Searching non-standard interactions with atmospheric neutrinos at ESSnuSB

This paper investigates the potential of the proposed ESSnuSB far detector to constrain non-standard neutrino interactions using atmospheric neutrinos, demonstrating that it can set competitive upper bounds on interaction parameters while highlighting the experiment's complementarity with accelerator-based programs and its impact on mass ordering and octant sensitivities.

The Gist

Imagine the universe is filled with a ghostly rain of tiny particles called neutrinos. These particles are created when cosmic rays hit the Earth's atmosphere, raining down on us from all directions. They are so elusive that they can pass through the entire Earth without bumping into anything, making them incredibly difficult to catch and study.

This paper is about a proposed experiment called ESSnuSB, which plans to build a massive underground "net" (a giant water tank) in Sweden to catch these atmospheric neutrinos. The researchers want to use this net not just to count the neutrinos, but to see if they are behaving exactly as our current laws of physics predict, or if they are doing something strange that hints at new physics.

Here is a breakdown of what they are looking for, using simple analogies:

1. The "Standard" vs. The "New" Rules

Think of the Standard Model of physics as a well-written rulebook for how neutrinos behave. It says that as neutrinos travel, they can "change costumes" (oscillate) from one type (flavor) to another—like a chameleon changing colors.

However, the researchers suspect there might be Non-Standard Interactions (NSI).

• The Analogy: Imagine neutrinos are cars driving on a highway. The Standard Model says the road is smooth and the cars follow predictable paths. NSI suggests there might be invisible "bumps" or "wind gusts" (interactions with matter) that push the cars off their expected paths in ways the rulebook doesn't explain.
• The Goal: The paper asks: "If we watch enough cars (neutrinos) drive through the Earth, can we detect these invisible bumps?"

2. The Experiment: A Giant Underwater Net

The ESSnuSB project is building two huge cylindrical water tanks deep inside a mine in Sweden.

• The Net: When a neutrino hits a water molecule, it creates a flash of light (like a spark in the dark). The sensors in the tank catch this light.
• The Data: They are simulating 5.4 million tons of water watching for 10 years. That's a massive amount of data, equivalent to catching a huge number of these "ghost" particles.
• The Method: They use powerful computer simulations (Monte Carlo) to predict what the data should look like if the "Standard Rules" are true. Then, they compare this to what the data looks like if those invisible "bumps" (NSI) exist.

3. What They Found (The Results)

The researchers ran their simulations to see how well this experiment could spot those invisible bumps.

• Setting Limits: They found that if they don't see any strange behavior, they can confidently say that these "invisible bumps" are very small. Specifically, they can rule out certain types of strange interactions with a high degree of certainty (90% confidence).
  • Analogy: It's like saying, "We looked at 10,000 cars, and none of them swerved. Therefore, we know for sure that the wind gusts pushing them off the road are weaker than 5 miles per hour."
• Specific Numbers: They calculated the maximum possible size of these interactions. For example, they can prove that a specific type of interaction (involving electron and muon neutrinos) is smaller than 0.053. This is a very tight constraint, meaning the "bumps" are very subtle if they exist at all.
• Comparison: Their proposed experiment is expected to be 3 to 4 times more sensitive than current experiments for some of these interactions. It's like upgrading from a pair of binoculars to a high-powered telescope.

4. The "Side Effects" on Other Measurements

The paper also checked if looking for these "bumps" would mess up their ability to measure other things they care about.

• The Mass Ordering: Physicists want to know which neutrino is the heaviest. The paper says that even if these "bumps" exist, the ESSnuSB experiment will still be able to figure out the mass order with very high confidence (over 6 sigma, which is a gold standard in physics).
• The "Octant": This refers to a specific angle in the neutrino's behavior. The paper concludes that even with the extra complexity of searching for new physics, the experiment will still be able to determine this angle accurately.

5. The Big Picture: Complementarity

The authors emphasize that this atmospheric neutrino study is a perfect partner to the main ESSnuSB experiment.

• The Main Experiment: Uses a beam of neutrinos shot from a machine (like a laser pointer) to study specific interactions.
• This Study: Uses the natural "rain" of atmospheric neutrinos coming from all angles.
• The Result: By combining the "laser" approach with the "rain" approach, they get a much fuller picture of the neutrino world. If one method misses a subtle "bump," the other might catch it.

Summary

In short, this paper is a "proof of concept" for a future experiment. It says: "If we build this giant water detector in Sweden and watch atmospheric neutrinos for a decade, we will be able to set very strict limits on whether neutrinos are interacting with matter in weird, new ways. Even if we don't find new physics, we will know exactly how small those new effects must be, and we will still be able to solve other major neutrino mysteries."

Technical Summary

Technical Summary: Searching Non-Standard Interactions with Atmospheric Neutrinos at ESSnuSB

Problem Statement
The standard paradigm of neutrino physics, characterized by three mixing angles, two mass-squared differences, and a CP-violating phase, has been constrained to 2–4% precision by global data. However, fundamental questions regarding the neutrino mass ordering, the $\theta_{23}$ octant, and the precise value of $\delta_{CP}$ remain. Furthermore, the potential existence of physics beyond the Standard Model (SM), specifically Non-Standard Interactions (NSI), requires investigation. NSI can manifest as additional charged-current (CC) or neutral-current (NC) interactions affecting neutrino production, detection, and propagation. While previous studies have examined NSI in the context of the ESSnuSB long-baseline neutrino beam program, the specific prospects for constraining matter-induced NC-NSI using atmospheric neutrinos at the proposed ESSnuSB far detector had not been fully explored.

Methodology
This work investigates the sensitivity of the ESSnuSB far detector to matter NSI parameters ($\epsilon^m_{\alpha\beta}$) using atmospheric neutrino data. The analysis relies on a comprehensive simulation and statistical framework:

• Simulation and Event Generation: Monte Carlo (MC) samples were generated using the GENIE neutrino event generator, simulating atmospheric neutrino interactions with energies $E_\nu \in [0.1, 100]$ GeV. The geometry corresponds to a Water Cherenkov detector with a fiducial mass of 540 kt, located in the Zinkgruvan mine (approx. 360 km from the ESS source, 1 km rock overburden).
• Exposure: The analysis assumes a total exposure of 5.4 Mt$\cdot$year, equivalent to 10 years of data taking.
• Oscillation Framework: Neutrino oscillations were implemented via a reweighting algorithm using the GLoBES software, extended with the snu add-on to include NSI effects in probability calculations. The matter density profile was modeled using a PREM profile with 81 steps.
• Detector Effects: Events were categorized into electron-like ($\nu_e, \bar{\nu}_e$) and muon-like ($\nu_\mu, \bar{\nu}_\mu$) samples. Detector efficiencies (ranging from 54% to 69% depending on flavor) and energy/zenith angle resolutions (30% for sub-GeV, 10% for multi-GeV energy; $10^\circ$ for zenith) were applied. Charge identification was not assumed, treating neutrinos and antineutrinos of the same flavor within the same bin.
• Statistical Analysis: A $\chi^2$ minimization was performed using a binned likelihood function (Poisson statistics) over 100 energy bins and 20 zenith angle bins. Systematic uncertainties (flux normalization, cross-section, zenith angle dependence, energy tilt, and detector efficiency) were incorporated via the pull method with five nuisance parameters.
• Parameter Space: The study focuses on the six matter NSI parameters: off-diagonal complex parameters $\epsilon^m_{e\mu}, \epsilon^m_{e\tau}, \epsilon^m_{\mu\tau}$ and diagonal differences $\epsilon^m_{ee} - \epsilon^m_{\mu\mu}, \epsilon^m_{\tau\tau} - \epsilon^m_{\mu\mu}$. The analysis assumes Normal Ordering (NO) for the true neutrino mass hierarchy and varies the standard oscillation parameters ($\theta_{23}, \Delta m^2_{31}, \delta_{CP}$) within their $3\sigma$ global fit ranges.

Key Contributions and Results
The paper derives expected upper bounds on NSI parameters and evaluates the impact of NSI on standard oscillation measurements:

1. Constraints on NSI Parameters:
   Assuming Normal Ordering and minimizing over the complex phases ($\phi^m_{\alpha\beta}$), the ESSnuSB far detector is projected to set the following 90% Confidence Level (CL) upper bounds:

   • $|\epsilon^m_{e\mu}| < 0.053$
   • $|\epsilon^m_{e\tau}| < 0.057$
   • $|\epsilon^m_{\mu\tau}| < 0.021$
   • $\epsilon^m_{ee} - \epsilon^m_{\mu\mu} < 0.075$ (positive values only; negative values show no significant bound)
   • $|\epsilon^m_{\tau\tau} - \epsilon^m_{\mu\mu}| < 0.031$

   If the complex phases are fixed to zero, the bounds improve significantly (e.g., $|\epsilon^m_{e\mu}| < 0.016$). The study notes that while these bounds improve upon current limits for $\epsilon^m_{e\mu}$, $\epsilon^m_{e\tau}$, and $\epsilon^m_{\tau\tau} - \epsilon^m_{\mu\mu}$ by factors of roughly 1.3 to 3.9, the existing IceCube constraint on $|\epsilon^m_{\mu\tau}|$ ($< 0.0041$) remains more stringent than what ESSnuSB can achieve with atmospheric neutrinos.

2. Impact on Mass Ordering and $\theta_{23}$ Octant:
   The presence of NSI introduces additional free parameters, potentially degrading the sensitivity to standard oscillation parameters.

   • Mass Ordering: Even with one matter NSI parameter allowed to vary freely, the sensitivity to rule out the wrong mass ordering remains at approximately $6.1\sigma$ CL or higher, well above the $5\sigma$ discovery threshold.
   • $\theta_{23}$ Octant: The sensitivity to determine the $\theta_{23}$ octant is reduced by $0.1\sigma - 0.4\sigma$ CL compared to the standard interaction case but remains at a minimum of $2.6\sigma$ CL.

3. Systematic Robustness:
   The analysis investigated potential impacts from $\nu_\mu/\nu_e$ flux ratio uncertainties, flavor mis-identification (up to 2%), and atmospheric muon backgrounds. These factors were found to have negligible effects on the derived NSI bounds (changes $< 5\%$).

Significance
The paper claims that atmospheric neutrino data collected at the ESSnuSB far detector offers a unique and complementary avenue to the primary long-baseline beam program for probing new physics. Specifically, the results highlight:

• Complementarity: The atmospheric program provides constraints on NSI parameters that are distinct from and complementary to those obtained from the accelerator beam, particularly for the diagonal difference $\epsilon^m_{ee} - \epsilon^m_{\mu\mu}$, for which no prior experimental bounds existed for atmospheric neutrinos.
• Robustness of Physics Goals: The study demonstrates that the search for NSI does not compromise the primary physics goals of ESSnuSB; the experiment retains sufficient sensitivity to resolve the neutrino mass ordering and the $\theta_{23}$ octant even in the presence of non-standard matter effects.
• Feasibility: The work establishes the feasibility of using the ESSnuSB Water Cherenkov detectors for atmospheric neutrino physics, leveraging the 1 km rock overburden to suppress backgrounds and the large fiducial mass to accumulate significant statistics.