Neutrino Kaleidoscope Experiment

• Neutrino Kaleidoscope is an experimental program that fuses a TeV-scale, ultra-collimated neutrino beam with a large-volume telescope to probe non-standard oscillation phenomena.
• It employs precise beam geometry, flux density control, and flavor tagging to achieve sensitivity to sterile neutrino mixing and Lorentz invariance violation beyond traditional methods.
• The innovative design enables high event statistics and in situ calibration for rare interaction searches, advancing our understanding of quantum gravity-scale effects.

The Neutrino Kaleidoscope is the experimental paradigm and scientific program that pairs a high-energy muon accelerator—capable of generating a TeV-scale, ultra-collimated neutrino beam—with a gigaton-scale neutrino telescope (such as IceCube, KM3NeT, or P-ONE), in order to conduct precision searches for non-standard oscillation phenomena, including sterile neutrino mixing and Lorentz invariance violation, at unprecedented energy and baseline regimes. By exploiting the extraordinary flux density, flavor purity, and geometric matching of accelerator-produced neutrinos with large-volume detectors, the Neutrino Kaleidoscope enables a new class of terrestrial oscillation experiments sensitive to quantum gravity-scale new physics and rare interaction channels (Kamp et al., 12 Aug 2025).

1. Experimental Configuration: Geometry, Flux, and Beam Matching

The Neutrino Kaleidoscope requires (1) a high-energy muon accelerator, typically designed for $\mathcal{O}(1-10)$ TeV muon beams, and (2) a neutrino telescope with instrumented volume on the $\sim100$ m to kilometer scale, such as IceCube, KM3NeT, or P-ONE. In this setup, muon decays ($$\mu^\pm \to \nu_\mu/\bar\nu_\mu + \nu_e/\bar\nu_e + e^\pm$$) generate a neutrino beam with an intrinsic angular spread $\theta \approx 1/\gamma$ (with $\gamma = E_\mu/m_\mu$), resulting in a beam spot size on the order of 100 m for $E_\mu \sim 5$ TeV. This is well-matched to the transverse size of large-volume neutrino telescopes at typical source-detector baselines (3000–12,000 km).

Proper geometry requires orienting an accelerator straight section, beam dump, or collision point at a downward angle dictated by the baseline and Earth's curvature—examples given include angles of $13^\circ$ (Fermilab–P-ONE), $34^\circ$ (Fermilab–KM3NeT), and $66^\circ$ (Fermilab–IceCube). Beam divergence must be tightly controlled, as excess divergence reduces beam intensity within the detector core. Optical techniques and possible mechanical movers are suggested for optimizing beam delivery.

Large telescopes distinguish flavor signatures via the observed topology: track-like signatures from $\nu_\mu$ charged-current (CC) interactions, and cascades (showers) from $\nu_e$ CC and neutral current interactions. The beam's monochromatic flavor content, energy, and spatial correlations provide a uniquely controlled and reconstructible experimental environment (Kamp et al., 12 Aug 2025).

2. Sensitivity to Sterile Neutrino Mixing via Active–Sterile Resonance

The Neutrino Kaleidoscope offers compelling sensitivity to sterile neutrinos, especially in the “3+1” framework (three active plus one eV-scale sterile state). For TeV-scale neutrinos traversing Earth, oscillations into sterile states are strongly modified by coherent forward scattering in matter (the Mikheyev–Smirnov–Wolfenstein effect):

$$i \frac{d}{dx} \begin{pmatrix} \nu_\alpha \ \nu_S \end{pmatrix} = \begin{pmatrix} -\frac{\delta m^2}{4E} \cos 2\theta_{\alpha\alpha} \pm_\alpha \frac{G_F N_e}{\sqrt{2}} & \frac{\delta m^2}{4E} \sin 2\theta_{\alpha\alpha} \ \frac{\delta m^2}{4E} \sin 2\theta_{\alpha\alpha} & \frac{\delta m^2}{4E} \cos 2\theta_{\alpha\alpha} \end{pmatrix} \begin{pmatrix} \nu_\alpha \ \nu_S \end{pmatrix}$$

where $\alpha\in\{e,\mu\}$ and the matter potential term is positive (negative) for neutrinos (antineutrinos). Resonant enhancement occurs when

$$\frac{\delta m^2}{4E} \cos 2\theta_{\alpha\alpha} = \frac{G_F N_e}{\sqrt{2}}$$

allowing even small vacuum mixing to yield large transitions—particularly for muon or electron neutrinos at multi-TeV energies over Earth-scale baselines. The intense, flavor-pure Kaleidoscope beam means $\mathcal{O}(10^8)$–$\mathcal{O}(10^9)$ events per year can be collected, permitting direct measurement of tiny “active-to-sterile” transition probabilities and surpassing current terrestrial bounds by orders of magnitude (Kamp et al., 12 Aug 2025).

3. Probing Lorentz Invariance Violation and Planck-scale New Physics

The Neutrino Kaleidoscope is optimized to probe quantum gravity and Lorentz invariance violation (LIV) via oscillations driven by Standard Model Extension (SME) operators:

$$i \frac{d}{dx} \begin{pmatrix} \nu_\mu \ \nu_\tau \end{pmatrix} = \left[ \frac{\delta m_{31}^2}{4E} \begin{pmatrix} -\cos 2\theta_{23} & \sin 2\theta_{23} \ \sin 2\theta_{23} & \cos 2\theta_{23} \end{pmatrix} + \mathcal{V} \right] \begin{pmatrix} \nu_\mu \ \nu_\tau \end{pmatrix}$$

with $\mathcal{V}$ encoding Lorentz-violating potentials. In the SME formalism, these potentials are parametrized by Wilson coefficients ($a_L^\mu, c_L^{\mu\nu}$, etc.) and can show explicit sidereal modulation:

$$\mathcal{V}_{\mu\tau} = \mathcal{C} + \mathcal{A}_s \sin(\omega_\oplus T_\oplus) + \mathcal{A}_c \cos(\omega_\oplus T_\oplus) + \mathcal{B}_s \sin(2\omega_\oplus T_\oplus) + \mathcal{B}_c \cos(2\omega_\oplus T_\oplus)$$

where $\omega_\oplus$ is the sidereal frequency and $T_{\oplus}$ sidereal time. Because the Kaleidoscope configuration provides continuous flux with known energy, flavor, and sidereal phase, oscillation probability deviations can be analyzed via Fourier decomposition in time or energy, leading to constraints on SME coefficients down to double-Planck-suppressed levels for operator dimension $d=6$ (i.e., effective couplings $\sim 1/E_P^2$, with $E_P = 1.22 \times 10^{19}$ GeV) (Kamp et al., 12 Aug 2025).

For the oscillation probability,

$$P_{\nu_\mu \rightarrow \nu_\tau} = L^2 \left| \left( \frac{\delta m_{31}^2}{4E} \right) \sin 2\theta_{23} + \mathcal{V}_{\mu\tau} \right|^2 + \mathcal{O}(L^4)$$

where $L$ is the baseline. This scaling, together with high energy and large statistics, provides unique sensitivity to tiny LIV effects.

4. Advantages in Systematics, Statistics, and Oscillation Channel Control

In the Neutrino Kaleidoscope, systematic uncertainties endemic to standard long-baseline experiments—such as beam normalization, source flux shape, and uncertain path length—are tightly constrained or eliminated:

• The spectral and spatial control from the accelerator allows for detailed in situ calibration and precision energy–flavor mapping.
• The geometric match ensures nearly all beam neutrinos intercept the detector, with event samples reaching hundreds of millions per year, making even small oscillation probabilities measurable.
• Flavors are tagged with high fidelity by topology, and with waterfall energy calibration, differential oscillation probabilities by energy and sidereal phase are accessible.

These features enable searches for oscillations with dependence $P\sim L E^n$ or $P\sim LE$ (for higher-dimensional SME operators), as opposed to the canonical $L/E$ dependence of standard oscillations, and remove many degeneracies present in atmospheric or non-monochromatic sources.

5. Non-Oscillation Physics and Rare Channel Searches

Beyond oscillations, the Kaleidoscope provides opportunities for rare process investigation given its event rate and energy reach:

• Dimuon events from charm, $W$-boson, or trident production are accessible with distinctive double-track signatures, opening precision studies of QCD and electroweak processes in the TeV regime.
• Rare non-standard interactions or anomalous neutrino–nucleon processes may be identified with high statistical significance.
• Deep inelastic scattering and precise cross-section measurements in previously inaccessible kinematics become possible (Kamp et al., 12 Aug 2025).

6. Quantitative and Formulaic Summary

Central formulas specifying the sensitivity and operational principle include (all appear in the cited work):

Oscillation Channel	Evolution/Resonance Equation
Active–sterile (in matter)	$$i \frac{d}{dx} (\nu_\alpha, \nu_S)^T = \begin{pmatrix} -\frac{\delta m^2}{4E} \cos2\theta_{\alpha\alpha} \pm \frac{G_FN_e}{\sqrt2} & \frac{\delta m^2}{4E} \sin2\theta_{\alpha\alpha} \ \frac{\delta m^2}{4E} \sin2\theta_{\alpha\alpha} & \frac{\delta m^2}{4E} \cos2\theta_{\alpha\alpha} \end{pmatrix} (\nu_\alpha, \nu_S)^T$$
SME (LIV)	$i \frac{d}{dx}(\nu_\mu,\nu_\tau)^T = \left[ \frac{\delta m_{31}^2}{4E} \mat{ -\cos2\theta_{23} & \sin2\theta_{23} \ \sin2\theta_{23} & \cos2\theta_{23} } + \mathcal{V} \right] (\nu_\mu,\nu_\tau)^T$
SME potential	$$\mathcal{V}_{\mu\tau} = \mathcal{C} + \mathcal{A}_s \sin(\omega_\oplus T_\oplus) + \mathcal{A}_c \cos(\omega_\oplus T_\oplus) + \mathcal{B}_s \sin(2\omega_\oplus T_\oplus) + \mathcal{B}_c \cos(2\omega_\oplus T_\oplus)$$
Sensitivity scaling	$$|p|^{d-3} |\mathcal{A}_c^d| \simeq |\mathcal{A}_c^3|$$ (for dimension $d$ operator)

These equations provide the mathematical backbone for the experimental reach in non-standard scenarios.

7. Outlook and Context in Oscillation Physics

The Neutrino Kaleidoscope is uniquely situated to extend searches for non-standard interactions—sterile neutrinos, LIV, and Planck-suppressed effects—beyond the limitations of current terrestrial and atmospheric neutrino experiments. The approach leverages advances in both accelerator and detector technology, and the program is complementary to, but also more sensitive in key channels than, atmospheric and astrophysical studies due to its geometric and flux control.

A plausible implication is that the Neutrino Kaleidoscope configuration will play a central role in closing open questions in high-energy neutrino phenomenology and may provide unique empirical access to exotic operators predicted by quantum gravity and other extensions of the Standard Model (Kamp et al., 12 Aug 2025).