pith. sign in

arxiv: 2605.27506 · v1 · pith:75D3NPD6new · submitted 2026-05-26 · ✦ hep-ph · astro-ph.CO· astro-ph.HE

Neutrino-antineutrino superfluidity

Damiano F. G. Fiorillo , Georg G. Raffelt , G\"unter Sigl This is my paper

Pith reviewed 2026-06-29 16:47 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COastro-ph.HE
keywords neutrino superfluiditypairing instabilityoccupation number discontinuityFermi surfacecollective neutrino interactionsweak interactionscontinuum limit
0
0 comments X

The pith

For standard weak interactions, neutrino-antineutrino pairing instabilities require discontinuities in the occupation number and disappear in the continuum limit.

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

The paper checks whether collective weak interactions among dense neutrinos can produce pairing instabilities that reorganize momentum distributions, as occurs in ordinary fermion superfluids. It concludes that such instabilities appear only when the occupation number has abrupt jumps, for example at a sharp Fermi surface. Discrete energy bins in calculations can falsely create these jumps and generate spurious instabilities. The effect vanishes once the energy spectrum is taken continuous. This sets a clear boundary on when standard-model neutrino collective behavior can induce superfluid-like reorganization.

Core claim

For standard weak interactions, pairing instabilities can arise only in the presence of discontinuities in the occupation number, such as the sharp Fermi surface responsible for superconductivity in metals. However, discretized energy spectra can mimic such discontinuities and artificially generate superfluid instabilities. These spurious instabilities disappear in the continuum limit.

What carries the argument

Discontinuities in the neutrino occupation number, which alone permit pairing instabilities under standard weak interactions.

If this is right

  • Pairing instabilities are possible only when the neutrino distribution contains a sharp Fermi surface or similar discontinuity.
  • Numerical models that discretize the energy spectrum can produce artificial instabilities that are absent in the true continuum.
  • Standard weak interactions alone cannot reorganize neutrino momenta into a superfluid state without occupation discontinuities.
  • Collective flavor oscillations remain distinct from any pairing instability under the same interaction assumptions.

Where Pith is reading between the lines

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

  • Non-standard interactions or additional collective effects would be required to produce pairing instabilities in the absence of occupation discontinuities.
  • Simulations of neutrino transport in supernovae or neutron-star mergers should adopt continuum limits to avoid spurious pairing signals.
  • The result constrains the parameter space in which neutrino superfluidity could affect astrophysical observables without invoking new physics.

Load-bearing premise

Neutrino interactions follow only the standard weak force and no other effects allow pairing without jumps in how many neutrinos occupy each momentum state.

What would settle it

A dispersion-relation calculation performed with a fully continuous neutrino energy spectrum that shows no imaginary frequencies for pairing modes.

read the original abstract

Despite their feeble interactions, dense astrophysical neutrinos can behave collectively, exchanging flavor through waves of the neutrino plasma. Can collective interactions also induce pairing instabilities and reorganize the neutrino momentum distribution, in analogy to the superfluid instability of fermions? We show that, for standard weak interactions, pairing instabilities can arise only in the presence of discontinuities in the occupation number, such as the sharp Fermi surface responsible for superconductivity in metals. However, discretized energy spectra can mimic such discontinuities and artificially generate superfluid instabilities. These spurious instabilities disappear in the continuum limit.

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

0 major / 2 minor

Summary. The paper claims that for standard weak interactions, pairing instabilities leading to neutrino-antineutrino superfluidity can arise only in the presence of discontinuities in the occupation number (e.g., a sharp Fermi surface). It further shows that apparent instabilities from discretized energy spectra are artifacts that disappear in the continuum limit.

Significance. If the central derivation holds, the result clarifies the physical conditions for superfluid instabilities in dense neutrino plasmas without invoking non-standard physics or additional collective effects. It is a parameter-free result scoped explicitly to standard weak interactions and directly addresses a potential numerical artifact, which is a strength for applications in supernova and neutron-star modeling.

minor comments (2)
  1. [Abstract] Abstract: the central claim is stated clearly but the abstract provides no derivation outline, error analysis, or explicit statement of how the continuum limit is taken; this makes initial verification difficult even though the full text presumably contains the steps.
  2. The manuscript should explicitly confirm that the derivation remains valid when the weak interaction Hamiltonian is written in the standard current-current form without higher-order corrections.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the accurate summary of our central claims, and the recommendation of minor revision. The referee's description correctly identifies both the physical result (pairing instabilities require occupation-number discontinuities for standard weak interactions) and the numerical finding (discretized spectra produce spurious instabilities that vanish in the continuum). No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper's central claim—that pairing instabilities for standard weak interactions require discontinuities in the occupation number, with discretized artifacts vanishing in the continuum limit—is presented as a direct derivation from the interaction Hamiltonian and the structure of the neutrino plasma equations. No load-bearing step reduces to a fitted parameter, self-citation chain, or definitional equivalence; the result follows from the explicit form of the weak interaction vertices and the continuum limit of the mode equations. The analysis is scoped to standard interactions without invoking prior author results as uniqueness theorems or ansatzes. This is the normal case of an independent derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that neutrino collective behavior is governed exclusively by standard weak interactions and that occupation number discontinuities are the sole trigger for pairing.

axioms (1)
  • domain assumption Standard weak interactions govern the collective neutrino plasma behavior
    Explicitly invoked in the abstract as the condition under which the pairing result holds.

pith-pipeline@v0.9.1-grok · 5622 in / 1063 out tokens · 34588 ms · 2026-06-29T16:47:25.478979+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 1 Pith paper

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

  1. Neutrino helicity oscillations in astrophysical environments: a many-body approach

    hep-ph 2026-05 unverdicted novelty 5.0

    Many-body neutrino calculations in simple momentum-state configurations yield helicity conversion probabilities orders of magnitude above mean-field results due to momentum exchange.

Reference graph

Works this paper leans on

59 extracted references · 50 canonical work pages · cited by 1 Pith paper · 17 internal anchors

  1. [1]

    Cooper,Bound electron pairs in a degenerate Fermi gas,Phys

    L.N. Cooper,Bound electron pairs in a degenerate Fermi gas,Phys. Rev.104(1956) 1189

    1956

  2. [2]

    Bardeen, L.N

    J. Bardeen, L.N. Cooper and J.R. Schrieffer,Theory of superconductivity,Phys. Rev.108 (1957) 1175. – 12 –

    1957

  3. [3]

    Superfluidity of the cosmological neutrino “sea

    V.L. Ginzburg and G.F. Zharkov, “Superfluidity of the cosmological neutrino “sea”.”JETP Lett.5(1967) 223–225. Translated fromZhETF Pis’ma5(1967) 275–277

    1967

  4. [4]

    Ginzburg,Superfluidity and superconductivity in the universe,J

    V.L. Ginzburg,Superfluidity and superconductivity in the universe,J. Stat. Phys.1(1969) 3–24

    1969

  5. [5]

    Cosmological Neutrino Condensates

    D.G. Caldi and A. Chodos,Cosmological neutrino condensates,hep-ph/9903416

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    Neutrino Superfluidity

    J.I. Kapusta,Neutrino superfluidity,Phys. Rev. Lett.93(2004) 251801 [hep-th/0407164]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  7. [7]

    Majorana Neutrino Superfluidity and Stability of Neutrino Dark Energy

    J.R. Bhatt and U. Sarkar,Majorana Neutrino Superfluidity and Stability of Neutrino Dark Energy,Phys. Rev. D80(2009) 045016 [0805.2482]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  8. [8]

    Addazi, S

    A. Addazi, S. Capozziello, Q. Gan and A. Marcian` o,Dark energy and neutrino superfluids, Phys. Dark Univ.37(2022) 101102 [2208.03591]

    work page arXiv 2022

  9. [9]

    Chodos and F

    A. Chodos and F. Cooper,Neutrino condensation from a new Higgs-like interaction,Phys. Rev. D102(2020) 113003 [2004.03731]

    work page arXiv 2020

  10. [10]

    Dvornikov,Superfluidity in neutrino clusters,J

    M. Dvornikov,Superfluidity in neutrino clusters,J. Phys. G51(2024) 075201 [2310.04806]

    work page arXiv 2024

  11. [11]

    Samuel,Neutrino oscillations in dense neutrino gases,Phys

    S. Samuel,Neutrino oscillations in dense neutrino gases,Phys. Rev. D48(1993) 1462

    1993

  12. [12]

    Bimodal Coherence in Dense Self-Interacting Neutrino Gases

    S. Samuel,Bimodal coherence in dense selfinteracting neutrino gases,Phys. Rev. D53(1996) 5382 [hep-ph/9604341]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  13. [13]

    Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment I: Correlated Neutrino Trajectories

    H. Duan, G.M. Fuller, J. Carlson and Y.-Z. Qian,Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: Correlated neutrino trajectories,Phys. Rev. D74(2006) 105014 [astro-ph/0606616]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  14. [14]

    "Classical" instabilities and "quantum" speed-up in the evolution of neutrino clouds

    R.F. Sawyer,“Classical” instabilities and “quantum” speed-up in the evolution of neutrino clouds,hep-ph/0408265

    work page internal anchor Pith review Pith/arXiv arXiv

  15. [15]

    The multi-angle instability in dense neutrino systems

    R.F. Sawyer,The multi-angle instability in dense neutrino systems,Phys. Rev. D79(2009) 105003 [0803.4319]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  16. [16]

    Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion-Relation Approach

    I. Izaguirre, G. Raffelt and I. Tamborra,Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion-Relation Approach,Phys. Rev. Lett.118(2017) 021101 [1610.01612]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  17. [17]

    Tamborra and S

    I. Tamborra and S. Shalgar,New Developments in Flavor Evolution of a Dense Neutrino Gas, Annu. Rev. Nucl. Part. Sci.71(2021) 165 [2011.01948]

    work page arXiv 2021

  18. [18]

    Richers and M

    S. Richers and M. Sen,Fast Flavor Transformations, inHandbook of Nuclear Physics, I. Tanihata, H. Toki and T. Kajino, eds., pp. 1–17 (2022), DOI [2207.03561]

    work page arXiv 2022

  19. [19]

    Johns, S

    L. Johns, S. Richers and M.-R. Wu,Neutrino Oscillations in Core-Collapse Supernovae and Neutron Star Mergers,Annu. Rev. Nucl. Part. Sci.75(2025) 399 [2503.05959]

    work page arXiv 2025

  20. [20]

    Raffelt, H.-T

    G.G. Raffelt, H.-T. Janka and D.F.G. Fiorillo,Neutrinos from core-collapse supernovae, 2509.16306. To be published in the Encyclopedia of Particle Physics (2026)

    work page arXiv 2026

  21. [21]

    Speed-up of neutrino transformations in a supernova environment

    R.F. Sawyer,Speed-up of neutrino transformations in a supernova environment,Phys. Rev. D 72(2005) 045003 [hep-ph/0503013]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  22. [22]

    Neutrino cloud instabilities just above the neutrino sphere of a supernova

    R.F. Sawyer,Neutrino cloud instabilities just above the neutrino sphere of a supernova,Phys. Rev. Lett.116(2016) 081101 [1509.03323]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  23. [23]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Theory of neutrino slow flavor evolution. Part I. Homogeneous medium,JHEP04(2025) 146 [2412.02747]. – 13 –

    work page arXiv 2025

  24. [24]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Dispersion relation of the neutrino plasma: unifying fast, slow, and collisional instabilities,JHEP01(2026) 147 [2505.20389]

    work page arXiv 2026

  25. [25]

    Johns,Collisional Flavor Instabilities of Supernova Neutrinos,Phys

    L. Johns,Collisional Flavor Instabilities of Supernova Neutrinos,Phys. Rev. Lett.130(2023) 191001 [2104.11369]

    work page arXiv 2023

  26. [26]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Theory of neutrino fast flavor evolution. Part I. Linear response theory and stability conditions,JHEP08(2024) 225 [2406.06708]

    work page arXiv 2024

  27. [27]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Theory of neutrino fast flavor evolution. Part II. Solutions at the edge of instability,JHEP12(2024) 205 [2409.17232]

    work page arXiv 2024

  28. [28]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Theory of neutrino slow flavor evolution. Part II. Space-time evolution of linear instabilities,JHEP06(2025) 146 [2501.16423]

    work page arXiv 2025

  29. [29]

    Fiorillo, H.-T

    D.F.G. Fiorillo, H.-T. Janka and G.G. Raffelt,Neutrino-Mass-Driven Instabilities as the Earliest Flavor Conversion in Supernovae,Phys. Rev. Lett.135(2025) 231003 [2507.22985]

    work page arXiv 2025

  30. [30]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Lepton number crossings are insufficient for flavor instabilities,2507.22987

    work page arXiv

  31. [31]

    Johns and A

    L. Johns and A. Kost,Local-equilibrium theory of neutrino oscillations,2506.03271

    work page arXiv

  32. [32]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Collective Flavor Conversions Are Interactions of Neutrinos with Quantized Flavor Waves,Phys. Rev. Lett.134(2025) 211003 [2502.06935]

    work page arXiv 2025

  33. [33]

    Flavomon ray tracing in matter gradients

    D.F.G. Fiorillo and G.G. Raffelt,Flavomon ray tracing in matter gradients,2604.18689

    work page internal anchor Pith review Pith/arXiv arXiv

  34. [34]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Fast Flavor Conversions at the Edge of Instability in a Two-Beam Model,Phys. Rev. Lett.133(2024) 221004 [2403.12189]

    work page arXiv 2024

  35. [35]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Quasi-linear theory of fast flavor instabilities in homogeneous environments,2603.28854

    work page arXiv

  36. [36]

    Neutrino-antineutrino correlations in dense anisotropic media

    J. Serreau and C. Volpe,Neutrino-antineutrino correlations in dense anisotropic media,Phys. Rev. D90(2014) 125040 [1409.3591]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  37. [37]

    Collective neutrino-antineutrino pair oscillations

    S.-J. Huang and M.-R. Wu,Collective neutrino-antineutrino pair oscillations,2604.25687

    work page internal anchor Pith review Pith/arXiv arXiv

  38. [38]

    Sawyer,Neutrino-anti-neutrino instability in dense neutrino systems, with applications to the early universe and to supernovae,2206.09290

    R.F. Sawyer,Neutrino-anti-neutrino instability in dense neutrino systems, with applications to the early universe and to supernovae,2206.09290

    work page arXiv

  39. [39]

    Sawyer,Fast flavor evolution in dense neutrino systems, as described in quantum field theory,Phys

    R.F. Sawyer,Fast flavor evolution in dense neutrino systems, as described in quantum field theory,Phys. Rev. D108(2023) 093001 [2304.01987]

    work page arXiv 2023

  40. [40]

    Fiorillo, G.G

    D.F.G. Fiorillo, G.G. Raffelt and G. Sigl,Collective neutrino-antineutrino oscillations in dense neutrino environments?,Phys. Rev. D109(2024) 043031 [2401.02478]

    work page arXiv 2024

  41. [41]

    Fulde and R.A

    P. Fulde and R.A. Ferrell,Superconductivity in a Strong Spin-Exchange Field,Phys. Rev.135 (1964) A550

    1964

  42. [42]

    Larkin and Y.N

    A.I. Larkin and Y.N. Ovchinnikov,Nonuniform state of superconductors,Sov. Phys. JETP20 (1965) 762. Translated fromZh. Eksp. Teor. Fiz.47(1964) 1136

    1965

  43. [43]

    Gor’kov and T.K

    L.P. Gor’kov and T.K. Melik-Barkhudarov.Contribution to the Theory of Superfluidity in an Imperfect Fermi Gas,Sov. Phys. JETP13(1961) 1018. Translated fromZhETF40(1961) 1452

    1961

  44. [44]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Slow and fast collective neutrino oscillations: Invariants and reciprocity,Phys. Rev. D107(2023) 043024 [2301.09650]. – 14 –

    work page arXiv 2023

  45. [45]

    Self-induced conversion in dense neutrino gases: Pendulum in flavour space

    S. Hannestad, G.G. Raffelt, G. Sigl and Y.Y.Y. Wong,Self-induced conversion in dense neutrino gases: Pendulum in flavour space,Phys. Rev. D74(2006) 105010 [astro-ph/0608695]. Erratum:Phys. Rev. D76(2007) 029901

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  46. [46]

    Padilla-Gay, I

    I. Padilla-Gay, I. Tamborra and G.G. Raffelt,Neutrino Flavor Pendulum Reloaded: The Case of Fast Pairwise Conversion,Phys. Rev. Lett.128(2022) 121102 [2109.14627]

    work page arXiv 2022

  47. [47]

    J. Liu, L. Johns, H. Nagakura, M. Zaizen and S. Yamada,Dynamical equilibria of fast neutrino flavor conversion,2509.26418

    work page arXiv

  48. [48]

    Single-wave solutions of the neutrino fast flavor system. Part I. Mechanical properties

    D.F.G. Fiorillo and G.G. Raffelt,Single-wave solutions of the neutrino fast flavor system. Part I. Mechanical properties,2601.15372

    work page internal anchor Pith review Pith/arXiv arXiv

  49. [49]

    Raffelt,N-mode coherence in collective neutrino oscillations,Phys

    G.G. Raffelt,N-mode coherence in collective neutrino oscillations,Phys. Rev. D83(2011) 105022 [1103.2891]. Erratum:Phys. Rev. D104(2021) 089902

    work page arXiv 2011

  50. [50]

    Invariants of Collective Neutrino Oscillations

    Y. Pehlivan, A.B. Balantekin, T. Kajino and T. Yoshida,Invariants of Collective Neutrino Oscillations,Phys. Rev. D84(2011) 065008 [1105.1182]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  51. [51]

    Johns, H

    L. Johns, H. Nagakura, G.M. Fuller and A. Burrows,Neutrino oscillations in supernovae: angular moments and fast instabilities,Phys. Rev. D101(2020) 043009 [1910.05682]

    work page arXiv 2020

  52. [52]

    Padilla-Gay, I

    I. Padilla-Gay, I. Tamborra and G.G. Raffelt,Neutrino fast flavor pendulum. II. Collisional damping,Phys. Rev. D106(2022) 103031 [2209.11235]

    work page arXiv 2022

  53. [53]

    Johns and S

    L. Johns and S. Rodriguez,Collisional flavor pendula and neutrino quantum thermodynamics, 2312.10340

    work page arXiv

  54. [54]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,Flavor solitons in dense neutrino gases,Phys. Rev. D107 (2023) 123024 [2303.12143]

    work page arXiv 2023

  55. [55]

    Fiorillo, I

    D.F.G. Fiorillo, I. Padilla-Gay and G.G. Raffelt,Collisions and collective flavor conversion: Integrating out the fast dynamics,Phys. Rev. D109(2024) 063021 [2312.07612]

    work page arXiv 2024

  56. [56]

    Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior

    D.F.G. Fiorillo and G.G. Raffelt,Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior,2601.18880

    work page internal anchor Pith review Pith/arXiv arXiv

  57. [57]

    Fiorillo and G.G

    D.F.G. Fiorillo and G.G. Raffelt,The ubiquitous flavor pendulum,2602.02655

    work page arXiv

  58. [58]

    Fiorillo, G.G

    D.F.G. Fiorillo, G.G. Raffelt and G. Sigl,Inhomogeneous Kinetic Equation for Mixed Neutrinos: Tracing the Missing Energy,Phys. Rev. Lett.133(2024) 021002 [2401.05278]

    work page arXiv 2024

  59. [59]

    Sigl and G

    G. Sigl and G. Raffelt,General kinetic description of relativistic mixed neutrinos,Nucl. Phys. B406(1993) 423. – 15 –

    1993