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arxiv: 2607.05221 · v1 · pith:3QEHAF6W · submitted 2026-07-06 · hep-ph · astro-ph.CO

Pathways and impediments towards a detection of the relic neutrino wind

Andrew J. Long , Michiru Uwabo-Niibo , Masahide Yamaguchi This is my paper

Reviewed by Pith2026-07-07 22:45 UTCglm-5.2pith:3QEHAF6Wopen to challenge →

classification hep-ph astro-ph.CO
keywords cosmic neutrino backgroundCNB windrelic neutrino detectiontritium beta decaydipolar anisotropyDirac vs Majorana neutrinosneutrino captureangular correlation
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The pith

Relic neutrino wind detection needs 100,000x more data than flux

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

The cosmic neutrino background (CNB) — relic neutrinos from the early universe — should exhibit a dipolar anisotropy in flux due to Earth's motion relative to the CNB rest frame, an effect the authors call the CNB wind. This paper calculates how difficult it would be to detect that wind using tritium beta decay experiments, which capture relic neutrinos and produce electrons just above the beta-decay endpoint. The authors find that although the neutrino flux anisotropy itself can be large (of order the wind velocity divided by the neutrino thermal velocity), the resulting anisotropy in the recoiling electron distribution is far smaller — about one part in a thousand for Dirac neutrinos and one part in a million for Majorana neutrinos. The Majorana suppression arises because the leading helicity-dependent angular correlation term cancels when both helicities contribute equally. Consequently, detecting the CNB wind would require an exposure (detector mass times observation time) at least 100,000 times larger than what is needed to merely detect the CNB flux, and if the experimental energy resolution is poorer than the neutrino mass scale, systematic uncertainties must also be controlled at an exceptionally demanding level.

Core claim

The central quantitative result is a scaling relation: the dipole-to-monopole ratio of the electron capture rate is suppressed to roughly 10^{-3} for nonrelativistic Dirac neutrinos and 10^{-6} for Majorana neutrinos, despite the underlying neutrino flux anisotropy being potentially order unity for heavy neutrinos. This suppression comes from two sources — the small outgoing electron velocity (v_e/c ~ 0.1) and a partial cancellation in the nuclear form-factor combination controlling the electron-neutrino angular correlation. For Majorana neutrinos, an additional cancellation occurs because the leading helicity-odd term in the angular correlation vanishes when positive and negative helicities

What carries the argument

The dipolar anisotropy in the electron angular distribution from neutrino capture on tritium, parametrized as a cos(theta) modulation whose amplitude relative to the isotropic rate scales as (|C_B|/3C_A) times (v_w/v_bar_nu) times v_star, where C_A and C_B are nuclear form-factor combinations, v_w is the CNB wind velocity, and v_star is the outgoing electron velocity.

If this is right

  • Any future tritium-based CNB experiment aiming beyond flux detection toward anisotropy measurements faces an exposure requirement of order 10^7 g yr or more for Dirac neutrinos, far beyond current proposals like PTOLEMY (~100 g yr).
  • The Dirac-versus-Majorana distinction in the wind signal is parametrically large (a factor of m_nu/T_nu ~ 10^3), meaning a wind detection could in principle determine the neutrino's fundamental nature — but only if the exposure and angular systematics control are achievable.
  • The cancellation of the normalization nuisance parameter in the dipole analysis (due to symmetric angular binning) means the wind search is robust against overall rate uncertainties but fragile against angular anisotropies in the background at the 10^{-3} (Dirac) or 10^{-6} (Majorana) level.
  • Energy sideband data could in principle constrain the fake-dipole background parameter, offering a calibration pathway that does not exist for the simpler flux measurement.

Where Pith is reading between the lines

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

  • If gravitational clustering of relic neutrinos in the Milky Way shifts the CNB rest frame away from the CMB rest frame, both the magnitude and direction of the wind change, and the fixed-template analysis used here would need to become a full dipole-vector fit — weakening sensitivity but not changing the exposure scaling.
  • The 10^5 exposure penalty factor suggests that intermediate CNB science goals — such as measuring the neutrino energy spectrum or testing the dispersion relation — may have difficulty levels between the flux and wind measurements, and a systematic ranking of these goals by required exposure would be a natural extension.
  • If helicity rotations from gravitational inhomogeneities or magnetic fields partially depolarize the CNB, the sharp Dirac/Majorana contrast in the wind signal would blur, potentially making the wind measurement a probe of cosmological helicity evolution rather than purely of neutrino nature.

Load-bearing premise

The analysis assumes the tritium beta-decay background is perfectly isotropic in the laboratory frame. A residual dipolar anisotropy in the background at the 10^{-3} level (for Dirac neutrinos) or 10^{-6} level (for Majorana) — arising from detector geometry, electron transport, or target substrate effects — would mimic or obscure the CNB wind signal. The paper acknowledges this but defers detailed modeling.

What would settle it

If a tritium experiment with exposure of order 10^7 g yr and sub-meV energy resolution failed to observe a cos(theta) modulation in the endpoint electron rate at the predicted 10^{-3} (Dirac) or 10^{-6} (Majorana) level, the CNB wind model or the assumed CNB rest frame would be called into question.

Figures

Figures reproduced from arXiv: 2607.05221 by Andrew J. Long, Masahide Yamaguchi, Michiru Uwabo-Niibo.

Figure 1
Figure 1. Figure 1: Differential flux of incident neutrinos. Solid curves are calculated by evaluating the integral [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Differential capture rate for Dirac neutrinos as a function of the angle between the recoiling [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The minimum exposure Ξ required for CNB searches as a function of the effective energy [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The maximum systematic uncertainty σα allowed for a 3σ detection of the CNB flux in the endpoint-rate analysis strategy. The nuisance parameter α, which rescales the signal and background, has a Gaussian prior with variance σ 2 α. Color and dashing are the same as in [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
read the original abstract

A direct detection of the cosmic neutrino background (CNB) in laboratories on Earth has been called the ``holy grail'' of experimental neutrino physics, but a still more glorious prize awaits. Beyond simply detecting the presence of relic neutrinos and measuring their flux, one may aspire to measure their energy distribution, polarization, anisotropies, temporal variation, and other properties. In this work we focus on the CNB wind, which is the approximately dipolar anisotropy in the CNB flux resulting from the relative velocity of the CNB rest frame and the lab frame. We consider a CNB detection strategy based on measuring the angular distribution of recoiling electrons at the tritium $\beta$-decay endpoint. In order to quantify the difficulty of detecting the CNB wind, we calculate the required exposure (detector mass times observation duration) for a $3\sigma$ discovery. We find that detecting the CNB wind would require an exposure that is at least $10^{5}$ times larger than what's required for detecting the CNB flux alone. Additionally if the experimental energy resolution were to exceed the neutrino mass scale, then an exceptionally good control of systematic uncertainties would also be required. For nonrelativistic neutrinos, the Majorana wind signal is suppressed relative to the Dirac case by the cancellation of the leading helicity-odd angular-correlation term, leading parametrically to an exposure penalty of order $(m_\nu/T_\nu)^2$.

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 / 7 minor

Summary. This manuscript quantifies the difficulty of detecting the cosmic neutrino background (CNB) wind — the dipolar anisotropy in the relic neutrino flux induced by Earth's motion relative to the CNB rest frame — via the angular distribution of recoiling electrons in tritium beta decay endpoint measurements. The authors derive the capture rate anisotropy from standard ΛCDM initial conditions and Standard Model weak interactions (Sec. 2), validate analytical approximations against direct numerical integration to ~0.02% (Fig. 2), model the beta-decay background and finite energy resolution (Sec. 3), and construct a profile-likelihood framework with Asimov data to project 3σ discovery sensitivities (Sec. 4). The central results are: (1) detecting the CNB wind requires an exposure at least ~10^5 times larger than detecting the CNB flux alone, and (2) for nonrelativistic Majorana neutrinos, the wind signal is suppressed relative to the Dirac case by a factor of order (m_ν/T_ν)^2 due to helicity cancellation in the angular-correlation term. The paper also derives requirements on systematic uncertainty control, including a fake-dipole nuisance parameter constrained by sideband data.

Significance. The paper addresses a well-motivated and timely question: how much harder is it to measure CNB anisotropy than to detect the CNB flux? The quantitative answer (the 10^5 exposure penalty and the Dirac/Majorana scaling) is a useful benchmark for the field and is derived cleanly. The analytical approximations in Sec. 2 are validated against direct numerical integration (Fig. 2), lending confidence to the parametric scaling results. The statistical framework (Sec. 4) is standard and correctly applied, and the introduction of the fake-dipole nuisance parameter ζ with a sideband calibration strategy (Eqs. 4.14–4.17) is a thoughtful treatment of the most dangerous systematic. The Dirac/Majorana separation via the helicity-odd angular-correlation term is a concrete, falsifiable prediction. The work is primarily a feasibility/phenomenology study rather than a detector design proposal, and it is appropriately scoped as such.

major comments (2)
  1. Sec. 4.3, Eqs. (4.14)–(4.17): The sideband calibration of the fake-dipole nuisance ζ assumes that ζ is energy-independent over the 2∆E_eff separation between the signal bin and the sideband bin. In a realistic PTOLEMY-type experiment with magnetic electron transport and a 2D tritium substrate, the angular acceptance is likely energy-dependent (different cyclotron radii, scattering probabilities, and quantum initial-state effects at different energies). If the energy-dependent component of the fake dipole is comparable to the signal-level requirement (~10^-3 for Dirac, ~10^-6 for Majorana per Eq. 4.11), the sideband would be an incomplete calibrator of ζ and the systematics-limited sensitivity would degrade. The manuscript acknowledges energy-dependent effects in Sec. 3.2 (Eq. 3.13) but does not assess their impact on the sideband strategy. This is the most load-bearing untested premise:
  2. Sec. 4.3, Eq. (4.11): The requirement σ_κ ≲ 1/3 for the multiplicative dipole-response calibration is presented as a separate systematic floor, but the manuscript does not discuss whether this is achievable or what calibrates it. Unlike ζ, which has a sideband handle, κ appears unconstrained by any in-situ data in the proposed analysis. For the Majorana case where the signal is already suppressed by (m_ν/T_ν)^2, even a modest multiplicative angular-response uncertainty could dominate. The authors should clarify whether κ can be constrained by the same sideband data or by external calibration, and if not, whether this represents a harder floor than ζ for the Majorana case.
minor comments (7)
  1. Sec. 2.2, Eq. (2.22): The rough numerical estimate for |δΓ_CNB/Γ_CNB,0| ~ 10^-6 for Majorana neutrinos uses a specific combination of nuclear form factors (C_B/3C_A ~ 10^-2). It would help the reader to see this numerical value broken down explicitly, since the C_B ≈ -0.50 and C_A ≈ 5.49 values give |C_B|/(3C_A) ≈ 0.030, not 10^-2. Clarifying which approximation enters this estimate would make the parametric scaling more transparent.
  2. Sec. 3.4: The text mentions that CRES-based reconstruction of parallel and transverse momentum components is under development [74], but does not state what angular resolution would be needed for the two-bin (forward-backward) analysis. A brief comment on whether the angular resolution achievable in near-term PTOLEMY prototypes is compatible with the binning assumed here would strengthen the practical assessment.
  3. Fig. 3, right panel: The y-axis range extends to 10^24 g·yr. It would be useful to mark, on both panels, the approximate exposure of currently envisioned next-generation experiments (e.g., PTOLEMY ~100 g·yr) as a horizontal reference line, to make the gap between current plans and the wind-detection requirement visually immediate.
  4. Sec. 5.1: The text states that for the effectively massless benchmark (m_ν = 10^-5 eV), the Dirac and Majorana rates become nearly identical because the neutrinos are relativistic. It would be worth noting explicitly that this regime is not physically realized for the normal or inverted hierarchy (where at least two eigenstates are nonrelativistic), so the convergence of Dirac/Majorana curves at small m_ν should not be over-interpreted.
  5. Appendix A, Eq. (A.5): The estimate ϵ ~ 10^-14 (m_ν/0.1 eV)^2 is used to justify neglecting the decoupling-era mass correction. This is clearly negligible, but a one-sentence explanation of why this correction is distinct from the boost-induced m_ν/T_ν scaling (which is not negligible) would help readers avoid confusion.
  6. Sec. 1, line 2 of the Introduction: 'What what is the velocity v_w' — duplicated 'what'.
  7. Sec. 3.1, footnote 4: The statement that the beta-decay background need not be exactly isotropic is important and could perhaps be elevated from a footnote to the main text, given its centrality to the dipole analysis strategy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for a careful reading and constructive comments. Both major comments identify legitimate gaps in our discussion of systematic uncertainties for the endpoint-dipole analysis. We address each below and describe revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: Sec. 4.3, Eqs. (4.14)-(4.17): The sideband calibration of the fake-dipole nuisance zeta assumes energy-independence over the 2*Delta_E_eff separation. In a realistic PTOLEMY-type experiment, angular acceptance is likely energy-dependent, which could make the sideband an incomplete calibrator of zeta.

    Authors: The referee is correct that energy-dependent angular acceptance effects are not assessed in our sideband discussion, and we agree this is the most load-bearing untested premise of the sideband strategy. We will revise the manuscript to address this point explicitly. Specifically, we will add a discussion in Sec. 4.3 decomposing the fake dipole into an energy-independent component zeta_0 and an energy-dependent component delta_zeta(E), and explain that the sideband constrains zeta_0 but not delta_zeta. We will note that if delta_zeta is comparable to the signal-level requirements (~10^-3 for Dirac, ~10^-6 for Majorana), the sideband calibration would be incomplete and the systematics-limited sensitivity would degrade. We will also discuss possible mitigation strategies, including using multiple sideband bins at different energies to interpolate the energy-dependent component, and note that a full assessment requires detector-specific modeling beyond the scope of this work. We agree this is an important caveat that must be stated clearly. revision: yes

  2. Referee: Sec. 4.3, Eq. (4.11): The requirement sigma_kappa < 1/3 for the multiplicative dipole-response calibration is presented as a separate systematic floor, but the manuscript does not discuss whether this is achievable or what calibrates it. Unlike zeta, kappa appears unconstrained by any in-situ data. For the Majorana case, even a modest multiplicative angular-response uncertainty could dominate.

    Authors: The referee raises a valid point. The parameter kappa is indeed not constrained by the sideband data as currently formulated, since the sideband contains no CNB signal and therefore cannot calibrate the multiplicative response of the signal template. We will revise the manuscript to clarify this explicitly. We will add a discussion of possible calibration strategies for kappa, including: (1) in-situ calibration using a known angular-asymmetric source (e.g., the angular-selective photoelectron sources developed by KATRIN, which we already cite in the context of angular reconstruction), (2) the use of the beta-decay background itself as a cross-check on angular acceptance uniformity (though this tests isotropy rather than the dipole response), and (3) the fact that kappa enters as a multiplicative uncertainty on the signal, so it does not create a fake signal but rather degrades the signal normalization. We will explicitly state that for the Majorana case, where the signal is already suppressed by (m_nu/T_nu)^2, kappa represents a potentially harder floor than zeta, since zeta can in principle be constrained by sideband data while kappa cannot be constrained by the same in-situ data. We will note that our benchmark value sigma_kappa = 0.1 is a phenomenological assumption and that achieving the required sigma_kappa < 1/3 for a 3-sigma discovery is necessary but not obviously sufficient, particularly for Majorana neutrinos where the signal-to-background ratio is far worse and the multiplicative uncertainty on the signal template could dominate the error budget. We will add a sentence emphasizing that a full assessment of kappa requires detector-specific angular response modeling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; the derivation is self-contained against standard physics inputs.

full rationale

The paper's central claims — the 10^5 exposure penalty and the (m_ν/T_ν)^2 Majorana suppression — are derived from first principles using Standard Model weak interaction structure (G_F, V_ud, U_ei), nuclear matrix elements from independent calculations [68,69], and standard ΛCDM cosmology. The helicity factors A(s_ν) and B(s_ν) in Eqs. (2.10)–(2.11) are cited from [19] (co-authored by Long), but these are standard results of the V–A weak interaction, not an ansatz or fitted relation. The paper independently validates its analytical approximations against direct numerical integration of Eq. (2.6) (Fig. 2, agreement at 0.02%), providing an internal cross-check. No parameter is fitted to data and then presented as a prediction. The nuisance parameters (α, κ, ζ) are introduced as phenomenological control parameters with stated assumptions, not as derived quantities. The self-citation [19] provides the established formalism for neutrino capture on tritium, which is independently reproducible and not load-bearing in a circular sense. The one point of mild concern is that the signal-to-background ratio condition and Gaussian smearing approach both follow [19], but these are standard treatments, not unverified claims that would force the conclusion. Score 1 reflects the minor self-citation for formalism without any reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The paper uses standard physical constants and benchmark parameters. No new particles, forces, or entities are introduced. The free parameters are experimental nuisance parameters and neutrino mass benchmarks, not fitted constants of a new theory.

free parameters (5)
  • σ_α = 0.1 (conservative), 0.001 (optimistic)
    Nuisance parameter for endpoint normalization uncertainty, chosen phenomenologically based on PTOLEMY and KATRIN benchmarks (Sec. 4.2).
  • σ_κ = 0.1
    Nuisance parameter for multiplicative angular-response uncertainty, chosen as a reference scale (Sec. 4.3).
  • σ_ζ
    Nuisance parameter for residual background dipole, treated as a free control parameter constrained by the sensitivity requirement (Sec. 4.3).
  • m_ν = 10^-5, 0.01, 0.1 eV
    Neutrino mass benchmark values used to illustrate the scaling of the required exposure (Sec. 5).
  • ΔE_eff = varied
    Effective energy resolution, treated as an independent experimental parameter (Sec. 3.2).
axioms (4)
  • domain assumption The CNB rest frame coincides with the CMB rest frame.
    Invoked in Sec. 2.1 to set the wind velocity v_w ≈ 370 km/s. This is a standard ΛCDM prediction but is unverified for the CNB.
  • domain assumption The beta-decay background is isotropic in the laboratory frame.
    Invoked in Sec. 3.1 to simplify the dipole extraction. The paper notes this may not hold in realistic detector geometries.
  • domain assumption Helicity is conserved after neutrino decoupling.
    Invoked in Sec. 2.2 to distinguish Dirac and Majorana cases. Expected to be a good approximation but small helicity rotations exist.
  • ad hoc to paper Gravitational clustering effects on the CNB distribution are neglected.
    Stated in Sec. 2.1 footnote 2 to simplify the analysis to an order-of-magnitude estimate.

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