Pith. sign in

REVIEW 3 major objections 4 minor 33 references

Baryogenesis from a Majorana Fermion Coupled to Quarks

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper claims that a Majorana fermion coupled to quark-like fermions through a dimension-six vector-vector interaction can generate the observed baryon asymmetry of the Universe from a baryon-symmetric start, over a mass range from…

desk verdict A legitimate Boltzmann-equation extension of the authors' earlier rate computations, with a novel scattering-dominance result and a useful n-nbar reach overlay, but the central mass-range claim rests on unvalidated fit functions from the companion paper. read the letter →

arxiv 2411.13231 v2 pith:D6J3OUQV submitted 2024-11-20 hep-ph

Shrihari Gopalakrishna , Rakesh Tibrewala This is my paper · ORCID
classification hep-ph
keywords baryogenesisbaryonasymmetryoftheUniverseMajoranafermiondimension-sixeffectiveoperatorBoltzmannequationsneutron-antineutronoscillationCPviolationearly
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

This paper argues that a single effective theory—a Majorana fermion $X$ coupled to quark-like fermions $Q$ through a dimension-six four-fermion vector-vector interaction—can generate the observed baryon asymmetry of the Universe starting from a baryon-symmetric state. The authors set up the Boltzmann equations for the $X$ and net baryon number densities in the expanding early Universe, import the thermally averaged decay and scattering rates from their earlier computation, and solve the equations numerically at nine benchmark points. They find that the observed yield $Y_B \approx 0.85\times10^{-10}$ is reproduced for masses $M_\chi\in(10^4,10^{16})$ GeV with appropriately chosen couplings, and that scattering processes play the dominant role in two of the three benchmark classes. The low-mass end of this region predicts neutron-antineutron oscillation rates that upcoming experiments could test, which is why the claim matters beyond cosmology.

What carries the argument

The load-bearing object is the dimension-six four-fermion vector-vector effective operator $(g/\Lambda^2)(\overline{D^c}\gamma_\mu D)(\bar{X}\gamma^\mu U)$, with a Majorana mass splitting for the fermion $X$ that violates baryon number and supplies the CP-violating phases. The cosmological machinery is the pair of coupled Boltzmann equations for the yield $Y_X=n_X/s$ and $Y_B=n_B/s$, whose collision terms are the thermally averaged rates for decay $X\to QQQ$, scattering $X Q^c\to QQ$, and $\Delta B=2$ scattering $QQQ\to Q^c Q^c Q^c$, together with their conjugate and inverse processes. A CPT-unitarity relation, imported from the earlier study, fixes the sign of the inverse-decay contribution and turns the departure of $Y_X$ from equilibrium into a net baryon number. The terrestrial probe is the neutron-antineutron oscillation rate $\Delta m_{n\bar n}=g^2 s_{\rm eff}^2/(\Lambda^4 M_\chi)\,\langle\bar n|Q_{VV}|n\rangle$, which connects the BAU-compatible parameter region to experiments.

What would settle it

Compute the exact one- and two-loop thermally averaged rates for the decay, scattering, and $\Delta B=2$ channels at the benchmark points and re-solve the Boltzmann equations; if the resulting yield contours move away from $Y_B^{\rm obs}$ by more than the observational precision, the claimed mass range is not robust. Alternatively, a null result from a neutron-antineutron oscillation search reaching the sensitivity the paper associates with $M_\chi\sim 10^4$–$10^6$ GeV would rule out the low-mass branch of the viable parameter space.

Watch

Extended reading notes

Core claim

The central claim is that, beginning from a baryon-antibaryon symmetric early Universe, the decay and scattering of a pseudo-Dirac Majorana fermion $X$ with quark-like partners $Q$ can produce the presently observed baryon asymmetry over a very wide range of mass scales. Solving the coupled Boltzmann equations for $Y_X(x)$ and $Y_B(x)$ with the thermally averaged rates of Ref. [5], the paper exhibits explicit benchmark points where the asymptotic yield equals $Y_B^{\rm obs}\approx 0.85\times10^{-10}$. In benchmark classes BP-A and BP-B the asymmetry builds up mainly through the scattering channel $X\,Q^c\to QQ$; in BP-C, constructed with a suppressed scattering rate, decay $X\to QQQ$ dominates. The paper further derives the induced neutron-antineutron oscillation rate in the viable region and maps the current Super-Kamiokande bound onto the parameter space, showing that the lower mass branch is already being probed.

Load-bearing premise

The load-bearing premise is that the thermally averaged rates imported from the earlier work—especially the CP-violating differences $\Delta\Gamma$ and $\Delta\sigma v$ and the $\Delta B=2$ rate $\Gamma_1$—are represented accurately enough by the fit functions used here. The fits are said only to mimic the magnitude and $x$ dependence, with no uncertainty estimates, and BP-C's $x$-dependence is copied from BP-A; if the true rates differ, the computed baryon yield, the claimed mass range, and the neutron-antineutron reach all shift.

Editorial extensions

If this is right

  • If the central claim is right, the observed baryon asymmetry can be produced by new physics at any mass between roughly $10^4$ and $10^{16}$ GeV, so low-energy experiments, not just high-energy colliders, can test baryogenesis.
  • In the BP-A and BP-B benchmark classes, scattering generates most of the asymmetry; any related theory that keeps only decay channels would underestimate the yield and misidentify the viable parameter region.
  • The low-mass branch, $M_\chi\sim 10^4$–$10^6$ GeV, predicts neutron-antineutron oscillation rates within about three orders of magnitude of the current Super-Kamiokande bound, so next-generation searches have a concrete target.
  • If electroweak sphalerons partially wash out the generated baryon number, the viable parameter contours shift to the $1/w_{\rm tot}$ level, but the mechanism still has regions that reproduce the observed asymmetry.

Reading between the lines

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

  • Because the Boltzmann solutions rely on fit functions that only mimic the loop rates and carry no uncertainty estimates, the claimed mass range should be read as indicative; a direct evaluation of the exact thermally averaged rates is the natural next test.
  • BP-C is constructed by copying BP-A's $x$-dependence with rescaled normalizations, so its 'decay-dominated' conclusion is less independent than the BP-A/BP-B results and should be treated as an illustrative scenario.
  • The neutron-antineutron reach currently uses a Fierz-rearranged scalar-operator lattice matrix element; a direct lattice computation for the vector operator would sharpen or shift the mass reach shown in the paper.
  • The same Boltzmann framework, with the rates replaced, could be applied to other four-fermion operators (for example scalar-scalar interactions), which the paper's model-independent presentation invites.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This paper extends the authors' earlier effective-theory framework for baryogenesis with a Majorana fermion X coupled to quark-like fermions Q via a dimension-six vector-vector four-fermion operator. The authors set up Boltzmann equations for the X yield and the baryon yield, using thermally averaged decay and scattering rates imported from Ref. [5], including X -> QQQ decay, X Qc -> QQ scattering, and Delta B=2 scattering. They linearize the equations for small YB, solve numerically for nine benchmark points (BP-nX with mass scales M_chi = 10^6, 10^9, 10^12 GeV and rate families A, B, C), and choose the coupling g and mass-to-cutoff ratio M_chi/Lambda so that YB/Y_obs = 1. They find the observed BAU can be obtained for M_chi in (10^4, 10^16) GeV, with scattering processes dominant in families A and B and decay dominant in family C. They also translate the viable low-mass region into neutron-antineutron oscillation rates and compare with Super-Kamiokande and future HIBEAM/NNBAR sensitivity.

Significance. If the central numerical claim holds, the paper provides explicit parameter choices in a concrete effective theory for which the observed BAU is reproduced, and it highlights an experimentally testable low-mass window via n-nbar oscillation. The Boltzmann-equation framework is standard, the linearization in YB is appropriate, and the numerical solutions in Figs. 3-6 appear internally consistent. The authors are also transparent that g and M_chi/Lambda are calibrated to YB/Y_obs = 1, which is parameter fitting rather than a derivation from independent inputs; this is not circular. The main significance is therefore conditional on the reliability of the imported rate functions, which are the load-bearing input to every numerical result. The n-nbar oscillation rate provides a genuinely external observable that could falsify the low-mass part of the claimed parameter space, and the emphasis on scattering over decays is a useful contrast to the usual decay-only treatments.

major comments (3)
  1. [Appendix C, Eqs. (33)-(35)] The paper states that the fit functions in Eqs. (33)-(35) "mimic adequately well the magnitude and x dependence" of the rates computed in Ref. [5], but it provides no residuals, validation plots, or uncertainty estimates. Since Delta Gamma and Delta sigma v enter linearly in the source term of Eq. (17), an unquantified error in their normalization or x dependence directly rescales YB and therefore shifts the g and M_chi/Lambda values needed to reach YB/Y_obs = 1. The claimed mass range M_chi in (10^4, 10^16) GeV in Sec. 4.2 is extracted from contours built on these fits, so this is not a cosmetic issue. Please provide a direct comparison of the fit functions to the original computed rates, or give an estimate of the induced error on YB.
  2. [Table 1 and Sec. 4.2 (BP-C)] BP-C is not derived from any loop computation: its Delta Gamma and Delta sigma v normalizations are hand-assigned and its x dependence is copied from BP-A, as stated in Sec. 4.1. The BP-nC families therefore test a toy parameterization rather than the model of Sec. 2, and the statement in the Abstract that "this theory" explains the BAU over M_chi in (10^4, 10^16) GeV includes the 10^4 GeV lower bound coming from BP-nB and BP-nC. Either restrict the central model claim to BP-A and BP-B, or justify BP-C as an independent representative of other related theories and clearly label the BP-nC results as such.
  3. [Eq. (13) and Sec. 5] The sign structure of the source term in Eq. (13), including the imaginary-part and real-intermediate-state cancellations, is imported from Ref. [5] without re-derivation, and the paper notes the sign of the n_X^eq term is opposite to a naive calculation. Given that this sign determines whether the source term has the assumed form, a concise derivation or a reference to the specific equations in Ref. [5] would substantially strengthen the paper. As written, the reader cannot independently verify the most delicate ingredient of the Boltzmann equation.
minor comments (4)
  1. [Sec. 6] There is a typo: "neucleosynthesis" should be "nucleosynthesis", and in Sec. 5 the phrase "washed out significantly due by" should be corrected.
  2. [Fig. 5 and Sec. 4.3] The red kappa_nbar contours are hard to distinguish from the BAU contours in Fig. 5; plotting them in a separate panel or with clearer line styles would improve readability. The text states the same kappa_nbar dependence holds for all three columns, but only the right column is shown; a brief explanation of why would be helpful.
  3. [Appendix B, Eq. (29)] The variable x_b is defined as M/\Lambda only in Appendix B, but it is used earlier in Sec. 4.2. Please define it in the main text or use a consistent notation.
  4. [Sec. 4.2 (BP-1B)] For BP-1B the final YB depends on the initial overdensity delta_X(x_b), and the value delta_X = 8 is chosen to reproduce the observed BAU; this dependence on UV-completion details should be stated prominently when BP-1B is used to support the claimed mass range.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the BAU value is an explicit calibration target, the collision terms come from prior same-author computations with stated assumptions, and the n-nbar observable provides an independent external check.

full rationale

The paper's central numerical claim is a parameter-existence statement, not a prediction: Table 1 states 'These choices all give the observed BAU, i.e. YB(xe)/Yobs_B = 1', and Sec. 4.2 says it solves the BE and 'find[s] for what choices of Mχ, Mχ/Λ, g, we obtain the observed BAU.' The observed asymmetry is therefore a calibration target, and nothing in Eqs. (14)-(17) is set up so that YB=Yobs follows by definition; the equation is a standard coupled BE whose source and washout terms are independent inputs. The CP-violating rates and x-dependence used in the collision terms are imported from Refs. [4,5] (Appendix C, Eqs. (33)-(35)); these are self-citations, but they are computations with stated benchmark assumptions (BP-A, BP-B, pseudo-Dirac limit) that do not contain the target BAU, so the citation is load-bearing but not circular. The fit-function character of Eqs. (33)-(35) is a correctness/uncertainty risk, not a circularity. The n-nbar rate (Eqs. (18)-(19)) uses a lattice matrix element from Ref. [27], providing an external observable that the calibrated region must also satisfy. BP-C is openly constructed ('BP-C has been introduced in the present study to explore a different possibility'), so its decay-dominated asymmetry is a deliberately chosen scenario, not a claimed derivation from the model.

Assumptions & free parameters 8 free parameters · 9 assumptions · 3 invented entities

The calculation rests on many choices inherited from the authors' earlier work or fixed by hand: the effective operator, the pseudo-Dirac mass hierarchy, the dominance of one Majorana state, chemical equilibrium assumptions, numerical rate fits, and initial X abundance. The observed BAU is used to choose g, Mχ/Λ, and rate normalizations, so the model has several internal degrees of freedom; the n-nbar oscillation rate provides the main external handle.

free parameters (8)
  • g (effective coupling of X to Q) = 0.25, 0.008, 0.048, 0.065, 0.009, 0.065, 0.024, 0.022, 0.087 for BP-1A to BP-3C
    Chosen in Table 1 so each benchmark solves to YB/Y_obs = 1; the wide-mass claim holds only for these hand-picked values.
  • Mχ/Λ (mass-to-cutoff ratio) = 1/10 for all except BP-3B with 1/50
    Controls rate normalizations and the n-nbar rate; selected per benchmark point.
  • MQ/Mχ (mass ratio for quark-like fermions) = 1/4 for BP-A, 1/20 for BP-B and BP-C
    Sets phase space and temperature dependence of the rates; not scanned over.
  • δX(xb) (initial X abundance relative to equilibrium) = varied 0.1, 1, 10, 100; nominal 8 for BP-1B
    Free parameter when X is never in thermal equilibrium; final BAU in BP-1B depends on it.
  • BP-C rate rescaling factors = (2/5)σ0v, (5/2)Δσ01v, (1/30)Γ0
    Hand-chosen modifications in Table 1 to generate a decay-dominated benchmark; not derived from the Lagrangian.
  • Fit coefficients in rate parametrizations (Eqs. (33)-(35)) = e.g., 1.7e-6, -1.4e-9, 12.7, -0.04, 0.4 for BP-A
    Fit to the earlier loop calculations; no error bars, and the numerical BAU inherits their uncertainty.
  • αw (sphaleron B+L survival fraction) = unspecified, 0 < αw < 1
    Introduced for partial washout in Sec. 5; not computed, so the main results implicitly assume no additional washout or that wtot is known.
  • seff (effective quark mixing into n-nbar operator) = varied through κ contours in Fig. 5
    Enters the n-nbar rate in Eq. (19); used to evaluate experimental reach, independent of the BAU fit.
assumptions (9)
  • standard math Radiation-dominated FRW expansion with H = 1.66 sqrt(g*) T^2/M_Pl and entropy conservation; standard early-universe thermodynamics
    Used throughout Sec. 3 and Appendix A to convert time evolution to x = Mχ/T and to define yields.
  • domain assumption Relativistic degrees of freedom g* = g*S = 106.75, with only SM content and no right-handed neutrinos
    Taken in Appendix A for the Hubble rate and entropy density; changes slightly if new states are relativistic.
  • ad hoc to paper Only the X2 Majorana mass eigenstate contributes to the asymmetry; the paper labels it X with mass M
    Introduced in Sec. 2 from Ref. [5]'s finding that X2 dominates; simplifies treatment but is an assumption.
  • domain assumption Pseudo-Dirac limit (Mn - Mχ)/Mχ << 1 and MQ/Mχ << 1, with U-D mass difference neglected
    Used in Sec. 3 and Table 1 (MQ/Mχ = 1/4 or 1/20) to reduce to a single Q species and simple chemical potentials.
  • domain assumption QED processes maintain Q-Qbar chemical equilibrium with μQbar = -μQ and Q density e^{μQ/T} n_Q^(0)
    Assumed in Sec. 3 to relate nB to μQ; standard for EM-charged states in equilibrium.
  • ad hoc to paper CPT and unitarity relations, and the sign structure of the inverse-decay and real-intermediate-state contributions in Eq. (13), are taken from Ref. [5] without re-derivation
    Load-bearing for the Boltzmann equations; the paper states these are explained in Ref. [5].
  • ad hoc to paper The fit functions in Eqs. (33)-(35) adequately represent the thermally averaged rates computed in Ref. [5]
    All numerical BAU results depend on these fits; the paper provides no error estimate.
  • domain assumption The Universe starts baryon symmetric, YB(xb)=0, and X is either in thermal equilibrium at xb (δX=1) or has an overdensity from a UV completion
    Initial conditions in Sec. 4.2 and Appendix B; in BP-1B the final asymmetry depends on this choice.
  • domain assumption Baryon number generated on Q transfers faithfully to SM quarks through mixing, with only a parameterized sphaleron washout αw
    Secs. 2 and 5; the main numerical results do not include a specific washout factor.
invented entities (3)
  • Majorana fermion X (X2 mass eigenstate of split Dirac fermion χ) independent evidence
    purpose: Source of baryon number violation and CP violation; decays and scatters to QQQ generating BAU
    Predicted n-nbar oscillation rates in Sec. 4.3 and potential collider signatures give falsifiable handles, though masses and couplings are calibrated to the observed BAU.
  • Quark-like color-triplet fermions Q = {U,D} independent evidence
    purpose: Carry baryon number in the effective theory and mix with SM quarks to transfer the asymmetry
    Mixing leads to n-nbar oscillation and flavor-changing observables; direct searches at future colliders are mentioned.
  • Baryon-number-violating Majorana masses and UV-completion scalars ΦB (B = -2) and Φ1
    purpose: Generate the X Majorana mass and baryon number violation in example UV completions
    No direct experimental handle is developed in this paper; they are consistency examples from Ref. [4] and Appendix B.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Baryogenesis from a Majorana Fermion Coupled to Quarks." pith.science (2026). https://pith.science/paper/D6J3OUQV

@misc{pith2026241113231,
  author       = {Pith},
  title        = {Pith review of: Baryogenesis from a Majorana Fermion Coupled to Quarks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D6J3OUQV}},
  note         = {Machine review of arXiv:2411.13231}
}
abstract

In the theory with a Majorana fermion ($X$) coupled to quark-like fermions ($Q$) via a dimension-six four-fermion vector-vector interaction, we have computed in an earlier work the baryon asymmetry generated in the decay and scattering processes of the $X$ with $Q$. In this work we consider such processes in the expanding early Universe, set up the Boltzmann equations governing the $X$ and net baryon number densities, and numerically solve them in example benchmark points, taking the thermally averaged decay and scattering rates and their temperature dependence from the earlier study. We find that starting from a baryon symmetric Universe at early time, the presently observed baryon asymmetry of the Universe (BAU) can be explained in this theory over a wide range of mass scales, $M_\chi\in (10^4,10^{16})$ GeV for appropriately chosen couplings. We find that scattering processes play a crucial role in generating the baryon asymmetry in this theory. We present our results in a general manner that should be useful not just in our theory, but also in other related theories that share the essential ingredients. Our results should help guide promising ways to probe such new physics in terrestrial experiments. For instance, in regions of parameter space that yield the observed BAU, we present the rate for neutron-antineutron oscillation and discuss the prospects for observing this in upcoming experiments.

Figures

Figures reproduced from arXiv: 2411.13231 by the authors.

Figure 1
Figure 1. The dimensionless thermally averaged decay rate and difference (top row), and scattering [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. The dimensionless thermally averaged decay rate [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. For the benchmark points BP-1X, 2X, 3X (left, middle, right columns), BP-nA, nB, nC [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Contours of the final YB{Y pobsq B for variations about the benchmark points BP-1X, 2X, 3X (left, middle, right columns), and BP-nA, nB, nC (top-two, middle-two, bottom-two rows), with only the parameters along the axes varied. The benchmark point values are shown as t…
Figure 5
Figure 5. Figure 5: Contours of the final YB{Y pobsq B (black lines) for the benchmark points BP-1X, 2X, 3X (left, middle, right columns), and BP-nA, nB, nC (top, middle, bottom rows), with only the parameters along the axes varied. The light shaded region is where the X is decoupled at x…
Figure 6
Figure 6. Figure 6: The final YBpxeq{Y pobsq B for the benchmark points BP-1X, 2X, 3X (left, middle, right columns), for BP-nA, nB, nC (top, middle, bottom rows), with all contributions included (light￾gray), from decay asymmetry only i.e. ∆σ v “ 0 (dashed), scattering asymmetry only i.e.…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

33 extracted references · 5 canonical work pages

  1. [5]

    Baryon Asymmetry from the Decay and Scattering of a Majorana Fermion Pair Coupled to Quarks

    S. Gopalakrishna and R. Tibrewala, “Baryon Asymmetry from the Decay and Scattering of a Majorana Fermion Pair Coupled to Quarks,” [arXiv:2311.14636 [hep-ph]]

    work page Pith review arXiv

  2. [1]

    Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,

    A. D. Sakharov, “Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,” Pisma Zh. Eksp. Teor. Fiz.5, 32-35 (1967) doi:10.1070/PU1991v034n05ABEH002497

    doi:10.1070/pu1991v034n05abeh002497 1967

  3. [2]

    The Early Universe,

    E. W. Kolb and M. S. Turner, “The Early Universe,” Front. Phys. 69, 1-547 (1990) doi:10.1201/9780429492860

    doi:10.1201/9780429492860 1990

  4. [3]

    Baryogenesis,

    J. M. Cline, “Baryogenesis,” [arXiv:hep-ph/0609145 [hep-ph]]

    arXiv

  5. [4]

    Effective Theory for Baryogenesis with a Majorana Fermion Pair Coupled to Quarks

    S. Gopalakrishna and R. Tibrewala, “Effective theory for baryogenesis with a Majorana fermion pair coupled to quarks,” Phys. Rev. D 107, no.11, 115029 (2023) doi:10.1103/PhysRevD.107.115029 [arXiv:2211.12115 [hep-ph]]

    work page Pith review arXiv 2023

  6. [6]

    The role of CP violating scatterings in baryogenesis - case study of the neutron portal,

    I. Baldes, N. F. Bell, A. Millar, K. Petraki and R. R. Volkas, “The role of CP violating scatterings in baryogenesis - case study of the neutron portal,” JCAP 11, 041 (2014) doi:10.1088/1475-7516/2014/11/041 [arXiv:1410.0108 [hep-ph]]

    arXiv 2014

  7. [7]

    LHC Signatures of a Vector-like b’,

    S. Gopalakrishna, T. Mandal, S. Mitra and R. Tibrewala, “LHC Signatures of a Vector-like b’,” Phys. Rev. D 84, 055001 (2011) doi:10.1103/PhysRevD.84.055001 [arXiv:1107.4306 [hep-ph]]

    arXiv 2011

  8. [8]

    LHC Signatures of Warped-space Vectorlike Quarks,

    S. Gopalakrishna, T. Mandal, S. Mitra and G. Moreau, “LHC Signatures of Warped-space Vectorlike Quarks,” JHEP08, 079 (2014) doi:10.1007/JHEP08(2014)079 [arXiv:1306.2656 [hep- ph]]

    arXiv 2014

Show all 33 references
  1. [9]

    Baryogenesis from Oscillations of Charmed or Beautiful Baryons,

    K. Aitken, D. McKeen, T. Neder and A. E. Nelson, “Baryogenesis from Oscillations of Charmed or Beautiful Baryons,” Phys. Rev. D 96, no.7, 075009 (2017) doi:10.1103/PhysRevD.96.075009 [arXiv:1708.01259 [hep-ph]]

    2017 arXiv

  2. [10]

    Planck 2018 results. VI. Cosmological parameters,

    N. Aghanim et al. [Planck], “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641, A6 (2020) [erratum: Astron. Astrophys. 652, C4 (2021)] doi:10.1051/0004- 6361/201833910 [arXiv:1807.06209 [astro-ph.CO]]

    2020 arXiv

  3. [11]

    Review of particle physics,

    S. Navas et al. [Particle Data Group], “Review of particle physics,” Phys. Rev. D 110, no.3, 030001 (2024) doi:10.1103/PhysRevD.110.030001

    2024 doi

  4. [12]

    Baryogenesis Without Grand Unification,

    M. Fukugita and T. Yanagida, “Baryogenesis Without Grand Unification,” Phys. Lett. B 174, 45-47 (1986) doi:10.1016/0370-2693(86)91126-3

    1986 doi

  5. [13]

    Baryogenesis via leptogenesis,

    M. A. Luty, “Baryogenesis via leptogenesis,” Phys. Rev. D 45, 455-465 (1992) doi:10.1103/PhysRevD.45.455

    1992 doi

  6. [14]

    Baryon Number Generation in the Early Universe,

    E. W. Kolb and S. Wolfram, “Baryon Number Generation in the Early Universe,” Nucl. Phys. B 172, 224 (1980) [erratum: Nucl. Phys. B 195, 542 (1982)] doi:10.1016/0550-3213(82)90012-8

    1980 doi

  7. [15]

    CP-noninvariance and baryon asymmetry of the universe,

    V. A. Kuzmin, “CP-noninvariance and baryon asymmetry of the universe,” Pisma Zh. Eksp. Teor. Fiz. 12, no.6, 335-337 (1970)

    1970

  8. [16]

    The Future of Elementary Particle Physics,

    S. L. Glashow, “The Future of Elementary Particle Physics,” NATO Sci. Ser. B 61, 687 (1980) doi:10.1007/978-1-4684-7197-7 15 24

    1980 doi

  9. [17]

    Local B-L Symmetry of Electroweak Interactions, Majorana Neutrinos and Neutron Oscillations,

    R. N. Mohapatra and R. E. Marshak, “Local B-L Symmetry of Electroweak Interactions, Majorana Neutrinos and Neutron Oscillations,” Phys. Rev. Lett.44, 1316-1319 (1980) [erratum: Phys. Rev. Lett. 44, 1643 (1980)] doi:10.1103/PhysRevLett.44.1316

    1980 doi

  10. [18]

    Neutron-Anti-Neutron Oscillation: Theory and Phenomenology,

    R. N. Mohapatra, “Neutron-Anti-Neutron Oscillation: Theory and Phenomenology,” J. Phys. G 36, 104006 (2009) doi:10.1088/0954-3899/36/10/104006 [arXiv:0902.0834 [hep-ph]]

    2009 arXiv

  11. [19]

    Neutron-Antineutron Oscillations: Theoretical Status and Experimental Prospects,

    D. G. Phillips, II, W. M. Snow, K. Babu, S. Banerjee, D. V. Baxter, Z. Berezhiani, M. Bergevin, S. Bhattacharya, G. Brooijmans and L. Castellanos, et al.“Neutron-Antineutron Oscillations: Theoretical Status and Experimental Prospects,” Phys. Rept. 612, 1-45 (2016) doi:10.1016/...

    2016 arXiv

  12. [20]

    Post-Sphaleron Baryogenesis,

    K. S. Babu, R. N. Mohapatra and S. Nasri, “Post-Sphaleron Baryogenesis,” Phys. Rev. Lett. 97, 131301 (2006) doi:10.1103/PhysRevLett.97.131301 [arXiv:hep-ph/0606144 [hep-ph]]

    2006 arXiv

  13. [21]

    Post-Sphaleron Baryogenesis and an Upper Limit on the Neutron-Antineutron Oscillation Time,

    K. S. Babu, P. S. Bhupal Dev, E. C. F. S. Fortes and R. N. Mohapatra, “Post-Sphaleron Baryogenesis and an Upper Limit on the Neutron-Antineutron Oscillation Time,” Phys. Rev. D 87, no.11, 115019 (2013) doi:10.1103/PhysRevD.87.115019 [arXiv:1303.6918 [hep-ph]]

    2013 arXiv

  14. [22]

    Implications of an Improved Neutron- Antineutron Oscillation Search for Baryogenesis: A Minimal Effective Theory Analysis,

    C. Grojean, B. Shakya, J. D. Wells and Z. Zhang, “Implications of an Improved Neutron- Antineutron Oscillation Search for Baryogenesis: A Minimal Effective Theory Analysis,” Phys. Rev. Lett. 121, no.17, 171801 (2018) doi:10.1103/PhysRevLett.121.171801 [arXiv:1806.00011 [hep-ph]]

    2018 arXiv

  15. [23]

    Probing baryogenesis with neutron-antineutron oscillations,

    K. Fridell, J. Harz and C. Hati, “Probing baryogenesis with neutron-antineutron oscillations,” JHEP 11, 185 (2021) doi:10.1007/JHEP11(2021)185 [arXiv:2105.06487 [hep-ph]]

    2021 arXiv

  16. [24]

    Neutron-antineutron oscillation search using a 0.37 megaton-years exposure of Super-Kamiokande,

    K. Abe et al. [Super-Kamiokande], “Neutron-antineutron oscillation search using a 0.37 megaton-years exposure of Super-Kamiokande,” Phys. Rev. D 103, no.1, 012008 (2021) doi:10.1103/PhysRevD.103.012008 [arXiv:2012.02607 [hep-ex]]

    2021

  17. [25]

    On Baryon and Lepton Number Violation,

    P. Fileviez Perez, A. Pocar, K. S. Babu, L. J. Broussard, V. Cirigliano, S. Gardner, J. Heeck, E. Kearns, A. J. Long and S. Raby, et al. “On Baryon and Lepton Number Violation,” [arXiv:2208.00010 [hep-ph]]

    arXiv

  18. [26]

    New high-sensitivity searches for neutrons converting into antineutrons and/or sterile neutrons at the HIBEAM/NNBAR experiment at the European Spallation Source,

    A. Addazi, K. Anderson, S. Ansell, K. S. Babu, J. L. Barrow, D. V. Baxter, P. M. Bentley, Z. Berezhiani, R. Bevilacqua and R. Biondi, et al.“New high-sensitivity searches for neutrons converting into antineutrons and/or sterile neutrons at the HIBEAM/NNBAR experiment at the Eu...

    2021 arXiv

  19. [27]

    Neutron- antineutron oscillations from lattice QCD,

    E. Rinaldi, S. Syritsyn, M. L. Wagman, M. I. Buchoff, C. Schroeder and J. Wasem, “Neutron- antineutron oscillations from lattice QCD,” Phys. Rev. Lett. 122, no.16, 162001 (2019) doi:10.1103/PhysRevLett.122.162001 [arXiv:1809.00246 [hep-lat]]

    2019 arXiv

  20. [28]

    Baryon Number Violation via Majorana Neutrinos in the Early Universe, at the LHC, and Deep Underground,

    H. Davoudiasl and Y. Zhang, “Baryon Number Violation via Majorana Neutrinos in the Early Universe, at the LHC, and Deep Underground,” Phys. Rev. D 92, no.1, 016005 (2015) doi:10.1103/PhysRevD.92.016005 [arXiv:1504.07244 [hep-ph]]

    2015 arXiv

  21. [29]

    Symmetry Breaking Through Bell-Jackiw Anomalies,

    G. ’t Hooft, “Symmetry Breaking Through Bell-Jackiw Anomalies,” Phys. Rev. Lett. 37, 8-11 (1976) doi:10.1103/PhysRevLett.37.8 25

    1976 doi

  22. [30]

    A Saddle Point Solution in the Weinberg-Salam Theory,

    F. R. Klinkhamer and N. S. Manton, “A Saddle Point Solution in the Weinberg-Salam Theory,” Phys. Rev. D 30, 2212 (1984) doi:10.1103/PhysRevD.30.2212

    1984 doi

  23. [31]

    On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe,

    V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, “On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe,” Phys. Lett. B 155, 36 (1985) doi:10.1016/0370-2693(85)91028-7

    1985 doi

  24. [32]

    Cosmological baryon and lepton number in the presence of electroweak fermion number violation,

    J. A. Harvey and M. S. Turner, “Cosmological baryon and lepton number in the presence of electroweak fermion number violation,” Phys. Rev. D 42, 3344-3349 (1990) doi:10.1103/PhysRevD.42.3344

    1990 doi

  25. [33]

    Modern Cosmology,

    S. Dodelson, “Modern Cosmology,” Academic Press, 2003, ISBN 978-0-12-219141-1 26

    2003

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.