269,
  author       = {Pith},
  title        = {Pith review of: Baryogenesis via the CKM Matrix with Minimal Flavor Violation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SSYPNPFY}},
  note         = {Machine review of arXiv:2608.05269}
}
read the original abstract

It is often claimed Standard Model CP violation is insufficient for baryogenesis. We present a counterexample using minimal flavor violation (MFV) in which all CP-violating effects arise from the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Our scenario involves a leptoquark field with MFV-preserving interactions whose decays to Standard Model particles yield the observed baryon asymmetry in the early universe. Unlike previous efforts to realize baryogenesis through the CP violation of the CKM matrix, our scenario does not require any time-variation of model parameters.

Figures

Figures reproduced from arXiv: 2608.05269 by the authors.

Figure 1
Figure 1. FIG. 1: Leading Feynman diagrams for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Density plots of each baryon-asymmetry efficiency [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1: Conventions used to calculate the kinematic parts of Feynman diagrams for [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗

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Works this paper leans on

50 extracted references · 17 canonical work pages

  1. [1]

    The additionalB−Lasymmetry generated from right-handed neutrino decays is negligible

    work page

  2. [2]

    Lepton number washout is efficient (r L ≪1 where rL is the surviving fraction of depositedLnumber fromSdecays after ∆L= 2 processes take effect). Under these assumptions, the baryon asymmetry is YB ≈ 28 79 κ(1−r L) X i YSi ϵi (TRH ≳m i) (31) 5 10 5 10 2 101 104 107 γ 10 5 10 4 10 3 10 2 10 1 100 rα = rβ 1010 1011 1012 M/GeV = 1013 ϵ1 10 5 10 2 101 104 107...

    work page

  3. [3]

    Aghanimet al.(Planck), Astron

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    arXiv 2020

  4. [4]

    Can the Baryon Asymmetry Arise From Initial Conditions?

    G. Krnjaic, Phys. Rev. D96, 035041 (2017), arXiv:1606.05344 [hep-ph]

    work page Pith review arXiv 2017

  5. [5]

    Can baryon asymmetry be explained by a large initial value before inflation?

    K. Murai, F. Takahashi, M. Yamada, and W. Yin, Phys. Rev. D108, 083518 (2023), arXiv:2307.03049 [astro- ph.CO]

    work page Pith review arXiv 2023

  6. [6]

    A. D. Sakharov, Pisma Zh. Eksp. Teor. Fiz.5, 32 (1967)

    1967

  7. [7]

    Navaset al.(Particle Data Group), Phys

    S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

    2024

  8. [8]

    Jarlskog, Phys

    C. Jarlskog, Phys. Rev. Lett.55, 1039 (1985)

    1985

Show all 50 references
  1. [9]

    Jarlskog, Phys

    C. Jarlskog, Phys. Rev. D35, 1685 (1987)

    1987

  2. [10]

    Alam and S

    Z. Alam and S. P. Martin, Phys. Rev. D107, 013010 (2023), arXiv:2211.08576 [hep-ph]

    2023 arXiv

  3. [11]

    M. B. Gavela, P. Hernandez, J. Orloff, and O. Pene, Mod. Phys. Lett. A9, 795 (1994), arXiv:hep-ph/9312215

    1994 arXiv

  4. [12]

    M. B. Gavela, M. Lozano, J. Orloff, and O. Pene, Nucl. Phys. B430, 345 (1994), arXiv:hep-ph/9406288

    1994 arXiv

  5. [13]

    M. B. Gavela, P. Hernandez, J. Orloff, O. Pene, and C. Quimbay, Nucl. Phys. B430, 382 (1994), arXiv:hep- ph/9406289

    1994

  6. [14]

    Huet and E

    P. Huet and E. Sather, Phys. Rev. D51, 379 (1995), arXiv:hep-ph/9404302

    1995 arXiv

  7. [15]

    Berkooz, Y

    M. Berkooz, Y. Nir, and T. Volansky, Phys. Rev. Lett. 93, 051301 (2004), arXiv:hep-ph/0401012

    2004 arXiv

  8. [16]

    Perez and T

    G. Perez and T. Volansky, Phys. Rev. D72, 103522 (2005), arXiv:hep-ph/0505222

    2005 arXiv

  9. [17]

    Braconi, M.-C

    A. Braconi, M.-C. Chen, G. Gaswint, and G. Gaswint, Phys. Rev. D100, 015032 (2019), arXiv:1810.02522 [hep- ph]

    2019 arXiv

  10. [18]

    G. Elor, M. Escudero, and A. Nelson, Phys. Rev. D99, 035031 (2019), arXiv:1810.00880 [hep-ph]

    2019 arXiv

  11. [19]

    A. E. Nelson and H. Xiao, Phys. Rev. D100, 075002 (2019), arXiv:1901.08141 [hep-ph]

    2019 arXiv

  12. [20]

    Elor and R

    G. Elor and R. McGehee, Phys. Rev. D103, 035005 (2021), arXiv:2011.06115 [hep-ph]

    2021 arXiv

  13. [21]

    Davoudiasl, R

    H. Davoudiasl, R. Houtz, and S. Ipek, (2026), arXiv:2604.27099 [hep-ph]

    2026 arXiv

  14. [22]

    A. J. Buras, P. Gambino, M. Gorbahn, S. Jager, and L. Silvestrini, Phys. Lett. B500, 161 (2001), arXiv:hep- ph/0007085

    2001

  15. [23]

    D’Ambrosio, G

    G. D’Ambrosio, G. F. Giudice, G. Isidori, and A. Strumia, Nucl. Phys. B645, 155 (2002), arXiv:hep- ph/0207036

    2002

  16. [24]

    Cirigliano, G

    V. Cirigliano, G. Isidori, and V. Porretti, Nucl. Phys. B 763, 228 (2007), arXiv:hep-ph/0607068

    2007 arXiv

  17. [25]

    G. C. Branco, A. J. Buras, S. Jager, S. Uhlig, and A. Weiler, JHEP09, 004 (2007), arXiv:hep-ph/0609067

    2007 arXiv

  18. [26]

    Dorˇ sner, S

    I. Dorˇ sner, S. Fajfer, A. Greljo, J. F. Kamenik, and N. Koˇ snik, Phys. Rept.641, 1 (2016), arXiv:1603.04993 [hep-ph]

    2016 arXiv

  19. [27]

    V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, Phys. Lett. B155, 36 (1985)

    1985

  20. [28]

    Baumann, P

    D. Baumann, P. J. Steinhardt, and N. Turok, (2007), arXiv:hep-th/0703250

    2007 arXiv

  21. [29]

    Hooper and G

    D. Hooper and G. Krnjaic, Phys. Rev. D103, 043504 (2021), arXiv:2010.01134 [hep-ph]

    2021 arXiv

  22. [30]

    Bernal, C

    N. Bernal, C. S. Fong, Y. F. Perez-Gonzalez, and J. Turner, Phys. Rev. D106, 035019 (2022), arXiv:2203.08823 [hep-ph]

    2022 arXiv

  23. [31]

    Fukugita and T

    M. Fukugita and T. Yanagida, Phys. Rev. Lett.89, 7 131602 (2002), arXiv:hep-ph/0203194

    2002 arXiv

  24. [32]

    Akeret al.(KATRIN), Science388, adq9592 (2025), arXiv:2406.13516 [nucl-ex]

    M. Akeret al.(KATRIN), Science388, adq9592 (2025), arXiv:2406.13516 [nucl-ex]

    2025

  25. [33]

    Weinberg,Cosmology(2008)

    S. Weinberg,Cosmology(2008)

    2008

  26. [34]

    E. W. Kolb and M. S. Turner,The Early Universe, Vol. 69 (Taylor and Francis, 2019)

    2019

  27. [35]

    Kobayashiet al.(Super-Kamiokande), Phys

    K. Kobayashiet al.(Super-Kamiokande), Phys. Rev. D 72, 052007 (2005), arXiv:hep-ex/0502026

    2005 arXiv

  28. [36]

    J.-S. Yoo, Y. Aoki, P. Boyle, T. Izubuchi, A. Soni, and S. Syritsyn, Phys. Rev. D105, 074501 (2022), arXiv:2111.01608 [hep-lat]

    2022 arXiv

  29. [37]

    W. J. Marciano, Nucl. Phys. B Proc. Suppl.40, 3 (1995)

    1995

  30. [38]

    Heeck and D

    J. Heeck and D. Watkins, JHEP07, 170 (2024), arXiv:2405.18478 [hep-ph]

    2024 arXiv

  31. [39]

    Junget al.(Super-Kamiokande), Phys

    S. Junget al.(Super-Kamiokande), Phys. Rev. D113, 012015 (2026), arXiv:2510.26232 [hep-ex]

    2026

  32. [40]

    M. P. Bento, J. P. Silva, and A. Trautner, JHEP01, 024 (2024), arXiv:2308.00019 [hep-ph]

    2024 arXiv

  33. [41]

    Kajantie, M

    K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Phys. Rev. Lett.77, 2887 (1996), arXiv:hep-ph/9605288

    1996 arXiv

  34. [42]

    D’Onofrio, K

    M. D’Onofrio, K. Rummukainen, and A. Tranberg, Phys. Rev. Lett.113, 141602 (2014), arXiv:1404.3565 [hep-ph]

    2014 arXiv

  35. [43]

    Bigaran, J

    I. Bigaran, J. Isaacson, T. Kim, and K. Tame-Narvaez, Eur. Phys. J. C85, 811 (2025), [Erratum: Eur.Phys.J.C 85, 1260 (2025)], arXiv:2411.08714 [hep-ph]

    2025 arXiv

  36. [44]

    Bigaran, R

    I. Bigaran, R. Capdevilla, and U. Nierste, JHEP05, 123 (2025), arXiv:2408.06501 [hep-ph]

    2025 arXiv

  37. [45]

    D. V. Nanopoulos and S. Weinberg, Phys. Rev. D20, 2484 (1979)

    1979

  38. [46]

    Baryogenesis via the CKM Matrix with Minimal Flavor Violation

    A. Pilaftsis and T. E. J. Underwood, Nucl. Phys. B692, 303 (2004), arXiv:hep-ph/0309342. 1 SUPPLEMENTARY MATERIAL “Baryogenesis via the CKM Matrix with Minimal Flavor Violation” I. INV ARIANTS IN THE ST ANDARD MODEL FRAMEWORK In the SM, it is difficult to generate a baryon asy...

    2004 arXiv

  39. [47]

    The universe is initially reheated to a temperature ofT RH > mi and theS i are in equilibrium with the SM plasma as relativistic species

  40. [48]

    As the universe cools, theS i freeze out atT∼m i/10 and subsequently decay out of equilibrium atT S >10 12 GeV to generate aB+Lasymmetry

  41. [49]

    These interactions freeze out atT dec ∆L=2, which occurs beforeT∼10 12 GeV

    Lepton-violating (but baryon-preserving) interactions are efficient in betweenT S > T >1012 GeV and converts some of the pureB+Lasymmetry into aB−Lasymmetry by washing out lepton number. These interactions freeze out atT dec ∆L=2, which occurs beforeT∼10 12 GeV

  42. [50]

    When sphalerons become active atT sph ∼10 12 GeV, the remainingB+Lis erased and the but theB−L asymmetry of the universe is preserved for all later times. Schematically, the hierarchy of temperatures is TRH ≳T S ≳T dec ∆L=2 ≳T sph,(A40) where the last three of these are determ...

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Reviewed August 8, 2026 · model on record in the stance chip above.