Invisible jets from composite neutrinos

Diego Redigolo; Marco Costa; Matteo Borrello

REVIEW 3 major objections 5 minor 56 references

Invisible jets from composite neutrinos

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Invisible jets from a composite sector alter neutrino-nucleus scattering ratios, and NuTeV data already constrain the portal.

desk verdict A novel and cleanly worked-out signal that deserves refereeing, but the main NuTeV bound ignores its own conformal-window assumptions at the kinematic endpoints. read the letter →

arxiv 2507.12527 v1 pith:LRVQ3IRC submitted 2025-07-16 hep-ph hep-ex

Matteo Borrello , Marco Costa , Diego Redigolo This is my paper

classification hep-phhep-ex

keywords compositeneutrinosinvisiblejetsconformalwindowneutral-to-chargedcurrentrationeutrino-nucleusscatteringNuTeVSHiPForwardPhysicsFacility

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a neutrino coupled to a composite sterile sector can disintegrate during neutrino-nucleus scattering, producing an invisible jet, and that this process would appear as an energy-dependent enhancement of the neutral-to-charged current ratio. The authors compute the inclusive production rate from the conformal two-point function of the dark-sector operator, valid when the invisible jet invariant mass lies between the confinement scale and the ultraviolet scale. They show that NuTeV data already exclude part of the parameter space not covered by meson, Z, or Higgs invisible-decay searches, and that SHiP and the Forward Physics Facility could extend the reach. The same effect is suppressed for neutrino-electron scattering because the center-of-mass energy is set by the electron mass, so DUNE electron recoils are unlikely to see it.

What carries the argument

The load-bearing object is the fermionic conformal operator $\mathcal{O}_N$ of scaling dimension $\Delta_N = 7/2$ that couples to the muon neutrino through the portal in Eq. (1). The paper computes the inclusive invisible-jet production rate from the imaginary part of the conformal two-point function (Eq. (3)), which the optical theorem allows to be interpreted as a sum over dark-sector states. That yields the energy-scaling relation of Eq. (5): the ratio of BSM neutral-current events to charged-current events grows as $\bar{s} v^2/\Lambda_{\rm UV}^4$ times $(\bar{s}/\Lambda_{\rm UV}^2)^{\Delta_N-7/2}$, which for $\Delta_N=7/2$ is an enhancement linear in the mean neutrino energy. The invisible jet's invariant mass $m_N^2$ is the kinematic variable that separates the signal, which peaks at high $m_N$, from the Standard Model elastic background, which peaks at $m_N=0$, and the requirement $m_N^2 \lesssim s$ keeps the calculation inside the conformal window.

What would settle it

Use the FPF or SHiP sample to measure the neutral-to-charged current ratio in bins of neutrino energy $E_\nu$ in the perturbative $Q^2 > 2$ GeV$^2$ region. If $R_\nu(E_\nu)$ is flat over a range where $\Lambda_{\rm IR} < \sqrt{2 m_p E_\nu} < \Lambda_{\rm UV}$ and the predicted $\Delta g^2(s)$ from Eq. (5) would exceed the bin-level uncertainty by several $\sigma$, the central signal claim is falsified; a rise with the predicted slope would corroborate it. Repeating the measurement at two mean beam energies would isolate the $\bar{s}$-dependent term from any constant shift.

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Extended reading notes

Core claim

The paper's central claim is that a composite neutrino portal with operator dimension $\Delta_N = 7/2$ produces a calculable, energy-growing contribution to the neutral-current neutrino-nucleon cross section. Because the process is inclusive and the dark sector is a conformal continuum for $\Lambda_{\rm IR} \lesssim \sqrt{s} \lesssim \Lambda_{\rm UV}$, the inclusive cross section is fixed by the imaginary part of the conformal two-point function, ${\rm Im}[i\langle T[\mathcal{O}_N(p)\bar{\mathcal{O}}_N(-p)]\rangle] = A_\Delta p^{2\Delta_N-5}/p$. This translates into a correction $\Delta g^2(s)$ to the effective neutral-current coupling, so the neutral-to-charged current ratio becomes $R_\nu(s) = g_L^2 + r g_R^2 + \Delta g^2(s)$, with the correction growing with beam energy for $\Delta_N > 5/2$. The authors use this to reinterpret NuTeV's measurement of $g_L^2$ and to project sensitivities for SHiP and the Forward Physics Facility, and they exhibit a UV completion in which these neutrino-scattering probes outperform Higgs and Z invisible-decay bounds.

Load-bearing premise

The whole signal calculation assumes that between the confinement scale and the UV scale the dark sector is a conformal continuum, so the inclusive cross section is set by the imaginary part of the two-point function in Eq. (3) and continuum states, not single-particle resonances, dominate; if that conformal window does not extend over the relevant energies, or if dark hadronization changes the final state, the predicted event rates and bounds shift.

Editorial extensions

If this is right

NuTeV's neutral-current event sample already constrains the $(\Lambda_{\rm IR}, \Lambda_{\rm UV})$ plane beyond existing bounds from pion and kaon decays and from Z and Higgs invisible widths.
SHiP and the Forward Physics Facility can probe values of $\Lambda_{\rm UV}$ that current meson, electroweak, and Higgs constraints do not cover, using the inclusive neutral-to-charged current ratio.
Because the BSM contribution grows with $\bar{s}$ while Standard Model backgrounds grow more slowly, higher-energy neutrino beams gain sensitivity faster than simply increasing luminosity.
For DUNE electron recoils, the small center-of-mass energy $s_e = 2 m_e E_\nu$ suppresses the effect, so DUNE is unlikely to observe this signal except perhaps with an idealized narrow, higher-energy beam.
In models where the conformal window closes below the Higgs mass, Higgs and Z invisible-decay constraints are relaxed, leaving high-energy neutrino scattering as the leading probe.

Reading between the lines

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

The paper leaves implicit that an energy-binned reanalysis of existing NuTeV event rates could convert the measured constant shift into a direct measurement of the slope $dR_\nu/d\bar{s}$, which would distinguish this portal from energy-independent non-standard neutrino interactions.
A natural extension is to apply the same imaginary-part correlator to atmospheric neutrinos disintegrating in the Earth; the paper mentions the idea but does not quantify the event rate or the decay-back-to-SM signature.
If the dark sector is resonance-dominated rather than a conformal continuum, the signal would appear as narrow missing-mass peaks growing with energy instead of a smooth power law, and a search in $K \to \mu + \text{invisible}$ mass distributions would distinguish the two cases.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First, the genuinely new thing here is using the NC/CC ratio in neutrino-nucleus scattering as a probe of a composite neutrino portal, and applying it to NuTeV, SHiP, and the Forward Physics Facility. That is a real step beyond the partial-compositeness model it builds on, and the analytic cross sections in the core text and appendices are cleanly derived. The paper is also honest: it states its benchmark choices, does not fit a parameter back into the same data, and goes out of its way to show that Z and Higgs constraints can be relaxed in a UV completion. Good craft. It deserves a referee.

Now the load-bearing soft spot. The NuTeV bound is computed by integrating the CFT spectral function up to s for every event. For NuTeV, sqrt(s) reaches about 19 GeV, and the signal grows like s^2, so the highest-energy part of the flux dominates the yield. The paper states that the conformal calculation is valid only for Lambda_IR < sqrt(s) < Lambda_UV, but then uses events with sqrt(s) > Lambda_UV when deriving the exclusion, and gives no estimate of how much the bound shifts if the conformal window ends at Lambda_* below max sqrt(s), or if dark hadron resonances contaminate the lower edge. This is not a niche side condition; it is exactly the mechanism that produces the signal. The qualitative conclusion likely survives, but the numbers in Fig. 1 are softer than they look until this is checked.

Two smaller items: the SHiP upper band depends on epsilon_rej in Eq. (C31), which is never specified, so that band is presently a guess; and the NuTeV count 4.57e5 is used without an uncertainty, which matters for a paper whose main constraint is a measured event count. Both are fixable in revision.

The paper is for BSM and neutrino phenomenology readers. It is a serious contribution and should go to peer review, with a request that the authors study sensitivity to the conformal-window endpoints and resonance contamination, pin down epsilon_rej, and include NuTeV uncertainties. I would not cite the numbers as they stand; I would cite the idea once those are addressed.

Referee Report

3 major / 5 minor

Summary. The paper proposes that a composite sterile sector coupled to muon neutrinos through the portal operator in Eq. (1) can produce collimated invisible jets in neutral-current neutrino scattering. Using the optical theorem and the conformal spectral function in Eq. (3), the authors compute inclusive cross sections for scattering off electrons and nucleons, and define an energy-dependent correction to the neutral-to-charged current ratio. They derive a NuTeV exclusion, SHiP and Forward Physics Facility sensitivity projections, and meson, Z, and Higgs decay constraints, all presented in the (Λ_IR, Λ_UV) plane of Fig. 1. The paper also sketches a UV completion that relaxes the electroweak and Higgs constraints, and discusses an alternative dipole portal in Appendix D.

Significance. The paper introduces a new and distinctive experimental signature—neutrino disintegration into invisible jets—and shows that high-energy neutrino experiments can probe composite neutrino portals in parameter regions not covered by meson, Z, or Higgs invisible decay searches. The analytic derivation of the cross sections and the optical theorem relation is clear, and the benchmark choices (Δ_N = 7/2, c_N = 100, y_μ = 1, Λ_IR = 10 MeV) are declared rather than fitted, so the signal predictions are not circularly constructed from the data. If the underlying conformal-window assumption holds over the full kinematic range, the derived bounds and projections are novel and well motivated. However, the numerical reach estimates depend on two points that need sharper quantitative justification: the validity of the conformal spectral function up to the highest event energies and the treatment of non-calculable deep-inelastic background events in the SHiP projection.

major comments (3)

[Sec. IV, Eq. (3), and Fig. 1] The NuTeV exclusion is obtained by integrating the signal cross section over m_N^2 from 4Λ_IR^2 up to s using the conformal spectral function of Eq. (3) for every event. Because the NuTeV flux extends to E_ν near 200 GeV and the signal grows as s^2, the highest-√s events dominate the yield. The paper itself contemplates that the conformal window may end at an intermediate scale Λ_* below m_h in the UV completion of Eq. (6), but it does not demonstrate that the NuTeV bound is insensitive to the position of Λ_* or to dark-hadron resonance contamination near Λ_IR. Please quantify this sensitivity, for example by recomputing the bound with a sharp spectral cutoff at Λ_* = 10, 20, or 50 GeV, or by showing that the excluded region is dominated by events with √s well below any plausible endpoint.
[Appendix C2, Eq. (C31)] The upper edge of the SHiP sensitivity band in Fig. 1 is derived from the test statistic in Eq. (C31), which depends on the efficiency ϵ_rej for rejecting non-calculable DIS events. No numerical value or range for ϵ_rej is stated anywhere in the paper, so the inclusive SHiP projection is not reproducible and the width of the red band is not controlled. Please specify the assumed value of ϵ_rej, or show how the sensitivity varies as ϵ_rej ranges from 0 to 1.
[Sec. IV, NuTeV event-count bound] The NuTeV total-event constraint is imposed by requiring that the signal not exceed the observed 4.57 × 10^5 neutral-current events, with no uncertainty attached to that number, and the statement that a binned constraint was also derived from 'quoted uncertainties in individual NuTeV energy bins' is not backed by the details of that implementation. Since the exclusion boundary in Fig. 1 depends on the size of the assumed uncertainty or on how the bin-level likelihood was constructed, please provide the statistical treatment, including whether the event count is background-subtracted and how systematic uncertainties are included.

minor comments (5)

[Sec. II, Eq. (4)] The notation 'sin θ2_w' appears to be a typo for sin^2 θ_W; the same expression in the text should be made consistent with the standard weak mixing angle.
[Appendix C1, after Eq. (C3)] The phrase 'From now one we will focus' should read 'From now on we will focus'.
[Appendix B, after Eq. (B5)] The sentence 'the first two partial width agrees with Ref. [15]' should be grammatically corrected to 'the first two partial widths agree with Ref. [15]'.
[Fig. 1 caption] The caption describes the red SHiP band as corresponding to 'Q^2_SM > 2 GeV (lower line) and with all the events (upper line)', while the main text describes the band as coming from the purely perturbative bin (lower edge) and the inclusive analysis including the non-perturbative region (upper edge); please align the caption with the text.
[Sec. V] The phrase 'disintegrating in the earth' should read 'disintegrating in the Earth', and 'in this scenarios' should be 'in this scenario'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the signal cross section is computed from declared model inputs and compared to external data, with no fitted parameter recycled into a prediction.

full rationale

Walking the derivation chain, the central inputs are the operator in Eq. (1), the conformal spectral function in Eq. (3) with the benchmark choice c_N = 100, and the differential cross section in Eq. (7). The claimed energy-dependent enhancement of the neutral-to-charged current ratio follows from the model cross section scaled against the SM background, as in Eq. (5), and the NuTeV, SHiP, and FPF sensitivities are obtained by comparing these computed signal rates with external measured or expected event counts. The NuTeV bound in Sec. IV uses the explicit signal rate S = 1.7e3 (100 GeV/Λ_UV)^4 against the observed 4.57e5 NC events; Λ_UV is the constrained parameter, not a quantity fitted to the data and then re-used as a prediction. The 'consistency check' translating the g_L^2 bound of Ref. [28] into a constraint on Δg^2(s) is an external experimental constraint, not an input recycled from this paper. Meson, Z, and Higgs constraints are taken from PDG branching ratios and external BBN limits, and the cited prior work Ref. [15] has no author overlap with the present paper. The only self-citation, Ref. [43], refers to future work in preparation and is not load-bearing for any numerical result. The assumption that the conformal window (Eq. (3)) is reliable for Λ_IR ≲ √s ≲ Λ_UV is a physics assumption that could affect the robustness of the bounds, but it is not circular: no equation is defined in terms of the target result, and no fitted input is renamed as a prediction. I found no quote-exhibitable reduction of the claimed derivation to its own inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central claim rests on standard CFT machinery plus a specific strongly coupled hidden sector. The main free parameters are the two scales Lambda_IR and Lambda_UV, the operator dimension Delta_N, the coupling y_mu, the central charge c_N, and the unspecified rejection efficiency epsilon_rej. These are benchmark choices rather than fitted quantities, and the external comparisons use NuTeV event counts and SM branching ratios.

free parameters (6)

Lambda_UV (portal/UV scale) = scanned; lower bounds from data
The central scale in the portal operator Eq. (1); sensitivity plots give exclusion contours in (Lambda_IR, Lambda_UV). It is varied, not fit, but the quoted reach is the key output.
Lambda_IR (confinement scale) = 10 MeV benchmark
Used for lifetime estimates and kinematic cuts; BBN gives a lower bound, otherwise it is a free model input.
Delta_N (scaling dimension of O_N) = 7/2
Chosen by hand to make the signal UV-dominated and long-lived; appears in Eq. (2) and Sec. II.
y_mu (portal coupling) = 1
Set to 1 for all numerical projections; cross sections scale as y_mu^2.
c_N (central charge of dark sector) = 100 (A_N = 3.27)
Normalizes the conformal two-point function Eq. (3); chosen as an order-one-ish value.
epsilon_rej (non-calculable DIS rejection efficiency) = not specified
Appears in Eq. (C31); the upper edge of the SHiP sensitivity band depends on it, but no numeric value is given.

assumptions (5)

domain assumption The dark sector possesses a conformal window with mass gap Lambda_IR and UV cutoff Lambda_UV described by CFT two-point functions.
Used throughout; needed for Eq. (3) and for the inclusive cross sections.
domain assumption The optical theorem relates inclusive neutrino scattering to the imaginary part of the correlator <O_N O_Nbar>, with continuum dominance for Delta_N >= 7/2.
This is the bridge from CFT data to scattering rates; it enters in Sec. II after Eq. (3).
standard math Unitarity and conformal symmetry fix the two-point function normalization with positive central charge c_N.
Standard CFT result invoked in Appendix A and used in Eq. (3).
ad hoc to paper Dark-sector states live long enough that the produced jets are invisible inside the detector.
The whole invisible jet signature assumes this; the lifetime estimate in Eq. (2) follows from portal scaling but is not independently tested.
domain assumption QCD perturbation theory with standard PDFs applies for Q^2 > 2 m_p^2 and m_j^2 > 2 m_p^2.
Used to separate perturbative and non-perturbative regions in the nucleon scattering analysis, Sec. IV and App. C2.

invented entities (1)

Composite sterile sector and its dark continuum states (invisible jets) independent evidence
purpose: Produces neutrino disintegration into invisible jets and the NC/CC enhancement.
The model provides externally testable predictions: energy-dependent NC excess in neutrino-nucleus scattering at NuTeV, SHiP, and FPF. No current evidence exists, but the signal can be confirmed or excluded by experiments.

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Cite this review

Pith. "Pith review of Invisible jets from composite neutrinos." pith.science (2026). https://pith.science/paper/LRVQ3IRC

@misc{pith2026250712527,
  author       = {Pith},
  title        = {Pith review of: Invisible jets from composite neutrinos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LRVQ3IRC}},
  note         = {Machine review of arXiv:2507.12527}
}

read the original abstract

We propose a novel experimental probe of neutrino couplings to a composite sterile sector, leveraging the unique signature of neutrino disintegration into "invisible jets" in high-energy neutrino scattering. Focusing on scenarios where the invisible jet invariant mass significantly exceeds the confinement scale, we compute production rates within the conformal window. In this regime, invisible jet production leads to an energy-dependent enhancement of the neutral-to-charged current ratio in neutrino-nucleus scattering. Using NuTeV measurements, we derive new bounds and assess the sensitivity of upcoming experiments such as SHiP and the Forward Physics Facility at CERN. We sketch models where these probes surpass constraints from electroweak gauge boson and Higgs invisible branching ratios. In contrast, neutrino-electron scattering modifications are suppressed by the lower center-of-mass energy and are unlikely to be observable at DUNE.

Figures

Figures reproduced from arXiv: 2507.12527 by the authors.

**Figure 2.** FIG. 2. Log-likelihood for electron recoil events at DUNE [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Allowed kinematical region for DIS at SHiP assum [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4. Normalized differential decay width [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. Summary plot of the normalized fluxes. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6. Expected sensitivities from scattering over electrons for an incoming gaussian flux centered at energy [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: FIG. 7. Test statistics [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: FIG. 8. Kinematics in the ( [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.

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We first recompute the signal rate in step by step

Electron recoils For electron recoil events, the likelihood behavior can be understood analytically. We first recompute the signal rate in step by step. As in Eq. (7), the matrix element squared averaged on the initial spins can be split into 10 | ¯M |2 = | ¯ML|2 + | ¯MR|2 where ML (MR) involves the left-handed (right-handed) electron current. These are |...

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