⚛️ phenomenology

Probing non-unitarity of the PMNS matrix in P2SO and comparison with DUNE

This paper compares the sensitivity of the upcoming P2SO and DUNE long-baseline neutrino experiments to non-unitarity in the PMNS matrix, revealing their complementary strengths in constraining specific non-unitarity parameters and demonstrating how these effects significantly influence precision measurements of standard oscillation parameters.

Original authors: Sambit Kumar Pusty, Samiran Roy, Monojit Ghosh, Rukmani Mohanta

Published 2026-03-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sambit Kumar Pusty, Samiran Roy, Monojit Ghosh, Rukmani Mohanta

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 as a giant, complex orchestra. For decades, physicists believed they understood the music of the subatomic world perfectly. They thought they knew exactly how three specific "musicians" (called neutrinos) played together. These three neutrinos were the only ones in the band, and they followed a strict, perfect sheet of music called the PMNS matrix.

But recently, scientists started wondering: What if there are hidden musicians in the orchestra that we can't see?

This paper is like a detective story comparing two massive, high-tech "listening stations" (experiments) to see if they can catch these hidden musicians. The hidden musicians are called Heavy Neutral Leptons. If they exist, they mess up the perfect sheet of music, making the orchestra "non-unitary" (a fancy way of saying the music isn't perfectly balanced or complete).

Here is the breakdown of the paper using simple analogies:

1. The Mystery: The "Missing" Musicians

In the Standard Model of physics, we have three types of neutrinos (electron, muon, and tau). They dance and change into one another as they travel through space. This is called oscillation.

However, some theories suggest there are heavy, invisible neutrinos (like ghost musicians) that mix with the three visible ones. Because these ghosts are too heavy to be created in our experiments, they don't play directly. Instead, they subtly distort the dance of the visible neutrinos. This distortion is called Non-Unitarity (NU).

If these ghosts exist, they change the rules of the game. They might introduce new "twists" in the music (new sources of CP violation) that could explain why the universe is made of matter instead of antimatter.

2. The Detectives: DUNE vs. P2SO

To find these ghosts, the authors compare two upcoming super-powerful listening stations:

DUNE (Deep Underground Neutrino Experiment): Located in the US. It sends a beam of neutrinos 1,300 km through the Earth. Think of this as a short, intense sprint. It has a very powerful beam and a super-sensitive detector (Liquid Argon) that can see every detail of the neutrinos' dance.
P2SO (Protvino to Super-ORCA): A proposed experiment sending neutrinos from Russia to France (under the Mediterranean Sea). This is a long, slow marathon. The distance is huge (2,595 km), and the neutrinos travel through much denser rock and water.

The Analogy: Imagine trying to hear a whisper.

DUNE is like standing close to the speaker with a high-tech microphone. It hears the voice very clearly.
P2SO is like standing far away, but the wind (the Earth's matter) carries the sound in a specific way that might reveal secrets the close-up microphone misses.

3. The Findings: Who is Better at What?

The paper runs computer simulations to see which experiment is better at spotting the "ghosts" (the non-unitary effects).

DUNE is the "Alpha" Hunter: It is incredibly good at spotting the first type of ghost (parameter $\alpha_{11}$ ) and the "twist" in the music (parameter $\alpha_{21}$ ). It sets the strictest limits on these.
P2SO is the "Omega" Hunter: Because it travels such a long distance through dense matter, it is much better at spotting the third type of ghost (parameter $\alpha_{33}$ ) and the second type ( $\alpha_{22}$ ). The "matter effect" (the Earth acting like a lens) amplifies the signal for P2SO in a way DUNE can't match.

The Verdict: Neither is perfect alone. They are complementary. You need both the sprint (DUNE) and the marathon (P2SO) to get the full picture. If you only use one, you might miss the ghosts hiding in the other's blind spot.

4. The Side Effects: How Ghosts Mess Up the Music

The paper also asks: "If these ghosts exist, how does it ruin our ability to measure the known musicians?"

Confusing the Rhythm (Mass Hierarchy): The ghosts make it harder to tell if the neutrinos are arranged in a "Normal" or "Inverted" order. DUNE's ability to tell this apart drops a bit if the ghosts are there, but P2SO is surprisingly robust against this specific confusion.
The Octant Problem: We don't know if a specific angle ( $\theta_{23}$ ) is "high" or "low" (like a left or right turn). The ghosts can make it look like the angle is both at the same time, creating a "degeneracy" (a confusion where two different answers look the same). P2SO actually gets better at solving this if a specific ghost ( $\alpha_{33}$ ) is present, but gets confused by others.
The CP Violation (The "Handedness" of the Universe): This is the most important part. We want to know why the universe prefers matter over antimatter. The ghosts introduce a new twist in the music. If we don't account for them, we might think we found the answer, but we'd actually be measuring the wrong thing. The paper shows that these ghosts can completely hide the true answer if we aren't careful.

5. The Conclusion: Why This Matters

The authors conclude that we cannot ignore these potential ghosts.

If we build DUNE or P2SO and assume the "standard" music is perfect, we might misinterpret our data. We might think we've solved a mystery, only to realize later that a hidden ghost was pulling the strings.

The Takeaway:
To truly understand the universe's music, we need both listening stations. DUNE will catch the ghosts that hide in the short, intense bursts, while P2SO will catch the ones that hide in the long, deep journey through the Earth. Together, they will either prove that the orchestra is perfect, or they will reveal the hidden musicians that are changing the song of the universe.

In short: The universe might be playing a duet with a ghost, and we need two different microphones to hear it.

1. Problem Statement

The standard three-flavor neutrino oscillation framework assumes the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing matrix is unitary. However, various Beyond the Standard Model (BSM) theories, particularly those involving heavy neutral leptons (HNLs) or sterile neutrinos (e.g., Type-I, Inverse, or Linear Seesaw mechanisms), predict that the $3 \times 3$ active neutrino mixing matrix is non-unitary (NU).

This non-unitarity introduces:

New CP-violating phases ( $\phi_{ij}$ ).
Modifications to oscillation probabilities.
Potential degeneracies with standard oscillation parameters (mass ordering, $\theta_{23}$ octant, $\delta_{CP}$ ).

The paper addresses the critical need to quantify these NU effects and determine how upcoming long-baseline (LBL) experiments, specifically DUNE (Deep Underground Neutrino Experiment) and P2SO (Protvino to Super-ORCA), can constrain these parameters. It specifically investigates the complementarity of these two experiments, noting that P2SO operates with a significantly longer baseline (2595 km) and stronger matter effects compared to DUNE (1300 km).

2. Methodology

Theoretical Framework

The authors employ a model-independent parameterization of the NU mixing matrix $N$ . They define $N$ as the product of a lower triangular matrix ( $N_{NP}$ ) and the standard unitary PMNS matrix ( $U$ ):
$N = N_{NP} U = \begin{pmatrix} \alpha_{11} & 0 & 0 \\ \alpha_{21} & \alpha_{22} & 0 \\ \alpha_{31} & \alpha_{32} & \alpha_{33} \end{pmatrix} U$

Diagonal parameters ( $\alpha_{ii}$ ): Real numbers close to 1.
Off-diagonal parameters ( $\alpha_{ij}, i \neq j$ ): Complex numbers with small magnitudes, introducing new CP phases ( $\phi_{ij}$ ).
Focus: The study focuses on $\alpha_{11}, \alpha_{22}, \alpha_{33}$ and the off-diagonal $\alpha_{21}$ (with phase $\phi_{21}$ ), as $\alpha_{31}$ and $\alpha_{32}$ have negligible effects within current limits.

Analytical Expressions

The authors derive analytical expressions for transition probabilities ( $P_{\mu e}$ and $P_{\mu \mu}$ ) in the presence of NU. These expressions separate standard oscillation terms from NU-induced terms, highlighting how NU modifies the amplitude and introduces new interference terms dependent on $\phi_{21}$ .

Experimental Setup & Simulation

Tools: Simulations were performed using GLoBES software, with modifications to the probability engine to include NU effects.
DUNE: 1.2 MW beam, 40 kt Liquid Argon TPC, 1300 km baseline, 13 years runtime (6.5 yr $\nu$ + 6.5 yr $\bar{\nu}$ ).
P2SO: 450 kW beam, Super-ORCA detector (10x denser than ORCA), 2595 km baseline, 6 years runtime (3 yr $\nu$ + 3 yr $\bar{\nu}$ ).
Statistical Analysis: Sensitivity was estimated using the Poisson log-likelihood $\chi^2$ statistic. Systematic errors were handled via the "pull" method.
Parameters: Standard oscillation parameters were taken from NuFit 6.0 (Normal Hierarchy assumed). The analysis marginalized over $\theta_{23}$ , $\Delta m^2_{31}$ , and $\delta_{CP}$ , while testing one or multiple NU parameters simultaneously.

3. Key Contributions

Comparative Sensitivity Analysis: A direct, side-by-side comparison of P2SO and DUNE capabilities to constrain NU parameters, highlighting the role of baseline length and matter effects.
Decoupling Degeneracies: Investigation of how NU parameters correlate with standard parameters ( $\theta_{23}$ , $\Delta m^2_{31}$ , $\delta_{CP}$ ) and how these correlations affect the determination of the mass hierarchy and $\theta_{23}$ octant.
Matter Effect Dominance: Demonstration that P2SO's longer baseline and stronger matter effects provide unique sensitivity to specific NU parameters (specifically $\alpha_{33}$ ) that DUNE cannot match, and vice versa.
Impact of New CP Phases: Quantification of how the new phase $\phi_{21}$ creates degeneracies that degrade the precision of standard CP violation ( $\delta_{CP}$ ) and octant measurements.

4. Key Results

A. Constraints on NU Parameters

$\alpha_{11}$ : DUNE provides significantly stronger bounds than P2SO and improves upon current limits.
$\alpha_{21}$ : DUNE offers better constraints on the magnitude $|\alpha_{21}|$ . However, the sensitivity is highly dependent on the phase $\phi_{21}$ .
$\alpha_{22}$ : P2SO shows better sensitivity than DUNE, though neither improves significantly on current bounds.
$\alpha_{33}$ : P2SO provides the strongest bounds, significantly improving current limits. This is attributed to $\alpha_{33}$ not entering vacuum probabilities but contributing exclusively through matter effects, which are amplified in P2SO's 2595 km baseline.
Degeneracy: The sensitivity curve for $\alpha_{33}$ exhibits "wavy" behavior due to degeneracy with $\theta_{23}$ , which disappears when $\theta_{23}$ is fixed.

B. Impact on Standard Oscillation Sensitivities

Mass Hierarchy:
- $\alpha_{11}$ : Reduces mass hierarchy sensitivity in both experiments.
- $\alpha_{22}$ : Increases mass hierarchy sensitivity (counter-intuitively) because it enhances the disappearance channel ( $P_{\mu \mu}$ ) probability difference between Normal and Inverted Hierarchies.
- $\alpha_{33}$ : Has a negligible effect.
$\theta_{23}$ Octant:
- $\alpha_{22}$ : Generally reduces octant sensitivity. P2SO exhibits a specific "dip" in sensitivity around $\alpha_{22} \approx 0.96$ due to matter effects, a feature not seen in DUNE.
- $\alpha_{33}$ : Surprisingly enhances octant sensitivity.
- $\alpha_{21}$ : The phase $\phi_{21}$ plays a crucial role; marginalizing over $\phi_{21}$ creates degeneracy regions that degrade sensitivity, particularly for DUNE.
CP Violation ( $\delta_{CP}$ ):
- Sensitivity decreases in the presence of $\alpha_{11}$ and $\alpha_{22}$ .
- Sensitivity slightly increases with $\alpha_{33}$ .
- The presence of $\alpha_{21}$ introduces complex behavior; fixing $\phi_{21}$ improves sensitivity, while marginalizing it creates degeneracies that hinder $\delta_{CP}$ measurement.

C. Precision Contours

$\theta_{23}$ vs. $\Delta m^2_{31}$ : The presence of $\alpha_{22}$ $α_{22}$ and $\alpha_{21}$ $α_{21}$ causes significant distortions in the allowed parameter regions.
- P2SO shows degenerate regions for $\alpha_{22}$ due to octant degeneracy.
- DUNE shows degenerate regions for $\alpha_{21}$ , driven by the interplay of the new phase $\phi_{21}$ .
$\delta_{CP}$ vs. $\phi_{21}$ : DUNE provides tighter constraints on the correlation between the standard CP phase and the new NU phase compared to P2SO.

5. Significance and Conclusion

The paper establishes that DUNE and P2SO are highly complementary in the search for non-unitarity.

DUNE is superior for constraining $\alpha_{11}$ and $\alpha_{21}$ and resolving the correlation between $\delta_{CP}$ and $\phi_{21}$ .
P2SO, leveraging its extreme baseline and matter effects, is uniquely capable of constraining $\alpha_{33}$ and offers competitive sensitivity to $\alpha_{22}$ .

The study concludes that ignoring non-unitarity could lead to biased measurements of standard oscillation parameters. Specifically, the new CP phases and NU parameters can mimic or mask standard CP violation and mass ordering effects. Therefore, a joint analysis of P2SO and DUNE data is essential to robustly resolve the unknowns of neutrino physics and to either discover or tightly constrain the existence of heavy neutral leptons and sterile neutrinos. The results underscore that next-generation precision oscillation studies must account for NU to avoid false positives or negatives in determining the neutrino mass hierarchy and CP violation.