⚛️ phenomenology

CP violating signal at DUNE in presence of nonstandard interactions and the role of second oscillation maxima

This paper evaluates the Deep Underground Neutrino Experiment's (DUNE) potential to resolve the Dirac CP phase, mass ordering, and $\theta_{23}$ octant while distinguishing standard CP violation from nonstandard interactions, with a specific focus on the advantages offered by the second oscillation maximum.

Original authors: Rajrupa Banerjee, Jogesh Rout, Sudhanwa Patra, Poonam Mehta

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rajrupa Banerjee, Jogesh Rout, Sudhanwa Patra, Poonam Mehta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, invisible dance floor where tiny, ghostly particles called neutrinos are constantly changing their outfits. One moment they are wearing a "muon" costume, and the next, they've swapped it for an "electron" costume. This magical outfit change is called oscillation, and it's the only way we know these particles have mass at all.

For a long time, physicists thought they had the dance steps figured out. They knew the rhythm (mass differences) and the basic moves (mixing angles). But there was one huge mystery left: a secret twist in the dance called the CP phase (or $\delta$ ). If this twist exists, it means the universe treats matter and antimatter differently—like a dance partner who spins left when you expect them to spin right. Finding this twist is crucial because it might explain why we are here at all, instead of being a universe full of nothing but antimatter.

Enter DUNE (the Deep Underground Neutrino Experiment), a massive, high-tech detective agency built deep inside a mine in South Dakota. They shoot a beam of neutrinos from Fermilab in Illinois, 1300 kilometers away, hoping to catch them mid-dance.

The "Fake" Twist and the New Suspects

Here's the problem: The dance floor isn't empty. As neutrinos travel through the Earth, they bump into matter. This creates a "fake" twist that looks exactly like the real secret twist ( $\delta$ ). It's like trying to hear a whisper in a room full of loud music; the music (matter) makes it hard to tell if the whisper (the real CP phase) is actually there.

But wait, there's a twist within a twist. The paper suggests that there might be Non-Standard Interactions (NSI). Think of NSI as invisible, mischievous ghosts that are also messing with the dance. These ghosts could be changing the rhythm in ways we haven't seen before. If these ghosts are real, they make the job of finding the real secret twist even harder because they add more noise to the music.

The Secret Weapon: The Second "High Five"

So, how do we separate the real twist from the fake ones (both the Earth's matter and the NSI ghosts)? The authors of this paper suggest a clever trick: look at the second oscillation maximum.

Imagine the neutrinos are bouncing back and forth like a ball.

The First Maximum is the first time the ball hits the wall. This happens at a higher energy (around 2.6 GeV). It's loud and energetic, but the "fake" noise from the Earth is very strong here.
The Second Maximum is when the ball hits the wall a second time. This happens at a lower energy (around 0.86 GeV).

The paper's simulations suggest that the second hit is special. At this lower energy, the "fake" noise from the Earth is much quieter. It's like moving from a rock concert to a quiet library. Even if the mischievous NSI ghosts are there, the second maximum is a clearer place to hear the real whisper.

What the Simulations Show

The researchers didn't just guess; they ran massive computer simulations (using a tool called GLoBES) to see what would happen if DUNE ran for 7 years. They tested three scenarios:

Standard Interaction (SI): Just the Earth's matter noise.
Non-Standard Interactions (NSI): Earth noise + the mischievous ghosts (specifically using benchmark values of $\epsilon_{e\mu} = 0.05$ and $\epsilon_{e\tau} = -0.05$ ).
The Combo: Using two different beams of neutrinos at once.

Here is what their simulations suggest:

The Ghosts Make it Louder: When the NSI ghosts are present, the signal for CP violation actually gets stronger at the second maximum. In fact, the difference in the dance moves becomes nearly three times larger at the second maximum compared to the first when these ghosts are around.
The 120 GeV Beam (First Maximum): If DUNE uses its standard high-energy beam (120 GeV), it can find the CP violation with high confidence (over 5 $\sigma$ certainty) in the standard world. But if the NSI ghosts are there, the confidence jumps to over 10 $\sigma$ .
The 8 GeV Beam (Second Maximum): This beam is tuned to the quieter, second maximum. On its own, it struggles to reach the "gold standard" of 5 $\sigma$ discovery in a normal world. However, the paper suggests that if the NSI ghosts are real, this beam suddenly becomes very powerful, reaching just above 5 $\sigma$ .
The Ultimate Combo: The best strategy, according to these simulations, is to use both beams together. By running the 120 GeV beam for 6 years and the 8 GeV beam for 1 year, DUNE could potentially discover CP violation with a confidence level exceeding 12 $\sigma$ if NSI exists. This would allow them to solve the mystery for about 70% of all possible dance moves (values of $\delta$ ).

The Bottom Line

The paper doesn't claim to have found the NSI ghosts or the secret twist yet. Instead, it suggests that if these ghosts are real, the second oscillation maximum (the lower energy, second "hit") is the best place to look. It acts like a noise-canceling headphone that filters out the Earth's interference, making it easier to hear the true rhythm of the universe.

While the standard 120 GeV beam is a workhorse, the paper argues that adding the 8 GeV beam to the mix is essential for the future, especially if the universe is hiding these extra, non-standard interactions. It's a reminder that sometimes, to hear the truth, you need to listen to the quietest part of the song.

Technical Summary: CP Violating Signal at DUNE in Presence of Nonstandard Interactions and the Role of Second Oscillation Maxima

Problem Statement
While neutrino oscillation among three active flavors is well-established, three key unknowns remain: the Dirac CP phase ( $\delta$ ), the neutrino mass ordering, and the octant of $\theta_{23}$ . The Deep Underground Neutrino Experiment (DUNE) is designed to resolve these. However, a significant challenge arises in distinguishing "intrinsic" CP violation (arising from the phase $\delta$ in the PMNS matrix) from "extrinsic" or "fake" CP violation induced by matter effects during propagation. This problem is exacerbated in scenarios involving Non-Standard Interactions (NSI). NSI can introduce additional CP-violating phases and modify matter potentials, leading to parameter degeneracies that obscure the true value of $\delta$ . The paper addresses the difficulty of disentangling intrinsic CP effects from extrinsic effects (both standard matter and NSI-induced) and investigates whether the second oscillation maximum offers a viable solution to this problem.

Methodology
The authors employ a theoretical and phenomenological approach using the General Long Baseline Experiment Simulator (GLoBES) to model the DUNE experiment.

Theoretical Framework: The study utilizes a three-flavor oscillation framework including vector NSI. The evolution equation incorporates the standard matter potential ( $V_{CC}$ ) and NSI parameters ( $\epsilon_{\alpha\beta}$ ). The oscillation probability $P_{\mu e}$ is expanded perturbatively to isolate contributions from standard oscillations ( $P_0, P_1$ ) and NSI ( $P_2$ ).
Experimental Setup: The simulation assumes a 40 kton Liquid Argon Time Projection Chamber (LArTPC) at a baseline of 1300 km. Two beam configurations are analyzed: a 120 GeV proton beam (optimized for the first oscillation maximum at $\sim$ 2.6 GeV) and an 8 GeV beam (optimized for the second oscillation maximum at $\sim$ 0.86 GeV).
Parameters: The analysis assumes Normal Ordering (NO) and uses benchmark NSI values ( $\epsilon_{e\mu} = 0.05, \epsilon_{e\tau} = -0.05$ ) within their allowed $3\sigma$ ranges, while marginalizing over other standard oscillation parameters. Systematic uncertainties (e.g., 2% on matter density) are included.
Statistical Analysis: The CP violation discovery potential is quantified using a $\chi^2$ test statistic, comparing event spectra for a true CP phase $\delta_{true}$ against CP-conserving hypotheses ( $\delta = 0, \pi$ ). The study evaluates both total event rates and specific observables designed to isolate intrinsic CP effects, such as $\delta(\Delta P^{CP}_{\mu e}) = \Delta P^{CP}_{\mu e}(\delta) - \Delta P^{CP}_{\mu e}(\delta=0)$ .

Key Contributions and Results

Enhanced Sensitivity at the Second Oscillation Maximum: Theoretical analysis reveals that while the first oscillation maximum is dominated by matter-induced asymmetries that distort the intrinsic CP signal, the second oscillation maximum offers a region where matter effects are significantly reduced. In the presence of NSI, the CP-violating probability difference ( $\Delta P^{CP}_{\mu e}$ ) is amplified at the second maximum, reaching magnitudes nearly three times larger than at the first maximum for certain $\delta$ values.
Disentangling Intrinsic and Extrinsic Effects: The paper demonstrates that the term proportional to $\cos \delta$ (arising from NSI and matter effects) is less dominant at higher oscillation maxima compared to the $\sin \delta$ term (intrinsic CP). By utilizing the observable $\delta(\Delta P^{CP}_{\mu e})$ , the authors show that the second maximum allows for a more robust extraction of the intrinsic phase $\delta$ , particularly in CP-conserving regions ( $\delta \approx \pm 20^\circ$ ), where the "fake" CP effects are minimized.
Event Rate Analysis: Simulations indicate that NSI significantly enhances the $\nu_e$ appearance event rate in neutrino mode, particularly at $\delta = -90^\circ$ . While the 8 GeV beam (second maximum) alone does not reach $5\sigma$ discovery sensitivity for CP violation in the Standard Interaction (SI) scenario, the inclusion of NSI pushes this sensitivity slightly above $5\sigma$ .
Synergy of Dual-Beam Strategy: The most significant result is the complementarity of the two beam energies. A combined configuration (5 years of 120 GeV beam + 1 year of 8 GeV beam in neutrino mode, plus 1 year of 120 GeV in antineutrino mode) yields superior results. In the presence of NSI, this combined strategy extends the $5\sigma$ discovery reach to cover approximately 70% of the $\delta$ parameter space, compared to ~64% for the 120 GeV beam alone. The combined approach effectively leverages the high statistics of the first maximum and the reduced matter/NSI degeneracy of the second maximum.

Significance
The paper claims that the second oscillation maximum is a critical, yet often underutilized, resource for precision CP violation studies in the presence of new physics. The authors conclude that while NSI complicates the extraction of intrinsic CP violation by introducing additional phases and modifying matter potentials, the second oscillation maximum provides a "favorable environment" to mitigate these extrinsic effects. The study establishes that a dual-beam strategy at DUNE is not merely an option but a necessity for maximizing discovery potential in scenarios involving NSI. By accessing both oscillation maxima, DUNE can better disentangle intrinsic CP violation from extrinsic backgrounds, thereby improving the reliability of measuring the Dirac CP phase even when non-standard interactions are present.

The "Fake" Twist and the New Suspects

The Secret Weapon: The Second "High Five"

What the Simulations Show

The Bottom Line

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