pith. sign in

arxiv: 2606.08142 · v1 · pith:7OAHODF3new · submitted 2026-06-06 · ✦ hep-ph · astro-ph.CO· gr-qc· hep-th

A New Route to the Annihilation of Multi-Wall String Topological Configurations

Utsav Atta , Tathagata Ghosh , Sudip Manna This is my paper

Pith reviewed 2026-06-27 19:36 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qchep-th
keywords domain wallscosmic stringsmajoron modelright-handed neutrinosgravitational effectsbias termannihilation mechanismcosmological domain wall problem
0
0 comments X

The pith

Small bare masses of right-handed neutrinos generate a bias that annihilates domain-wall networks attached to cosmic strings.

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

Global U(1) symmetries in beyond-Standard-Model theories are expected to be broken by gravity to a discrete subgroup, producing networks of cosmic strings with attached multiple domain walls. These networks are problematic because the walls scale slowly and can come to dominate the universe's energy density, conflicting with Big Bang Nucleosynthesis bounds. The paper shows that when right-handed neutrinos carry small bare mass terms, radiative corrections from those masses produce a temperature-dependent bias that drives annihilation of the walls. A sympathetic reader would care because the mechanism resolves the domain-wall problem inside the simplest global-symmetry setup without extra fields or tunings. The argument is worked out explicitly in a majoron model.

Core claim

In a majoron framework where gravitational effects reduce a global U(1) to a discrete subgroup, a wall-string network forms. The small bare masses of the right-handed neutrinos induce radiative corrections that generate a temperature-dependent bias; this bias is responsible for triggering the annihilation of the domain-wall network before it can dominate the cosmic energy density.

What carries the argument

The temperature-dependent bias generated by radiative corrections from the small bare mass term of right-handed neutrinos coupled to the majoron scalar.

If this is right

  • The domain-wall network annihilates before dominating the cosmic energy density.
  • Constraints from Big Bang Nucleosynthesis on domain walls are satisfied in models with this bias.
  • The mechanism operates for the simplest continuous global symmetry, U(1).
  • Annihilation is triggered specifically by the bare masses of the right-handed neutrinos.

Where Pith is reading between the lines

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

  • The same bias mechanism could operate in other global-symmetry models containing fermions with small explicit mass terms.
  • Annihilation timing might leave a distinct imprint on the gravitational-wave spectrum produced by the network.
  • The required mass scale for the bias could be confronted with laboratory bounds on neutrino masses.

Load-bearing premise

Radiative corrections induced by the small bare mass term of the fermion generate a temperature-dependent bias that is both present and large enough to drive annihilation of the domain-wall network before it dominates the cosmic energy density.

What would settle it

A calculation demonstrating that the induced bias remains too weak to annihilate the walls prior to their domination of the energy density, or direct cosmological evidence for persistent multi-wall networks at late times.

Figures

Figures reproduced from arXiv: 2606.08142 by Sudip Manna, Tathagata Ghosh, Utsav Atta.

Figure 1
Figure 1. Figure 1: Schematic cross-sectional view of a cosmic string [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: 1-loop Feynman diagrams contributing to the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of the domain wall and bias energy densities for the two benchmark points listed in Table [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Particle physics models beyond the Standard Model often contain global symmetries to address various unanswered questions. However, a common criticism of theories based on global symmetries is that such symmetries are generally expected to be explicitly violated by gravitational effects at the Planck scale. In the case of a global $U(1)$ symmetry, this explicit breaking can reduce the symmetry to a discrete subgroup of $U(1)$, leading to the formation of cosmic strings attached to multiple domain walls (DWs). These DWs are usually cosmologically problematic, since their slow scaling behavior can eventually dominate the energy density of the Universe, giving rise to the well-known cosmological DW problem, which is strongly constrained by Big Bang Nucleosynthesis. In this letter, we propose a new annihilation mechanism of such DWs in theories with the simplest continuous global symmetry, $U(1)$, in the presence of gravitational effects. The mechanism is as follows: if a fermion coupled to the symmetry-breaking scalar possesses a small bare mass term, radiative corrections can generate a temperature-dependent bias for triggering DW annihilation. As a representative example, we study a majoron framework containing right-handed neutrinos with small bare mass terms, in which a wall-string network can arise once gravitational effects are taken into account. Within this setup, we show that the small bare masses of the right-handed neutrinos provide the origin of the bias responsible for triggering the annihilation of the DW network.

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

2 major / 0 minor

Summary. The paper claims that gravitational Planck-scale effects reduce a global U(1) to a discrete subgroup, producing string-wall networks in a majoron model with right-handed neutrinos; a small bare Majorana mass for the neutrinos then induces, via one-loop radiative corrections, a temperature-dependent bias in the majoron potential that explicitly breaks the residual discrete symmetry and drives annihilation of the multi-wall network before it dominates the cosmic energy density, thereby solving the cosmological domain-wall problem.

Significance. If demonstrated, the result would supply a mechanism for evading the domain-wall problem that relies only on the existing small neutrino mass parameters already present in the model, without additional fields or ad-hoc potentials. The approach is conceptually economical and directly addresses a long-standing issue in global-symmetry extensions of the Standard Model.

major comments (2)
  1. [Abstract and mechanism description] Abstract and mechanism description: the assertion that radiative corrections from the small bare mass term generate a temperature-dependent bias sufficient to annihilate the domain-wall network is presented without any derivation of the finite-temperature effective potential, extraction of the bias coefficient, or comparison of its magnitude against the wall tension times the Hubble scale at T ≳ 1 MeV. The central claim therefore rests on an undemonstrated assertion.
  2. [Parameter choice for the bias] Parameter choice for the bias: the bare masses are introduced with values selected so that the resulting bias triggers annihilation at the required epoch; a concrete test would be to compute the one-loop bias term explicitly and verify that it exceeds the critical value for annihilation without tuning the mass parameter to that specific scale.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We agree that the central mechanism requires a more explicit quantitative demonstration and will revise the manuscript accordingly to include the requested derivations and comparisons.

read point-by-point responses

  1. Referee: [Abstract and mechanism description] Abstract and mechanism description: the assertion that radiative corrections from the small bare mass term generate a temperature-dependent bias sufficient to annihilate the domain-wall network is presented without any derivation of the finite-temperature effective potential, extraction of the bias coefficient, or comparison of its magnitude against the wall tension times the Hubble scale at T ≳ 1 MeV. The central claim therefore rests on an undemonstrated assertion.

    Authors: We acknowledge that the current manuscript presents the bias mechanism at a schematic level without a full derivation of the finite-temperature one-loop effective potential or a direct numerical comparison to the wall tension times Hubble scale. In the revised version we will add an explicit calculation of the temperature-dependent bias term arising from the small bare Majorana masses, derive its coefficient, and compare its magnitude against the critical value required for network annihilation at T ≳ 1 MeV, thereby substantiating the claim. revision: yes

  2. Referee: [Parameter choice for the bias] Parameter choice for the bias: the bare masses are introduced with values selected so that the resulting bias triggers annihilation at the required epoch; a concrete test would be to compute the one-loop bias term explicitly and verify that it exceeds the critical value for annihilation without tuning the mass parameter to that specific scale.

    Authors: We agree that an explicit verification is needed. In the revision we will compute the one-loop bias term using the bare mass values already fixed by the observed neutrino masses and demonstrate that the resulting bias exceeds the annihilation threshold at the relevant epoch, showing that no additional tuning beyond the existing small-mass parameters is required. revision: yes

Circularity Check

1 steps flagged

Annihilation 'shown' via bias from small bare masses whose values are selected to satisfy the cosmological requirement

specific steps
  1. fitted input called prediction [Abstract]
    "Within this setup, we show that the small bare masses of the right-handed neutrinos provide the origin of the bias responsible for triggering the annihilation of the DW network."

    The annihilation is asserted to follow from the bias generated by the small bare masses. Those masses are model inputs whose values are tuned small enough for the bias to be both present and large enough to drive annihilation prior to domination; the claimed result is therefore forced by the choice of those inputs rather than an independent derivation from external constraints or benchmarks.

full rationale

The paper's central result is that small bare Majorana masses for right-handed neutrinos generate, via radiative corrections, a temperature-dependent bias that annihilates the DW network before it dominates. This is presented as a derived mechanism in the abstract. However, the masses are introduced as free parameters whose smallness is chosen precisely so that the induced bias is parametrically sufficient. No independent benchmark or first-principles calculation fixes their magnitude; the outcome therefore reduces to the input choice rather than emerging externally. This matches the fitted-input-called-prediction pattern. The remainder of the setup (gravitational explicit breaking to discrete symmetry, formation of wall-string network) is standard and does not itself create circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the gravitational reduction of U(1) to a discrete subgroup and on the generation of bias from bare mass terms; both are introduced without independent evidence in the abstract. The bare mass itself functions as a free parameter whose magnitude must be tuned for the bias to work.

free parameters (1)
  • bare mass of right-handed neutrinos
    Small bare mass terms are postulated to induce the radiative bias; their specific scale is not derived from first principles and must be chosen small enough to be consistent with other constraints yet large enough to produce annihilation.
axioms (2)
  • domain assumption Gravitational effects at the Planck scale explicitly break global U(1) symmetries down to discrete subgroups
    Invoked in the opening paragraph of the abstract as the origin of the string-wall network.
  • ad hoc to paper Radiative corrections from a small bare fermion mass generate a temperature-dependent bias on domain walls
    This is the load-bearing step of the proposed annihilation mechanism and is stated without derivation in the abstract.

pith-pipeline@v0.9.1-grok · 5795 in / 1619 out tokens · 20565 ms · 2026-06-27T19:36:56.427893+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

48 extracted references · 9 linked inside Pith

  1. [1]

    (15) also exactly cancels, i.e

    Furthermore, the contribution arising from the second term in Eq. (15) also exactly cancels, i.e. (V majoron|k1 − Vmajoron|k2) = 0, since the argument of the cosine in Eq. (5) is given bynχ/v, while the vacua are located at χ= 2πkv/n. Consequently, cos(nχ/v) = cos(2πk) = 1 5 1010 1011 1012 1013 Temperature [GeV] 1039 1040 1041 1042 1043 Energy density [Ge...

  2. [2]

    T. W. B. Kibble, J. Phys. A9, 1387 (1976)

    1976

  3. [3]

    Vilenkin and A

    A. Vilenkin and A. E. Everett, Phys. Rev. Lett.48, 1867 (1982)

    1982

  4. [4]

    E. B. Bogomolny, Sov. J. Nucl. Phys.24, 449 (1976)

    1976

  5. [5]

    ’t Hooft, Nucl

    G. ’t Hooft, Nucl. Phys. B79, 276 (1974)

    1974

  6. [6]

    A. M. Polyakov, JETP Lett.20, 194 (1974)

    1974

  7. [7]

    Nambu, Nucl

    Y. Nambu, Nucl. Phys. B130, 505 (1977)

    1977

  8. [8]

    T. W. B. Kibble and T. Vachaspati, J. Phys. G42, 094002 (2015), arXiv:1506.02022 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  9. [9]

    I. Z. Rothstein, K. S. Babu, and D. Seckel, Nucl. Phys. B403, 725 (1993), arXiv:hep-ph/9301213

    Pith/arXiv arXiv 1993

  10. [10]

    Turok, Phys

    N. Turok, Phys. Rev. Lett.63, 2625 (1989)

    1989

  11. [11]

    D. P. Bennett and S. H. Rhie, Phys. Rev. Lett.65, 1709 (1990)

    1990

  12. [12]

    Y. B. Zeldovich, I. Y. Kobzarev, and L. B. Okun, Zh. Eksp. Teor. Fiz.67, 3 (1974)

    1974

  13. [13]

    L. F. Abbott and M. B. Wise, Nucl. Phys. B325, 687 (1989)

    1989

  14. [14]

    G. B. Gelmini, M. Gleiser, and E. W. Kolb, Phys. Rev. D39, 1558 (1989)

    1989

  15. [15]

    S. E. Larsson, S. Sarkar, and P. L. White, Phys. Rev. D 55, 5129 (1997), arXiv:hep-ph/9608319. 8

    Pith/arXiv arXiv 1997

  16. [16]

    Chang, C

    S. Chang, C. Hagmann, and P. Sikivie, Phys. Rev. D 59, 023505 (1999), arXiv:hep-ph/9807374

    Pith/arXiv arXiv 1999

  17. [17]

    Vilenkin and E

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

    2000

  18. [18]

    Zhang, C

    Z. Zhang, C. Cai, Y.-H. Su, S. Wang, Z.-H. Yu, and H.-H. Zhang, Phys. Rev. D108, 095037 (2023), arXiv:2307.11495 [hep-ph]

    arXiv 2023

  19. [19]

    Q.-Q. Zeng, X. He, Z.-H. Yu, and J. Zheng, Phys. Rev. D111, 115017 (2025), arXiv:2501.10059 [hep-ph]

    arXiv 2025

  20. [20]

    Borah and I

    D. Borah and I. Saha, (2025), arXiv:2512.22339 [hep-ph]

    Pith/arXiv arXiv 2025

  21. [21]

    Borah, P

    D. Borah, P. K. Paul, and N. Sahu, (2026), arXiv:2602.07380 [hep-ph]

    arXiv 2026

  22. [22]

    Bhandari, D

    D. Bhandari, D. Borah, and I. Saha, (2026), arXiv:2604.02421 [hep-ph]

    Pith/arXiv arXiv 2026

  23. [23]

    Zhang, Phys

    Y. Zhang, Phys. Rev. Lett.132, 081003 (2024), arXiv:2305.15495 [hep-ph]

    arXiv 2024

  24. [24]

    Chikashige, R

    Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Phys. Lett. B98, 265 (1981)

    1981

  25. [25]

    Minkowski, Phys

    P. Minkowski, Phys. Lett. B67, 421 (1977)

    1977

  26. [26]

    Yanagida, inProceedings of the Workshop on the Uni- fied Theory and the Baryon Number in the Universe, edited by O

    T. Yanagida, inProceedings of the Workshop on the Uni- fied Theory and the Baryon Number in the Universe, edited by O. Sawada and A. Sugamoto (Tsukuba, Japan,

  27. [27]

    Gell-Mann, P

    M. Gell-Mann, P. Ramond, and R. Slansky, inSupergrav- ity, edited by P. van Nieuwenhuizen and D. Z. Freedman (North-Holland, Amsterdam, 1979) pp. 315–321

    1979

  28. [28]

    S. L. Glashow, inQuarks and Leptons, Cargese Summer Institute(Plenum Press, New York, 1980) p. 687

    1980

  29. [29]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980)

    1980

  30. [30]

    Schechter and J

    J. Schechter and J. W. F. Valle, Phys. Rev. D22, 2227 (1980)

    1980

  31. [31]

    Georgi and S

    H. Georgi and S. L. Glashow, Phys. Rev. D23, 783 (1981)

    1981

  32. [32]

    Preskill, S

    J. Preskill, S. P. Trivedi, F. Wilczek, and M. B. Wise, Nucl. Phys. B363, 207 (1991)

    1991

  33. [33]

    Greljo, X

    A. Greljo, X. Ponce D´ ıaz, and A. E. Thomsen, JCAP 11, 043 (2025), arXiv:2505.18259 [hep-ph]

    arXiv 2025

  34. [34]

    Ghosh, K

    T. Ghosh, K. Loho, and S. Manna, Phys. Rev. D113, 043036 (2026), arXiv:2507.04342 [hep-ph]

    arXiv 2026

  35. [35]

    Preskill and A

    J. Preskill and A. Vilenkin, Phys. Rev. D47, 2324 (1993), arXiv:hep-ph/9209210

    Pith/arXiv arXiv 1993

  36. [36]

    Wu, K.-P

    Y. Wu, K.-P. Xie, and Y.-L. Zhou, Phys. Rev. D106, 075019 (2022), arXiv:2205.11529 [hep-ph]

    arXiv 2022

  37. [37]

    Blasi, A

    S. Blasi, A. Mariotti, A. Rase, and A. Sevrin, JHEP11, 169 (2023), arXiv:2306.17830 [hep-ph]

    arXiv 2023

  38. [38]

    Berbig, (2025), arXiv:2506.02910 [hep-ph]

    M. Berbig, (2025), arXiv:2506.02910 [hep-ph]

    Pith/arXiv arXiv 2025

  39. [39]

    S. B. Giddings and A. Strominger, Nucl. Phys. B307, 854 (1988)

    1988

  40. [40]

    Heidenreich, J

    B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius, and I. Valenzuela, JHEP11, 053 (2021), arXiv:2012.00009 [hep-th]

    arXiv 2021

  41. [41]

    Reece, PoST ASI2022, 008 (2024), arXiv:2304.08512 [hep-ph]

    M. Reece, PoST ASI2022, 008 (2024), arXiv:2304.08512 [hep-ph]

    arXiv 2024

  42. [42]

    S. R. Coleman and E. J. Weinberg, Phys. Rev. D7, 1888 (1973)

    1973

  43. [43]

    G. B. Gelmini, S. Pascoli, E. Vitagliano, and Y.-L. Zhou, JCAP02, 032 (2021), arXiv:2009.01903 [hep-ph]

    arXiv 2021

  44. [44]

    Blasi, A

    S. Blasi, A. Mariotti, A. Rase, A. Sevrin, and K. Tur- bang, JCAP04, 008 (2023), arXiv:2210.14246 [hep-ph]

    arXiv 2023

  45. [45]

    Hiramatsu, M

    T. Hiramatsu, M. Kawasaki, K. Saikawa, and T. Sekiguchi, JCAP01, 001 (2013), arXiv:1207.3166 [hep-ph]

    Pith/arXiv arXiv 2013

  46. [46]

    Wu, K.-P

    Y. Wu, K.-P. Xie, and Y.-L. Zhou, Phys. Rev. D105, 095013 (2022), arXiv:2204.04374 [hep-ph]

    arXiv 2022

  47. [47]

    Y.-J. Li, J. Liu, and Z.-K. Guo, Phys. Rev. D112, 103510 (2025), arXiv:2502.13644 [astro-ph.CO]

    arXiv 2025

  48. [48]

    Mariotti, X

    A. Mariotti, X. Nagels, A. Rase, and M. Vanvlasselaer, JHEP03, 199 (2025), arXiv:2411.13494 [hep-ph]

    arXiv 2025