Searching for Extra Dimensions and Copies of the Standard Model with IceCube

Technical Summary: Searching for Extra Dimensions and Copies of the Standard Model with IceCube

Problem and Motivation
The hierarchy problem, characterized by the vast disparity between the electroweak scale and the Planck scale, remains a central open question in particle physics. The Standard Model (SM) requires extreme fine-tuning to stabilize the Higgs boson mass against quantum corrections if the ultraviolet cutoff is the Planck scale ($M_P \approx 1.22 \times 10^{19}$ GeV). Low-scale gravity theories propose that the fundamental scale of gravity ($M_f$) is much lower, potentially near the TeV scale, thereby alleviating this hierarchy. Two specific benchmark realizations of this concept are investigated:

1. The Arkani–Hamed–Dimopoulos–Dvali (ADD) model: Postulates $d$ compact extra spatial dimensions where gravity propagates, while the SM is confined to a 3-brane.
2. The Many-Species Framework: Proposes $N$ copies of the SM interacting only gravitationally, where the large number of species lowers the fundamental scale via the species bound.

Both frameworks predict the existence of additional sterile neutrino states (Dirac right-handed neutrinos) that couple to the SM via Yukawa interactions. These states induce matter-enhanced active–sterile transitions as neutrinos propagate through the Earth, potentially causing characteristic distortions in the energy and zenith-angle distributions of high-energy atmospheric neutrinos.

Methodology
The analysis utilizes 10.7 years of high-energy neutrino data (May 2011 – June 2022) collected by the IceCube Neutrino Observatory at the South Pole. The dataset comprises 368,071 upward-going, track-like events, primarily originating from charged-current (CC) interactions of muon neutrinos ($\nu_\mu$) and antineutrinos ($\bar{\nu}_\mu$). The sample is dominated by $\nu_\mu$ (~74%), with $\bar{\nu}_\mu$ constituting ~26%.

• Signal Mechanism: The models predict that sterile states, which do not experience neutral-current (NC) interactions, create a physical potential difference relative to active neutrinos. Because the sterile states are heavier than active ones, the Mikheyev–Smirnov–Wolfenstein (MSW) resonance condition is satisfied only for antineutrinos ($\bar{\nu}_\mu$). This leads to resonant flavor conversion and a flux deficit localized in energy and zenith angle for $\bar{\nu}_\mu$ traversing the Earth's core and mantle.
• Simulation and Reconstruction: The analysis employs a forward-folding procedure. Atmospheric neutrino fluxes (conventional, prompt, and astrophysical) are modeled, and propagation through the Earth is simulated using the nuSQuIDS framework with the Preliminary Reference Earth Model (PREM) density profile.
  • For the ADD model, the Kaluza-Klein (KK) tower is truncated to the first two dominant modes, resulting in a $(9 \times 9)$ Hamiltonian.
  • For the SM copies model, the full mixing is described by a $(6 \times 6)$ matrix.
• Statistical Analysis: A binned Poisson likelihood is constructed in reconstructed energy and zenith-angle bins. Systematic uncertainties (flux normalization, cross-sections, detector optical properties, etc.) are handled via nuisance parameters with appropriate priors. Exclusion limits are derived using the profile likelihood ratio and Wilks' theorem. The analysis distinguishes between "starting" events (interaction vertex inside the detector) and "through-going" events (muons entering from outside).

Key Contributions and Results
The study finds no significant deviation from the standard three-flavor neutrino oscillation framework (significance $\ll 3\sigma$). Consequently, exclusion limits are placed on the physical parameters of the low-scale gravity scenarios:

1. ADD Model Constraints:

   • The compactification radius ($R$) of the largest extra dimension is constrained to $R \lesssim 0.17$ µm at the 90% confidence level.
   • This limit holds for both normal and inverted neutrino mass orderings and is largely independent of the lightest neutrino mass ($m_0$).
   • The sensitivity improves with larger $m_0$ due to enhanced active–sterile mixing.
   • These results are competitive with or stronger than existing neutrino-oscillation constraints over large parts of the $m_0$ range and are complementary to direct mass bounds from KATRIN.

2. SM Copies Constraints:

   • Lower limits on the number of SM copies ($N$) are derived, reaching up to $N \gtrsim \mathcal{O}(400)$, depending on the mass factor ($\mu$) and the lightest neutrino mass.
   • The strongest constraints occur when the mass factor $\mu$ places the heavy sterile states at the eV scale, aligning resonances with the analysis energy window (0.5–100 TeV).
   • The exclusion regions exhibit complex structures (single vs. double peaks) depending on how resonances merge or vanish based on $m_0$ and mass ordering.

Significance
The paper claims that these results constitute the strongest terrestrial constraints to date in specific regions of the parameter space for both models, while probing previously unexplored regions in others. The work demonstrates that high-energy neutrino propagation through the Earth provides direct sensitivity to low-scale gravity realizations in the neutrino sector. By utilizing the unique matter effects over long baselines, IceCube offers a complementary probe to collider experiments and sub-millimeter gravity tests, effectively constraining the fundamental scale of gravity through the absence of predicted spectral distortions.