$\delta_{\rm CP}$-free constraints on NSI parameters $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$ using high-purity $\nu_\mu\,{\rm CC}$ events at IceCube DeepCore

Using a high-purity sample of atmospheric $\nu_\mu$ charged-current events from 7.5 years of IceCube DeepCore data, this study establishes $\delta_{\rm CP}$-free constraints on non-standard interaction parameters $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$ that are consistent with the Standard Model and complementary to long-baseline experiments.

The Gist

The Invisible Ghosts and the Ice Cube Detective

Imagine the universe is filled with trillions of invisible, ghostly particles called neutrinos. They are so shy and light that they can pass through entire planets without bumping into anything. Most of the time, they just zip right through us, the Earth, and everything else without a care in the world.

But sometimes, these ghosts play a game of "musical chairs" called oscillation. As they travel, a neutrino that starts as a "muon" type might transform into an "electron" type, or a "tau" type, and then back again. Scientists have a standard rulebook (the Standard Model) that predicts exactly how this game should play out.

However, some scientists suspect there are hidden rules we haven't discovered yet. They call these "Non-Standard Interactions" (NSI). Think of NSI as secret cheat codes or invisible magnets that might be slightly nudging the neutrinos, changing how they dance as they travel through the Earth.

The Detective: IceCube DeepCore

To catch these ghosts and see if they are cheating, scientists built a giant detector called IceCube at the South Pole. It's a massive cube of ice with thousands of sensors buried deep inside.

For this specific study, the researchers focused on a smaller, super-dense part of the detector called DeepCore. They looked at data collected over 7.5 years. Imagine this as a detective reviewing 7.5 years of security camera footage, looking for a specific type of ghost (the muon neutrino) that is supposed to survive a long journey through the Earth.

The Mystery: The "CP" Confusion

In the world of neutrinos, there's a tricky variable called $\delta_{CP}$ (delta CP). Think of this as a "phase shift" or a hidden dial on the neutrino's dance floor.

• In many experiments, if you try to measure the "cheat codes" (NSI), the hidden dial ($\delta_{CP}$) gets in the way. It's like trying to measure the wind speed while someone is constantly spinning a fan in front of your sensor. You can't tell if the wind is blowing or if the fan is just spinning. This is called degeneracy.

The Big Breakthrough of this Paper:
The researchers in this paper found a clever trick. They focused only on muon neutrinos that survived their journey (the "survival channel"). They discovered that for this specific type of ghost, the hidden dial ($\delta_{CP}$) barely matters at all. It's like finding a room in the house where the fan is turned off. This allowed them to measure the "cheat codes" (NSI) without the confusion of the hidden dial.

The Investigation: What Did They Find?

The team used a massive amount of data to ask: "Are these neutrinos behaving exactly as the standard rulebook says, or are they being nudged by secret forces?"

They looked at three specific types of potential nudges (parameters):

1. $\epsilon_{e\mu}$: A nudge between electron and muon types.
2. $\epsilon_{e\tau}$: A nudge between electron and tau types.
3. $\epsilon_{ee} - \epsilon_{\mu\mu}$: A difference in how electron and muon types interact with matter.

The Verdict:
After crunching the numbers, the answer was: No cheating detected.

The neutrinos behaved exactly as the standard rulebook predicted. The data was a perfect match for the "no secret forces" hypothesis.

The Results: Setting the Boundaries

Even though they didn't find new physics, the study was a huge success because it set the boundaries for where new physics could exist.

Imagine you are looking for a lost key in a dark room. You don't find the key, but you shine a flashlight and realize, "Okay, the key is definitely not under this rug, and it's not in this corner."

• The paper says: "If there are these secret nudges, they must be incredibly weak. We have ruled out any strong nudges."
• They provided very strict limits (bounds) on how strong these secret forces could possibly be.

Why This Matters

1. A Clean Look: Because they used the "survival channel" (muon neutrinos that didn't change), their results are "clean." They aren't confused by the hidden dial ($\delta_{CP}$). This makes their findings a perfect complement to other experiments that do get confused by the dial. It's like two detectives looking at the same crime scene from different angles; together, they get the full picture.
2. Future Clues: By proving that these secret nudges are either non-existent or very weak, they help future scientists know where to look next. If the "cheat codes" are this weak, maybe we need even bigger detectors or different types of neutrinos to find them.

In a Nutshell

This paper is a story of precision. The scientists used a giant ice detector to watch neutrinos travel through the Earth. They found a special way to look at them that removed the usual confusion. Their conclusion? The neutrinos are playing by the rules. There are no obvious "cheat codes" in the game of neutrino oscillations—at least not the ones they were looking for. This helps us understand the universe a little better by telling us exactly what isn't happening.

Technical Summary

1. Problem Statement and Motivation

• Context: While neutrino oscillations are well-established, several fundamental parameters remain unknown, including the CP-violating phase ($\delta_{CP}$), the octant of $\theta_{23}$, and the neutrino mass ordering. Furthermore, the mechanism generating neutrino mass suggests the existence of physics Beyond the Standard Model (BSM).
• The Specific Challenge: Non-Standard Interactions (NSI) of neutrinos with matter are a prominent BSM scenario. NSI parameters ($\varepsilon_{\alpha\beta}$) can significantly alter neutrino oscillation probabilities as they propagate through the Earth.
• The Degeneracy Issue: In long-baseline accelerator experiments (like NOvA or T2K), constraints on flavor-violating NSI parameters (specifically $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$) are often plagued by a $\delta_{CP}$ degeneracy. The appearance channels ($\nu_\mu \to \nu_e$) used in these experiments depend strongly on $\delta_{CP}$, making it difficult to disentangle the effects of NSI from the standard CP phase.
• Objective: This work aims to constrain the NSI parameters $\varepsilon_{e\mu}$, $\varepsilon_{e\tau}$, and the non-universal parameter $\varepsilon_{ee} - \varepsilon_{\mu\mu}$ using atmospheric neutrinos. The primary goal is to achieve constraints that are free from $\delta_{CP}$ degeneracy by utilizing a specific event sample where the oscillation probability is insensitive to $\delta_{CP}$.

2. Methodology

• Data Source: The analysis utilizes the publicly available IceCube DeepCore atmospheric neutrino dataset with a 7.5-year livetime (collected between 2011 and 2018).
• Event Selection ("Golden Sample"):
  • The study focuses on a high-purity sample of $\nu_\mu$ Charged-Current (CC) events.
  • Events are selected based on "direct" Cherenkov photons (minimizing scattering) to improve energy and angular resolution.
  • Events are classified using a Boosted Decision Tree (BDT) Particle Identification (PID) score. The analysis selects track-like (PID 0.75–1.0) and mixed (PID 0.55–0.75) events, achieving a $\nu_\mu$ CC purity of $\sim$80%.
  • The energy range is 6.3 – 158.5 GeV, and the zenith angle covers up-going events ($\cos \theta_z \in [-1, 0.1]$).
• Theoretical Framework:
  • The analysis employs a three-flavor oscillation framework including Neutral-Current (NC) NSI.
  • The effective Hamiltonian includes the standard matter potential modified by effective NSI parameters $\varepsilon_{\alpha\beta}$.
  • Key Insight: The survival probability $P(\nu_\mu \to \nu_\mu)$ is suppressed by a factor of $(\Delta m^2_{21}/\Delta m^2_{31}) \times \sin \theta_{13} \approx 0.005$ regarding $\delta_{CP}$ dependence. Therefore, using the $\nu_\mu$ survival channel allows for $\delta_{CP}$-free constraints on $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$.
• Statistical Analysis:
  • A binned $\chi^2$ analysis is performed comparing observed data against expected distributions under specific NSI hypotheses.
  • Systematic Uncertainties: The analysis incorporates 20 nuisance parameters covering detector effects (DOM efficiency, ice optical properties), atmospheric flux (Honda model), cross-sections, oscillation parameters, and background normalizations.
  • Fitting Strategy: NSI parameters are fitted one at a time while other NSI parameters are fixed to zero. $\delta_{CP}$ is fixed at $0^\circ$ (verified to have negligible impact).

3. Key Contributions

1. First $\delta_{CP}$-Free Constraints from IceCube: This is the first comprehensive study using IceCube DeepCore to constrain $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$ specifically leveraging the $\nu_\mu$ survival channel to eliminate $\delta_{CP}$ degeneracy.
2. High-Purity Sample Optimization: The work demonstrates the utility of the "golden event sample" (high-purity $\nu_\mu$ CC) for NSI searches, showing that despite lower statistics compared to inclusive samples, the purity provides robust, degeneracy-free limits.
3. Complementarity: The results provide crucial complementary constraints to long-baseline experiments (which rely on appearance channels) and atmospheric experiments like KM3NeT/ORCA.
4. Updated Limits: The analysis updates previous IceCube DeepCore results (based on 3 years of data) using an 8-year dataset, refining the sensitivity to NSI parameters.

4. Results

The data is found to be consistent with the Standard Model (no significant evidence for NSI). The following constraints are reported at 90% Confidence Level (C.L.):

• $\varepsilon_{e\mu}$ (Flavor Violating):

  • Best-fit magnitude: $|\varepsilon_{e\mu}| = 0.034$ (Phase $\phi_{e\mu} = 346.2^\circ$).
  • Upper Bound: $|\varepsilon_{e\mu}| \leq 0.12$.
  • Real-valued range: $[-0.11, 0.12]$.
  • Note: The phase cannot be constrained as the minimum $\chi^2$ prefers values near zero magnitude.

• $\varepsilon_{e\tau}$ (Flavor Violating):

  • Best-fit magnitude: $|\varepsilon_{e\tau}| = 0.11$ (Phase $\phi_{e\tau} = 8.8^\circ$).
  • Upper Bound: $|\varepsilon_{e\tau}| \leq 0.18$.
  • Real-valued range: $[-0.11, 0.18]$.
  • Note: Sensitivity improvement over the 3-year analysis is modest because $\varepsilon_{e\tau}$ primarily affects appearance channels, which have lower statistics in this $\nu_\mu$-dominated sample.

• $\varepsilon_{ee} - \varepsilon_{\mu\mu}$ (Flavor Conserving/Non-Universal):

  • Best-fit value: $-0.59$.
  • Constraint: No meaningful 90% C.L. bound could be placed due to limited sensitivity (this parameter mainly affects the $\nu_e$ appearance channel, which is sub-dominant in this sample).
  • However, values outside the interval $[-1.43, -1.11] \cup [-0.8, 1.08] \cup [1.20, 1.37]$ are excluded at 68.3% C.L.

• Comparison: The results are consistent with previous IceCube DeepCore results (3-year data) and other experiments like NOvA and KM3NeT/ORCA.

5. Significance

• Breaking Degeneracies: The primary significance of this work is the demonstration that atmospheric neutrino data, specifically the $\nu_\mu$ survival channel, can provide robust constraints on NSI parameters that are independent of the unknown CP phase $\delta_{CP}$. This resolves a major ambiguity present in accelerator-based analyses.
• Validation of Standard Model: The lack of deviation from the Standard Model hypothesis reinforces current oscillation paradigms and places tight limits on new physics scenarios involving flavor-changing neutral currents.
• Future Outlook: The study highlights the potential of upcoming high-statistics atmospheric neutrino experiments (e.g., IceCube Upgrade, KM3NeT/ORCA, Hyper-K, DUNE) to further probe these NSI parameters. The complementary nature of these measurements is essential for a complete global fit of neutrino properties.

In conclusion, this paper establishes that high-purity $\nu_\mu$ CC events from IceCube DeepCore are a powerful tool for constraining non-standard neutrino interactions, offering a unique, $\delta_{CP}$-independent perspective that complements existing long-baseline experimental data.