Effects of tau-neutrino detection on non-standard interactions at DUNE with a short discussion on the nature of neutrino mixing

This paper demonstrates that detecting tau neutrinos at the DUNE far detector significantly enhances sensitivity to Non-Standard Interactions, particularly the $\epsilon_{\mu\tau}$ parameter, while also improving constraints on mass hierarchy, CP violation, mixing octants, and the unitarity of the PMNS matrix.

The Gist

Imagine the universe is a giant, cosmic game of "musical chairs," but instead of people, the players are neutrinos—tiny, ghost-like particles that zip through everything without leaving a trace.

For decades, scientists have been watching these particles change their "flavors" (electron, muon, or tau) as they travel. This game is governed by a set of rules called the PMNS matrix. Think of this matrix as the "rulebook" for the game. For the game to be fair and the universe to make sense, this rulebook must be unitary. In plain English, "unitary" means the rulebook is complete: the probabilities of all the flavors adding up must equal 100%. If they don't, it means there's a hidden player (a "sterile" neutrino) or a new rule we haven't discovered yet.

The Problem: The "Tension" in the Rules

Currently, two major experiments (NOνA and T2K) are looking at these neutrinos. They are trying to figure out the exact rules of the game, specifically:

1. The Mass Hierarchy: Which neutrino is the heaviest? (Is it the "Normal" order or "Inverted"?)
2. CP Violation: Is the game fair, or does it treat particles differently than anti-particles?
3. The Octant: Is the mixing angle slightly above or below 50%?

Here's the catch: The two experiments are giving slightly different answers. It's like two referees watching the same soccer match and calling different fouls. This "tension" suggests that maybe the rulebook we have isn't the whole story. Scientists suspect Non-Standard Interactions (NSI)—secret, new forces that mess with the neutrinos as they travel through the Earth.

The New Player: The "Ghost" in the Room (Tau Neutrinos)

Most experiments only watch the "Electron" and "Muon" neutrinos. They rarely catch the Tau neutrino. Why?

• The Threshold: To create a Tau neutrino, you need a lot of energy, like trying to break a heavy stone with a pebble.
• The Disappearing Act: When a Tau neutrino interacts, it turns into a Tau particle, which instantly decays and vanishes, taking some energy with it. It's like a magician who appears on stage, does a trick, and leaves the stage before you can see where they went.

However, the DUNE experiment (Deep Underground Neutrino Experiment) is a massive detector deep underground in South Dakota, fed by a powerful beam from Illinois. It has enough energy to create these heavy Tau neutrinos and the technology to spot them.

What This Paper Did

The authors of this paper asked: "What if we actually catch these elusive Tau neutrinos at DUNE? Will it help us solve the mystery of the secret rules (NSI)?"

They ran complex computer simulations (like a video game of the universe) to see what happens if we add the "Tau channel" to our data.

The Key Findings (The "Aha!" Moments)

1. The "Magic Wand" Parameter ($\epsilon_{\mu\tau}$)
They found that among all the possible secret rules (NSI parameters), one specific rule stands out: $\epsilon_{\mu\tau}$.

• Analogy: Imagine the neutrinos are cars changing lanes. Most secret rules just make the cars drive a bit slower. But $\epsilon_{\mu\tau}$ is like a magical wand that makes the Muon car suddenly turn into a Tau car in a way that is very obvious.
• Result: Detecting Tau neutrinos is the best way to spot this specific secret rule. Without looking for Tau neutrinos, DUNE might miss this clue entirely.

2. The "Fake-Out" (The Degeneracy)
Here is the tricky part. While catching Tau neutrinos helps find the secret rule, it also creates a new confusion.

• The Analogy: Imagine you are trying to guess the weight of a mystery box. You have two scales. One scale says "Heavy," and the other says "Light." But there's a secret switch (the NSI phase) that can make the "Heavy" box look like the "Light" one, and vice versa.
• Result: Even with Tau neutrinos, DUNE can't easily tell if the neutrinos are "Normal" or "Inverted" heavy if this secret rule exists. The secret rule can "fake" the answer. However, if we already know the weight (hierarchy) from other channels, the Tau neutrinos become a super-powerful tool to measure the secret switch itself (the phase).

3. Checking the Rulebook (Unitarity)
The paper also looked at whether the "rulebook" (PMNS matrix) is complete.

• The Analogy: If you count the players in a game and the numbers don't add up, someone is hiding.
• Result: By catching Tau neutrinos, DUNE can check the "third row" of the rulebook much better than before. It helps prove that there are no "ghost players" (sterile neutrinos) hiding in the shadows, or at least puts very strict limits on how big they could be.

The Bottom Line

This paper is a roadmap for the future of DUNE. It argues that ignoring the Tau neutrino is a mistake.

• Without Tau neutrinos: DUNE is like a detective looking at a crime scene but ignoring the most important witness.
• With Tau neutrinos: DUNE becomes a super-sleuth. It can spot specific new physics (NSI) that other experiments miss, even if it can't always solve the "Mass Hierarchy" puzzle on its own.

In short: Catching the "ghost" Tau neutrino won't just confirm what we already know; it will open a new window to see if the laws of physics are hiding a secret. It turns DUNE from a standard observer into a discovery machine for the "Beyond Standard Model" universe.

Technical Summary

1. Problem Statement

The paper addresses two primary challenges in the field of neutrino physics:

• Resolving Experimental Tensions: There is a significant tension between the NO$\nu$A and T2K experiments regarding the best-fit values of the CP-violating phase ($\delta_{CP}$) and the octant of the mixing angle $\theta_{23}$, particularly under the assumption of Normal Hierarchy (NH). This tension suggests the potential existence of physics Beyond the Standard Model (BSM), specifically Non-Standard Interactions (NSI).
• The Role of $\nu_\tau$ Detection: While the Deep Underground Neutrino Experiment (DUNE) is designed to measure $\nu_\mu \to \nu_e$ appearance and $\nu_\mu$ disappearance, the direct detection of $\nu_\tau$ (and $\bar{\nu}_\tau$) appearance has historically been difficult due to high energy thresholds and reconstruction challenges. The paper investigates whether incorporating $\nu_\tau$ detection at DUNE can improve sensitivity to NSI parameters, resolve the NO$\nu$A/T2K tension, and constrain the unitarity of the PMNS mixing matrix.

2. Methodology

The authors employed a comprehensive simulation and statistical analysis framework:

• Theoretical Framework:

  • The study utilizes a 3-flavor neutrino oscillation framework extended with NSI parameters ($\epsilon_{\alpha\beta}$) in the matter potential Hamiltonian.
  • They specifically analyzed NSI parameters in the $e-\mu$, $e-\tau$, and $\mu-\tau$ sectors ($\epsilon_{e\mu}, \epsilon_{e\tau}, \epsilon_{\mu\tau}, \epsilon_{\mu\mu}, \epsilon_{\tau\tau}$).
  • Analytical approximations were used to identify that $\epsilon_{\mu\tau}$ provides the dominant contribution to $\nu_\mu \to \nu_\tau$ oscillation probabilities in the presence of matter effects, introducing a hierarchy-sensitive term proportional to $\cos \phi_{\mu\tau}$.

• Simulation Setup:

  • Experiment: DUNE with a baseline of 1300 km.
  • Fluxes: Used standard DUNE fluxes and a "tau-optimized" high-energy flux (to maximize events above the $\tau$ production threshold of $\sim 3.4$ GeV).
  • Detector: Simulated a Liquid Argon Time Projection Chamber (LArTPC) with energy resolution and efficiency functions based on previous DUNE studies and NO$\nu$A cross-section data.
  • Running Schemes: Five distinct exposure scenarios were simulated (5+5 years of $\nu/\bar{\nu}$ runs):
    1. $\mu + e$ (Standard)
    2. $\mu + \tau$
    3. $\mu + e + \tau$
    4. $\mu + \tau$ (with 1 year of high-energy flux)
    5. $\mu + e + \tau$ (with 1 year of high-energy flux)

• Statistical Analysis:

  • Used the GLoBES software to calculate the $\chi^2$ statistic between true and test event rates.
  • Performed marginalization over standard oscillation parameters ($\theta_{23}, \Delta m^2_{31}, \delta_{CP}$) and NSI parameters/phases.
  • Evaluated sensitivity to Mass Hierarchy, CP Violation, $\theta_{23}$ Octant, NSI phases, and NSI parameter magnitudes.

3. Key Contributions

• Systematic Comparison of Fluxes: The authors explicitly compared their flux predictions and detector simulations against previous studies (e.g., Refs [19, 21, 22]), utilizing updated flux files and a more detailed theoretical treatment of $\nu_\tau$ implications.
• Identification of $\epsilon_{\mu\tau}$ Dominance: They demonstrated that among all NSI parameters, $\epsilon_{\mu\tau}$ is the only one that induces a significant, observable effect in the $\nu_\tau$ appearance channel at DUNE, whereas other parameters ($\epsilon_{e\mu}, \epsilon_{e\tau}$) have negligible effects on $\nu_\tau$ appearance.
• Degeneracy Analysis: The paper provides a detailed analysis of the $\phi_{\mu\tau}$-hierarchy degeneracy, showing how the phase of the NSI parameter can mimic the mass hierarchy in $\nu_\tau$ channels, thereby reducing hierarchy sensitivity unless the hierarchy is known from other channels.
• Unitarity Constraints: The study extends the physics reach of DUNE to constrain the non-unitarity of the third row of the PMNS matrix ($\alpha_{21}, \alpha_{22}$), a parameter space previously constrained mainly by Charged Lepton Flavor Violation (CLFV) experiments.

4. Key Results

A. Mass Hierarchy and CP Violation Sensitivity

• Hierarchy: In the standard 3-flavor scenario, adding $\nu_\tau$ channels does not improve mass hierarchy sensitivity. In the presence of NSI (specifically $\epsilon_{\mu\tau}$), the hierarchy sensitivity of the $\nu_\tau$ channel is actually reduced due to the $\phi_{\mu\tau}$-hierarchy degeneracy. The $\nu_\mu \to \nu_e$ channel remains the primary driver for hierarchy determination.
• CP Violation: Similarly, $\nu_\tau$ detection does not significantly enhance CP violation sensitivity. The $\nu_e$ appearance channel dominates CP sensitivity.

B. Octant Sensitivity

• The $\nu_\tau$ appearance channels show no octant sensitivity for standard oscillations or in the presence of NSI. The $\nu_e$ and $\nu_\mu$ channels are required to resolve the octant of $\theta_{23}$.

C. NSI Parameter Sensitivity

• $\epsilon_{\mu\tau}$: This is the most critical finding. The $\nu_\tau$ appearance channel provides complementary sensitivity to $\epsilon_{\mu\tau}$.
  • The combined run ($5+5+1+1$ years with $\mu+e+\tau$) can constrain $|\epsilon_{\mu\tau}| < 0.07$ (NH) at 90% CL.
  • This approaches the current IceCube constraint ($|\epsilon_{\mu\tau}| < 0.02$ at 90% CL), making DUNE a powerful future probe for this specific parameter.
  • Crucially, $\nu_\tau$ data allows for the determination of the NSI phase $\phi_{\mu\tau}$ with higher precision (improving sensitivity by 1–2.5 $\sigma$) if the mass hierarchy is known.
• $\epsilon_{e\mu}$ and $\epsilon_{e\tau}$: Sensitivity to these parameters is driven almost entirely by the $\nu_e$ appearance channel. $\nu_\tau$ detection adds negligible value for these specific parameters.
• Diagonal Terms ($\epsilon_{\mu\mu}, \epsilon_{\tau\tau}$): Sensitivity is driven by $\nu_\mu$ disappearance statistics. $\nu_\tau$ channels provide comparable but not superior sensitivity to $\nu_e$ channels for these parameters.

D. Unitarity of the PMNS Matrix

• The study investigates the non-unitary mixing parameter $\alpha_{22}$ (related to the third row of the mixing matrix).
• The $5+5+1+1$ ($\mu+e+\tau$) running scheme can constrain $\alpha_{22} > 0.83$ at 3$\sigma$.
• This bound is stronger than the current global limit derived solely from neutrino oscillation data, demonstrating the unique value of $\nu_\tau$ detection in testing the fundamental unitarity of the PMNS matrix.

5. Significance and Conclusion

The paper concludes that while $\nu_\tau$ detection at DUNE does not improve the determination of standard oscillation parameters (Hierarchy, CP, Octant), it is essential for:

1. Constraining $\epsilon_{\mu\tau}$: It provides a unique, independent handle on this specific NSI parameter, which is the most likely candidate to resolve the NO$\nu$A/T2K tension via $\mu-\tau$ sector interactions.
2. Measuring NSI Phases: It significantly improves the precision of measuring the phase $\phi_{\mu\tau}$, breaking degeneracies that affect other channels.
3. Testing Unitarity: It offers a competitive path to constraining the non-unitarity of the third row of the PMNS matrix, potentially surpassing current limits from oscillation-only data.

The authors emphasize that future combined analyses of DUNE, IceCube, and KM3NeT data, leveraging $\nu_\tau$ appearance channels, will be crucial for refining NSI constraints and probing BSM physics in the neutrino sector.