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arxiv: 2509.10456 · v1 · submitted 2025-09-12 · ✦ hep-ph · astro-ph.CO· astro-ph.HE· hep-ex· hep-th

Gravitational Wave Signature and the Nature of Neutrino Masses: Majorana, Dirac, or Pseudo-Dirac?

Sudip Jana , Sudip Manna , Vishnu P.K This is my paper

Pith reviewed 2026-05-18 17:10 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COastro-ph.HEhep-exhep-th
keywords gravitational wavesneutrino massesMajorana neutrinosDirac neutrinosB-L symmetrycosmic stringsphase transitionsdomain walls
0
0 comments X

The pith

Different neutrino mass types produce distinct gravitational wave spectra via cosmic strings, phase transitions or domain walls.

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

The paper investigates whether gravitational waves can reveal the fermionic nature of neutrinos as Majorana, Dirac or pseudo-Dirac particles. It examines the minimal B-L gauge extension of the Standard Model, where the spontaneous breaking scale of B-L symmetry governs mass generation while keeping Yukawa couplings natural. Majorana neutrinos with high-scale breaking around 10^14 GeV produce local cosmic strings that generate a flat gravitational wave spectrum across broad frequencies. Dirac neutrinos with low-scale breaking near 10^7 GeV create peaked spectra from first-order phase transitions. Pseudo-Dirac scenarios yield kink-like features in the spectrum from domain wall annihilation.

Core claim

In the minimal B-L gauge extension of the Standard Model the quantum numbers of beyond-Standard-Model states fix the neutrino type while the scale of spontaneous B-L breaking selects the mass-generation mechanism and the associated gravitational wave source, yielding a flat spectrum from local cosmic strings for high-scale Majorana neutrinos, peaked spectra from first-order phase transitions for low-scale Dirac neutrinos, and kink-like features from domain wall annihilation for pseudo-Dirac cases.

What carries the argument

Spontaneous B-L symmetry breaking at a scale set by the neutrino type, which selects between local cosmic string formation, first-order phase transitions or domain wall annihilation as the gravitational wave source.

If this is right

  • A flat gravitational wave spectrum over a wide frequency band would indicate high-scale Majorana neutrino masses with cosmic string production.
  • A peaked gravitational wave spectrum would point to Dirac neutrinos arising from low-scale first-order phase transitions.
  • Kink-like features in the spectrum would suggest pseudo-Dirac neutrinos produced through domain wall annihilation.
  • These signals provide an indirect cosmological probe of lepton number violation or conservation that complements laboratory searches.

Where Pith is reading between the lines

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

  • Space-based interferometers sensitive to the relevant frequency bands could test the predicted spectral shapes in the coming decades.
  • The same symmetry-breaking logic may apply to other global or gauge symmetries beyond the neutrino sector.
  • Gravitational wave data could help prioritize which B-L model variants to search for at future colliders.
  • If confirmed, the connection would tie the smallness of neutrino masses directly to observable features of the early universe.

Load-bearing premise

The minimal B-L gauge extension of the Standard Model accurately captures neutrino mass generation and the dynamics of spontaneous symmetry breaking without dominant contributions from other new physics.

What would settle it

Detection of a gravitational wave spectrum whose shape and frequency range fail to match the flat, peaked or kinked prediction for any of the three neutrino types at the corresponding B-L breaking scale would undermine the proposed link.

Figures

Figures reproduced from arXiv: 2509.10456 by Sudip Jana, Sudip Manna, Vishnu P.K.

Figure 1
Figure 1. Figure 1: Schematic illustration of characteristic [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Characteristic gravitational wave spectra for three distinct nature of neutrino masses: Majorana (blue), Dirac [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Gravitational wave-sensitive vBL scales for effective Yukawa couplings (YD/M) ranging from 10−3 to 1, shown for Dirac, Pseudo-Dirac, and Majorana scenarios (yellow, red, and blue ‘I’s, respectively). GeV and ∼ 106 GeV, respectively) for Yukawa couplings of O(1), see [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The blue, yellow and red solid (dashed) lines repre [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The plot shows the gravitational wave spectra for [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

The fermionic nature of neutrinos and the origin of their tiny masses remain unresolved issues in particle physics, intrinsically connected to lepton number symmetry-conserved for Dirac, violated for Majorana, and effectively pseudo-Dirac when global symmetries invoked for conservation are broken by quantum gravity. We investigate whether distinctive gravitational-wave (GW) signatures can illuminate the nature of neutrino masses and their underlying symmetries, particularly in scenarios where Yukawa couplings are not unnaturally small. To this end, we consider the minimal $B-L$ gauge extension of the Standard Model, where quantum numbers of beyond-SM states determine the neutrino nature and the scale of spontaneous $B-L$ breaking governs mass generation. In this framework, we show that neutrinos yield characteristic GW spectra: Majorana neutrinos with high-scale breaking ($\sim 10^{14}$ GeV) produce local cosmic strings and a flat spectrum across broad frequencies, Dirac neutrinos with low-scale breaking ($\sim 10^{7}$ GeV) generate peaked spectra from first-order phase transitions, and pseudo-Dirac scenarios give kink-like features from domain wall annihilation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims that in the minimal B-L gauge extension of the Standard Model, the fermionic nature of neutrinos (Majorana, Dirac, or pseudo-Dirac) can be distinguished by characteristic gravitational wave signatures arising from the spontaneous breaking of B-L symmetry at scales chosen to generate realistic neutrino masses while keeping Yukawa couplings natural. Specifically, Majorana neutrinos at high scale (~10^{14} GeV) produce local cosmic strings with a flat GW spectrum, Dirac neutrinos at low scale (~10^7 GeV) generate peaked spectra from first-order phase transitions, and pseudo-Dirac scenarios produce kink-like features from domain wall annihilation.

Significance. If the central claims hold, this work could offer a novel cosmological probe of neutrino mass origins and lepton-number symmetries via future GW observations, linking particle-physics model choices to distinct spectral features. The approach is interesting in principle for connecting high-scale symmetry breaking to observable signals, but its significance is limited by unresolved tensions in the model assumptions.

major comments (1)
  1. [Abstract] Abstract: the premise that the framework considers 'scenarios where Yukawa couplings are not unnaturally small' and that 'the scale of spontaneous B-L breaking governs mass generation while keeping Yukawa couplings natural' is contradicted by the Dirac case. For v_{B-L} ∼ 10^7 GeV and m_ν ∼ 0.05 eV the relation m_ν ≈ y v_{B-L} requires y ∼ 5×10^{-18}, which is unnaturally small. This directly undermines the viability of the low-scale Dirac scenario and the claimed first-order phase transition signature as presented.
minor comments (1)
  1. The abstract refers to 'quantum numbers of beyond-SM states' determining neutrino nature; explicit listing of these charges and their relation to the three cases would improve clarity in the main text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for identifying an important inconsistency in the presentation of our assumptions, particularly regarding the Dirac neutrino scenario. We address the major comment below and agree that revisions to the abstract and related discussion are warranted to avoid overstating the naturalness of Yukawa couplings across all cases.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the premise that the framework considers 'scenarios where Yukawa couplings are not unnaturally small' and that 'the scale of spontaneous B-L breaking governs mass generation while keeping Yukawa couplings natural' is contradicted by the Dirac case. For v_{B-L} ∼ 10^7 GeV and m_ν ∼ 0.05 eV the relation m_ν ≈ y v_{B-L} requires y ∼ 5×10^{-18}, which is unnaturally small. This directly undermines the viability of the low-scale Dirac scenario and the claimed first-order phase transition signature as presented.

    Authors: We agree with the referee that the low-scale Dirac case is in tension with the stated premise. For v_{B-L} ∼ 10^7 GeV and m_ν ∼ 0.05 eV, the required Yukawa coupling is indeed y ∼ 5×10^{-18}, which is unnaturally small. The manuscript selects this scale specifically to enable a first-order phase transition in the B-L sector (producing a peaked GW spectrum), but we did not adequately qualify that this choice sacrifices the naturalness condition applied to the other scenarios. The Majorana case at ∼10^{14} GeV permits O(1) Yukawas via the seesaw mechanism, and the pseudo-Dirac case similarly allows more natural parameters; the Dirac case is presented as a contrasting phenomenological possibility rather than one satisfying the same naturalness criterion. We will revise the abstract to explicitly distinguish the cases, remove or qualify the blanket claim of 'keeping Yukawa couplings natural,' and add a clarifying paragraph in the introduction and model section explaining the trade-off for the Dirac scenario while retaining the GW signature analysis as an exploratory result. revision: yes

Circularity Check

1 steps flagged

GW spectra determined by scale choices selected to match neutrino masses

specific steps
  1. fitted input called prediction [Abstract]
    "Majorana neutrinos with high-scale breaking (∼10^{14} GeV) produce local cosmic strings and a flat spectrum across broad frequencies, Dirac neutrinos with low-scale breaking (∼10^{7} GeV) generate peaked spectra from first-order phase transitions, and pseudo-Dirac scenarios give kink-like features from domain wall annihilation."

    The quoted breaking scales are selected to produce realistic neutrino masses (high-scale seesaw for Majorana with natural Yukawas; low-scale for Dirac), so the associated GW spectra are statistically forced by these input choices rather than emerging as novel predictions from the model equations.

full rationale

The paper's central claim links neutrino type to distinct GW signatures via the B-L breaking scale in the minimal extension. However, the specific scales (∼10^14 GeV for Majorana, ∼10^7 GeV for Dirac) are chosen to reproduce realistic neutrino masses under the stated natural-Yukawa condition. This makes the resulting spectra (flat from strings, peaked from FOPT) direct consequences of the input scale selections rather than independent first-principles outputs. The derivation therefore reduces partially to the fitted inputs, though the overall framework retains some independent content in mapping quantum numbers to symmetry breaking patterns. No self-citation load-bearing or self-definitional steps are evident from the provided text.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the B-L extension framework and the chosen breaking scales that set both neutrino masses and the GW source type.

free parameters (1)
  • B-L breaking scale
    High scale ~10^14 GeV for Majorana and low scale ~10^7 GeV for Dirac are selected to generate observed neutrino masses without unnaturally small Yukawas.
axioms (1)
  • domain assumption Quantum numbers in the minimal B-L extension determine whether neutrinos are Majorana, Dirac or pseudo-Dirac.
    Invoked to tie spontaneous symmetry breaking directly to the neutrino mass mechanism.

pith-pipeline@v0.9.0 · 5741 in / 1333 out tokens · 40730 ms · 2026-05-18T17:10:10.131277+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages · 33 internal anchors

  1. [1]

    Gcn circular 38679

    “Gcn circular 38679.” https://gcn.nasa.gov/circulars/38679

    work page

  2. [2]

    Neutrinoless Double beta Decay in SU(2) x U(1) Theories,

    J. Schechter and J. W. F. Valle, “Neutrinoless Double beta Decay in SU(2) x U(1) Theories,”Phys. Rev. D25 (1982) 2951

    work page 1982

  3. [3]

    Neutrinoless double beta decay without vacuum Majorana neutrino mass,

    L. Gr´ af, S. Jana, O. Scholer, and N. Volmer, “Neutrinoless double beta decay without vacuum Majorana neutrino mass,”Phys. Lett. B859(2024) 139111,arXiv:2312.15016 [hep-ph]

    work page arXiv 2024

  4. [4]

    On the Quantitative Impact of the Schechter-Valle Theorem

    M. Duerr, M. Lindner, and A. Merle, “On the Quantitative Impact of the Schechter-Valle Theorem,” JHEP06(2011) 091,arXiv:1105.0901 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  5. [5]

    Addressing the Majorana vs. Dirac Question with Neutrino Decays

    A. B. Balantekin, A. de Gouvˆ ea, and B. Kayser, “Addressing the Majorana vs. Dirac Question with Neutrino Decays,”Phys. Lett. B789(2019) 488–495, arXiv:1808.10518 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [6]

    Distinguishing Dirac vs. Majorana neutrinos: a cosmological probe,

    B. Hernandez-Molinero, R. Jimenez, and C. Pena-Garay, “Distinguishing Dirac vs. Majorana neutrinos: a cosmological probe,”JCAP08no. 08, (2022) 038,arXiv:2205.00808 [hep-ph]

    work page arXiv 2022

  7. [7]

    Dirac and Majorana neutrino signatures of primordial black holes,

    C. Lunardini and Y. F. Perez-Gonzalez, “Dirac and Majorana neutrino signatures of primordial black holes,”JCAP08(2020) 014,arXiv:1910.07864 [hep-ph]

    work page arXiv 2020

  8. [8]

    Exploiting a future galactic supernova to probe neutrino magnetic moments,

    S. Jana, Y. P. Porto-Silva, and M. Sen, “Exploiting a future galactic supernova to probe neutrino magnetic moments,”JCAP09(2022) 079,arXiv:2203.01950 [hep-ph]

    work page arXiv 2022

  9. [9]

    Resonances of Supernova Neutrinos in Twisting Magnetic Fields,

    S. Jana and Y. Porto, “Resonances of Supernova Neutrinos in Twisting Magnetic Fields,”Phys. Rev. Lett.132no. 10, (2024) 101005,arXiv:2303.13572 [hep-ph]

    work page arXiv 2024

  10. [10]

    Signatures of quasi-Dirac neutrinos in diffuse high-energy astrophysical neutrino data,

    K. Carloni, Y. Porto, C. A. Arg¨ uelles, P. S. B. Dev, and S. Jana, “Signatures of quasi-Dirac neutrinos in diffuse high-energy astrophysical neutrino data,” arXiv:2503.19960 [hep-ph]

    work page arXiv

  11. [11]

    Analog of the Michel Parameter for Neutrino - Electron Scattering: A Test for Majorana Neutrinos,

    S. P. Rosen, “Analog of the Michel Parameter for Neutrino - Electron Scattering: A Test for Majorana Neutrinos,”Phys. Rev. Lett.48(1982) 842

    work page 1982

  12. [12]

    Distinguishing between Dirac and Majorana neutrinos in the presence of general interactions

    W. Rodejohann, X.-J. Xu, and C. E. Yaguna, “Distinguishing between Dirac and Majorana neutrinos in the presence of general interactions,”JHEP05 (2017) 024,arXiv:1702.05721 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  13. [13]

    Shining Light on the Mass Scale and Nature of Neutrinos with $e\gamma \to e\nu\overline{\nu}$

    J. M. Berryman, A. de Gouvˆ ea, K. J. Kelly, and M. Schmitt, “Shining light on the mass scale and nature of neutrinos witheγ→eν ν,”Phys. Rev. D98no. 1, (2018) 016009,arXiv:1805.10294 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    Different Varieties of Massive Dirac Neutrinos,

    L. Wolfenstein, “Different Varieties of Massive Dirac Neutrinos,”Nucl. Phys. B186(1981) 147–152

    work page 1981

  15. [15]

    On Pseudodirac Neutrinos, Neutrino Oscillations and Neutrinoless Double beta Decay,

    S. T. Petcov, “On Pseudodirac Neutrinos, Neutrino Oscillations and Neutrinoless Double beta Decay,” Phys. Lett. B110(1982) 245–249

    work page 1982

  16. [16]

    Lepton Number Violation With Quasi Dirac Neutrinos,

    J. W. F. Valle and M. Singer, “Lepton Number Violation With Quasi Dirac Neutrinos,”Phys. Rev. D 28(1983) 540

    work page 1983

  17. [17]

    Pseudo-Dirac Scenario for Neutrino Oscillations

    M. Kobayashi and C. S. Lim, “Pseudo Dirac scenario for neutrino oscillations,”Phys. Rev. D64(2001) 013003,arXiv:hep-ph/0012266

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  18. [18]

    µ→eγat a Rate of One Out of 10 9 Muon Decays?,

    P. Minkowski, “µ→eγat a Rate of One Out of 10 9 Muon Decays?,”Phys. Lett. B67(1977) 421–428

    work page 1977

  19. [19]

    Horizontal gauge symmetry and masses of neutrinos,

    T. Yanagida, “Horizontal gauge symmetry and masses of neutrinos,”Conf. Proc. C7902131(1979) 95–99

    work page 1979

  20. [20]

    Neutrino Mass and Spontaneous Parity Nonconservation,

    R. N. Mohapatra and G. Senjanovic, “Neutrino Mass and Spontaneous Parity Nonconservation,”Phys. Rev. Lett.44(1980) 912

    work page 1980

  21. [21]

    Complex Spinors and Unified Theories

    M. Gell-Mann, P. Ramond, and R. Slansky, “Complex Spinors and Unified Theories,”Conf. Proc. C790927 (1979) 315–321,arXiv:1306.4669 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1979

  22. [22]

    The Future of Elementary Particle Physics,

    S. L. Glashow, “The Future of Elementary Particle Physics,”NATO Sci. Ser. B61(1980) 687

    work page 1980

  23. [23]

    Gauging U(1) symmetries and the number of right-handed neutrinos

    J. C. Montero and V. Pleitez, “Gauging U(1) symmetries and the number of right-handed neutrinos,” Phys. Lett. B675(2009) 64–68,arXiv:0706.0473 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    Schizophrenic active neutrinos and exotic sterile neutrinos

    A. C. B. Machado and V. Pleitez, “Schizophrenic active neutrinos and exotic sterile neutrinos,”Phys. Lett. B 698(2011) 128–130,arXiv:1008.4572 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  25. [25]

    Quasi-Dirac neutrinos in a model with local $B-L$ symmetry

    A. C. B. Machado and V. Pleitez, “Quasi-Dirac neutrinos in a model with local B - L symmetry,”J. Phys. G40(2013) 035002,arXiv:1105.6064 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  26. [26]

    Dirac or Inverse Seesaw Neutrino Masses with $B-L$ Gauge Symmetry and $S_3$ Flavour Symmetry

    E. Ma and R. Srivastava, “Dirac or inverse seesaw neutrino masses withB−Lgauge symmetry andS 3 flavor symmetry,”Phys. Lett. B741(2015) 217–222, arXiv:1411.5042 [hep-ph]. 9

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  27. [27]

    Gauge $B-L$ Model with Residual $Z_3$ Symmetry

    E. Ma, N. Pollard, R. Srivastava, and M. Zakeri, “Gauge B−LModel with ResidualZ 3 Symmetry,”Phys. Lett. B750(2015) 135–138,arXiv:1507.03943 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  28. [28]

    Minimal radiative Dirac neutrino mass models

    J. Calle, D. Restrepo, C. E. Yaguna, and ´O. Zapata, “Minimal radiative Dirac neutrino mass models,”Phys. Rev. D99no. 7, (2019) 075008,arXiv:1812.05523 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  29. [29]

    Simplest Radiative Dirac Neutrino Mass Models

    S. Saad, “Simplest Radiative Dirac Neutrino Mass Models,”Nucl. Phys. B943(2019) 114636, arXiv:1902.07259 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  30. [30]

    Minimal realizations of Dirac neutrino mass from generic one-loop and two-loop topologies atd= 5,

    S. Jana, P. K. Vishnu, and S. Saad, “Minimal realizations of Dirac neutrino mass from generic one-loop and two-loop topologies atd= 5,”JCAP04 (2020) 018,arXiv:1910.09537 [hep-ph]

    work page arXiv 2020

  31. [31]

    Pseudo-Dirac Neutrinos in the New Standard Model

    A. de Gouvea, W.-C. Huang, and J. Jenkins, “Pseudo-Dirac Neutrinos in the New Standard Model,” Phys. Rev. D80(2009) 073007,arXiv:0906.1611 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  32. [32]

    Revisiting pseudo-Dirac neutrino scenario after recent solar neutrino data,

    S. Ansarifard and Y. Farzan, “Revisiting pseudo-Dirac neutrino scenario after recent solar neutrino data,” Phys. Rev. D107no. 7, (2023) 075029, arXiv:2211.09105 [hep-ph]

    work page arXiv 2023

  33. [33]

    Testing the Seesaw Mechanism and Leptogenesis with Gravitational Waves,

    J. A. Dror, T. Hiramatsu, K. Kohri, H. Murayama, and G. White, “Testing the Seesaw Mechanism and Leptogenesis with Gravitational Waves,”Phys. Rev. Lett.124no. 4, (2020) 041804,arXiv:1908.03227 [hep-ph]

    work page arXiv 2020

  34. [34]

    Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories,

    S. F. King, S. Pascoli, J. Turner, and Y.-L. Zhou, “Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories,”Phys. Rev. Lett.126no. 2, (2021) 021802, arXiv:2005.13549 [hep-ph]

    work page arXiv 2021

  35. [35]

    Gravitational waves from breaking of an extraU(1) inSO(10) grand unification,

    N. Okada, O. Seto, and H. Uchida, “Gravitational waves from breaking of an extraU(1) inSO(10) grand unification,”PTEP2021no. 3, (2021) 033B01, arXiv:2006.01406 [hep-ph]

    work page arXiv 2021

  36. [36]

    Confronting SO(10) GUTs with proton decay and gravitational waves,

    S. F. King, S. Pascoli, J. Turner, and Y.-L. Zhou, “Confronting SO(10) GUTs with proton decay and gravitational waves,”JHEP10(2021) 225, arXiv:2106.15634 [hep-ph]

    work page arXiv 2021

  37. [37]

    A predictive and testable unified theory of fermion masses, mixing and leptogenesis,

    B. Fu, S. F. King, L. Marsili, S. Pascoli, J. Turner, and Y.-L. Zhou, “A predictive and testable unified theory of fermion masses, mixing and leptogenesis,”JHEP11 (2022) 072,arXiv:2209.00021 [hep-ph]

    work page arXiv 2022

  38. [38]

    Gravitational wave pathway to testable leptogenesis,

    A. Dasgupta, P. S. B. Dev, A. Ghoshal, and A. Mazumdar, “Gravitational wave pathway to testable leptogenesis,”Phys. Rev. D106no. 7, (2022) 075027, arXiv:2206.07032 [hep-ph]

    work page arXiv 2022

  39. [39]

    Toward distinguishing Dirac from Majorana neutrino mass with gravitational waves,

    S. F. King, D. Marfatia, and M. H. Rahat, “Toward distinguishing Dirac from Majorana neutrino mass with gravitational waves,”Phys. Rev. D109no. 3, (2024) 035014,arXiv:2306.05389 [hep-ph]

    work page arXiv 2024

  40. [40]

    More accurate gravitational wave backgrounds from cosmic strings,

    J. M. Wachter, K. D. Olum, and J. J. Blanco-Pillado, “More accurate gravitational wave backgrounds from cosmic strings,”arXiv:2411.16590 [gr-qc]

    work page arXiv

  41. [41]

    Gravitational waves from cosmic strings for pedestrians,

    K. Schmitz and T. Schr¨ oder, “Gravitational waves from cosmic strings for pedestrians,”arXiv:2412.20907 [astro-ph.CO]

    work page arXiv

  42. [42]

    Stochastic gravitational wave background from smoothed cosmic string loops

    J. J. Blanco-Pillado and K. D. Olum, “Stochastic gravitational wave background from smoothed cosmic string loops,”Phys. Rev. D96no. 10, (2017) 104046, arXiv:1709.02693 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  43. [43]

    Gravitational radiation from cosmic strings,

    A. Vilenkin, “Gravitational radiation from cosmic strings,”Phys. Lett. B107(1981) 47–50

    work page 1981

  44. [44]

    Vilenkin and E

    A. Vilenkin and E. P. S. Shellard,Cosmic Strings and Other Topological Defects. Cambridge University Press, 7, 2000

    work page 2000

  45. [45]

    PTArcade,

    A. Mitridate, D. Wright, R. von Eckardstein, T. Schr¨ oder, J. Nay, K. Olum, K. Schmitz, and T. Trickle, “PTArcade,”arXiv:2306.16377 [hep-ph]

    work page arXiv

  46. [46]

    Gravitational Radiation from Cosmic Strings,

    T. Vachaspati and A. Vilenkin, “Gravitational Radiation from Cosmic Strings,”Phys. Rev. D31 (1985) 3052

    work page 1985

  47. [47]

    Unveiling the gravitational universe atµ-Hz frequencies,

    A. Sesanaet al., “Unveiling the gravitational universe atµ-Hz frequencies,”Exper. Astron.51no. 3, (2021) 1333–1383,arXiv:1908.11391 [astro-ph.IM]. [49]LISACollaboration, P. Amaro-Seoaneet al., “Laser Interferometer Space Antenna,”arXiv:1702.00786 [astro-ph.IM]

    work page arXiv 2021

  48. [48]

    Current status of space gravitational wave antenna DECIGO and B-DECIGO

    S. Kawamuraet al., “Current status of space gravitational wave antenna DECIGO and B-DECIGO,” PTEP2021no. 5, (2021) 05A105,arXiv:2006.13545 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  49. [49]

    Detecting a gravitational-wave background with next-generation space interferometers

    H. Kudoh, A. Taruya, T. Hiramatsu, and Y. Himemoto, “Detecting a gravitational-wave background with next-generation space interferometers,”Phys. Rev. D 73(2006) 064006,arXiv:gr-qc/0511145

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  50. [50]

    Laser interferometry for the big bang observer,

    G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner, and E. S. Phinney, “Laser interferometry for the big bang observer,”Class. Quant. Grav.23(2006) 4887–4894. [Erratum: Class.Quant.Grav. 23, 7361 (2006)]. [53]AEDGECollaboration, Y. A. El-Neajet al., “AEDGE: Atomic Experiment for Dark Matter and Gravity Exploration in Space,”EPJ Quant. Technol.7 (2020) ...

    work page arXiv 2006

  51. [51]

    Pushing towards the ET sensitivity using 'conventional' technology

    S. Hild, S. Chelkowski, and A. Freise, “Pushing towards the ET sensitivity using ’conventional’ technology,” arXiv:0810.0604 [gr-qc]. [55]LIGO ScientificCollaboration, B. P. Abbottet al., “Exploring the Sensitivity of Next Generation Gravitational Wave Detectors,”Class. Quant. Grav.34 no. 4, (2017) 044001,arXiv:1607.08697 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  52. [52]

    AION: An Atom Interferometer Observatory and Network,

    L. Badurinaet al., “AION: An Atom Interferometer Observatory and Network,”JCAP05(2020) 011, arXiv:1911.11755 [astro-ph.CO]

    work page arXiv 2020

  53. [53]

    Gravitational wave astronomy with the SKA

    G. Janssenet al., “Gravitational wave astronomy with the SKA,”PoSAASKA14(2015) 037, arXiv:1501.00127 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  54. [54]

    The International Pulsar Timing Array second data release: Search for an isotropic gravitational wave background,

    J. Antoniadiset al., “The International Pulsar Timing Array second data release: Search for an isotropic gravitational wave background,”Mon. Not. Roy. Astron. Soc.510no. 4, (2022) 4873–4887, arXiv:2201.03980 [astro-ph.HE]. [59]NANOGravCollaboration, G. Agazieet al., “The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background,”Astrophys. J. ...

    work page arXiv 2022

  55. [55]

    However, to justify CSs as the true source of this violins we have to wait for more data

    Particularly in [61], the working group mentioned about this LCSs as a potential source of this NG15 violins. However, to justify CSs as the true source of this violins we have to wait for more data

    work page

  56. [56]

    Gravitational waves from the minimal gauged $U(1)_{B-L}$ model

    T. Hasegawa, N. Okada, and O. Seto, “Gravitational waves from the minimal gaugedU(1) B−L model,”Phys. Rev. D99no. 9, (2019) 095039,arXiv:1904.03020 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  57. [57]

    Supercooled dark scalar phase transitions explanation of NANOGrav data,

    F. Costa, J. Hoefken Zink, M. Lucente, S. Pascoli, and S. Rosauro-Alcaraz, “Supercooled dark scalar phase transitions explanation of NANOGrav data,”Phys. Lett. B868(2025) 139634,arXiv:2501.15649 [hep-ph]

    work page arXiv 2025

  58. [58]

    The Effective potential at finite temperature in the Standard Model,

    M. E. Carrington, “The Effective potential at finite temperature in the Standard Model,”Phys. Rev. D45 (1992) 2933–2944

    work page 1992

  59. [59]

    Gravitational waves from the sound of a first order phase transition

    M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, “Gravitational waves from the sound of a first order phase transition,”Phys. Rev. Lett.112 (2014) 041301,arXiv:1304.2433 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  60. [60]

    Gravitational Radiation from First-Order Phase Transitions

    M. Kamionkowski, A. Kosowsky, and M. S. Turner, “Gravitational radiation from first order phase transitions,”Phys. Rev. D49(1994) 2837–2851, arXiv:astro-ph/9310044

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  61. [61]

    CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields

    C. L. Wainwright, “CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields,”Comput. Phys. Commun.183(2012) 2006–2013,arXiv:1109.4189 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  62. [62]

    Gravitational wave energy budget in strongly supercooled phase transitions

    J. Ellis, M. Lewicki, J. M. No, and V. Vaskonen, “Gravitational wave energy budget in strongly supercooled phase transitions,”JCAP06(2019) 024, arXiv:1903.09642 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  63. [63]

    Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions

    C. Capriniet al., “Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions,”JCAP04(2016) 001, arXiv:1512.06239 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  64. [64]

    Energy Budget of Cosmological First-order Phase Transitions

    J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, “Energy Budget of Cosmological First-order Phase Transitions,”JCAP06(2010) 028, arXiv:1004.4187 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  65. [65]

    Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories,

    H.-K. Guo, K. Sinha, D. Vagie, and G. White, “Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories,”JCAP01(2021) 001,arXiv:2007.08537 [hep-ph]

    work page arXiv 2021

  66. [66]

    However, the FOPT could be affected depending on the value ofλ sσ (and may occur for different benchmark values of the model parameters compare to theλ sσ = 0 benchmarks)

    If we introduceλ sσ(S∗S)σ 2 term in the Lagrangian, similar DW-phenomenology will be there as like the λsσ = 0 scenario. However, the FOPT could be affected depending on the value ofλ sσ (and may occur for different benchmark values of the model parameters compare to theλ sσ = 0 benchmarks). In addition, since vEW ≪v S, vσ, we are ignoring all interaction...

    work page

  67. [67]

    Planck 2013 results. XVI. Cosmological parameters

    Y. B. Zeldovich, I. Y. Kobzarev, and L. B. Okun, “Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry,”Zh. Eksp. Teor. Fiz. 67(1974) 3–11. [75]PlanckCollaboration, P. A. R. Adeet al., “Planck 2013 results. XVI. Cosmological parameters,”Astron. Astrophys.571(2014) A16,arXiv:1303.5076 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 1974

  68. [68]

    Detecting gravitational waves from cosmological phase transitions with LISA: an update,

    C. Capriniet al., “Detecting gravitational waves from cosmological phase transitions with LISA: an update,” JCAP03(2020) 024,arXiv:1910.13125 [astro-ph.CO]

    work page arXiv 2020

  69. [69]

    Gravitational Waves from Collapsing Domain Walls

    T. Hiramatsu, M. Kawasaki, and K. Saikawa, “Gravitational Waves from Collapsing Domain Walls,” JCAP05(2010) 032,arXiv:1002.1555 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  70. [70]

    Gravitational waves from domain walls in Pulsar Timing Array datasets,

    R. Z. Ferreira, A. Notari, O. Pujolas, and F. Rompineve, “Gravitational waves from domain walls in Pulsar Timing Array datasets,”JCAP02(2023) 001, arXiv:2204.04228 [astro-ph.CO]

    work page arXiv 2023

  71. [71]

    A review of gravitational waves from cosmic domain walls

    K. Saikawa, “A review of gravitational waves from cosmic domain walls,”Universe3no. 2, (2017) 40, arXiv:1703.02576 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  72. [72]

    [40], which associates a kink-like gravitational wave spectrum with the Dirac neutrino scenario

    We disagree with the conclusion of Ref. [40], which associates a kink-like gravitational wave spectrum with the Dirac neutrino scenario. We show that such a feature more naturally arises in the pseudo-Dirac case, where tiny Majorana masses are generated via Planck-suppressed operators from quantum gravity. In contrast, a genuinely Dirac scenario in our fr...

    work page

  73. [73]

    The Effective Potential and First-Order Phase Transitions: Beyond Leading Order

    P. B. Arnold and O. Espinosa, “The Effective potential and first order phase transitions: Beyond leading-order,”Phys. Rev. D47(1993) 3546, arXiv:hep-ph/9212235. [Erratum: Phys.Rev.D 50, 6662 (1994)]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  74. [74]

    Finite temperature field theory and phase transitions

    M. Quiros, “Finite temperature field theory and phase transitions,” inICTP Summer School in High-Energy Physics and Cosmology, pp. 187–259. 1, 1999. arXiv:hep-ph/9901312

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  75. [75]

    Model-independent energy budget of cosmological first-order phase transitions—A sound argument to go beyond the bag model,

    F. Giese, T. Konstandin, and J. van de Vis, “Model-independent energy budget of cosmological first-order phase transitions—A sound argument to go beyond the bag model,”JCAP07no. 07, (2020) 057, arXiv:2004.06995 [astro-ph.CO]

    work page arXiv 2020

  76. [76]

    Cosmological phase transitions: From perturbative particle physics to gravitational waves,

    P. Athron, C. Bal´ azs, A. Fowlie, L. Morris, and L. Wu, “Cosmological phase transitions: From perturbative particle physics to gravitational waves,”Prog. Part. Nucl. Phys.135(2024) 104094,arXiv:2305.02357 [hep-ph]

    work page arXiv 2024

  77. [77]

    Bubble nucleation in first order inflation and other cosmological phase transitions,

    M. S. Turner, E. J. Weinberg, and L. M. Widrow, “Bubble nucleation in first order inflation and other cosmological phase transitions,”Phys. Rev. D46(1992) 2384–2403

    work page 1992

  78. [78]

    The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition

    C. Caprini, R. Durrer, and G. Servant, “The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition,”JCAP12(2009) 024,arXiv:0909.0622 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  79. [79]

    Gravitational waves from the first order phase transition of the Higgs field at high energy scales

    R. Jinno, K. Nakayama, and M. Takimoto, “Gravitational waves from the first order phase transition of the Higgs field at high energy scales,” Phys. Rev. D93no. 4, (2016) 045024, arXiv:1510.02697 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016