⚛️ phenomenology

Interplay of CPT-Violating and CPT-Conserving Lorentz Invariance Violation at DUNE

This study demonstrates that Lorentz invariance violation, particularly through CPT-violating SME coefficients like $a_{ee}$ , $a_{\tau\tau}$ , $a_{e\mu}$ , and $a_{e\tau}$ , significantly degrades the DUNE experiment's sensitivity to CP violation by introducing parameter-specific correlations and degeneracies that reduce discovery significance below the $5\sigma$ threshold.

Original authors: Priyankush Deka, Arnab Sarker, Moon Moon Devi, Sushant K. Raut

Published 2026-07-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Priyankush Deka, Arnab Sarker, Moon Moon Devi, Sushant K. Raut

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

The Big Picture: Neutrinos on a Long Road Trip

Imagine neutrinos as tiny, ghost-like travelers on a very long road trip. In our current understanding of physics (the "Standard Model"), these travelers follow a very specific set of traffic rules. They can change their "flavor" (like changing from a red car to a blue car) as they travel, a phenomenon called oscillation.

Scientists are currently trying to solve a mystery about these travelers: Do they break the rules of time and space?

This paper focuses on a future experiment called DUNE (Deep Underground Neutrino Experiment). DUNE is like a massive, high-tech toll booth located 1,300 kilometers away from the starting line. Its job is to count exactly how many red cars turn into blue cars.

The authors of this paper are asking: What happens to our measurements if the road itself is slightly "bumpy" or "twisted" in a way that breaks the fundamental laws of physics?

The Two Types of "Bumps" (LIV)

The paper investigates two specific types of "bumps" in the road, known as Lorentz Invariance Violation (LIV). Think of these as two different ways the universe might be slightly broken:

The "Time-Flipper" (CPT-Violating): Imagine a rule where the road behaves differently for a car driving forward in time versus one driving backward. In physics, this is called CPT violation. The paper calls these parameters $a$ (like the letter 'a' for "anti-time").
The "Speed-Bump" (CPT-Conserving): Imagine a rule where the road is bumpy, but it affects everyone the same way, regardless of time direction. This is called CPT-conserving. The paper calls these parameters $c$ .

The main goal of the paper is to see what happens when both types of bumps exist at the same time. Do they cancel each other out? Do they make the road worse?

The Key Findings

1. The "Big Players" vs. The "Minor Players"

The authors found that not all bumps are created equal.

The Heavy Hitters: The diagonal bumps (specifically $a_{ee}$ and $a_{\tau\tau}$ ) and the off-diagonal bumps ( $a_{e\mu}$ and $a_{e\tau}$ ) are the most powerful. They are like giant potholes that drastically change how the cars behave.
The Lightweights: The corresponding "speed-bump" versions ( $c$ terms) are much weaker. They are like small pebbles on the road. While they do cause some wobbling, they don't shake the car as much as the giant potholes.

2. The "Magic Trick" of Hiding

The most interesting discovery is what happens when you mix the "Time-Flippers" ( $a$ ) and the "Speed-Bumps" ( $c$ ) together.

The Analogy: Imagine you are trying to hear a whisper (the true signal of physics). Suddenly, someone starts playing loud music (the $a$ -bumps) to drown it out. Then, someone else starts playing a different song (the $c$ -bumps).
The Result: Sometimes, the two songs accidentally sync up in a way that creates a "silence" or a confusing noise pattern that looks exactly like the original whisper.
In Physics Terms: The paper finds that the $a$ and $c$ parameters can cancel each other out or create degeneracies. This means the experiment might see a result that looks like "Standard Physics" even though the laws of the universe are actually broken. It's like a magician making a rabbit disappear by using two different tricks that hide the rabbit from view.

3. The "CP Violation" Mystery

One of the biggest goals of DUNE is to measure CP Violation.

The Analogy: Imagine the neutrinos are a couple. CP Violation is the "spark" that makes them act differently than their mirror-image partners (antimatter). If we can measure this spark perfectly, we understand why the universe is made of matter and not antimatter.
The Problem: The paper shows that if these "road bumps" (LIV) exist, they act like fog over the road.
- Without the fog, DUNE might be able to see the spark clearly (5-sigma certainty, which is the gold standard in science).
- With the fog (LIV), the spark becomes hard to see. The paper calculates that for a large chunk of possible scenarios, the certainty drops from a clear "Yes!" to a "Maybe" (below 3-sigma).
- Specifically, the "Time-Flipper" bumps ( $a$ ) are the main culprits that create this fog, but the "Speed-Bumps" ( $c$ ) make the fog even thicker when they are combined.

The Conclusion: Why This Matters

The authors conclude that we cannot just look for "Standard Physics" or "Broken Physics" separately. We have to look for them together.

If we ignore the possibility that the universe has these "bumps" (LIV), we might misinterpret our data. We might think we found a new law of physics when we actually just saw a reflection of an old one, or vice versa.

In short:

DUNE is the ultimate test drive for neutrinos.
LIV (the $a$ and $c$ parameters) are potential potholes in the road of reality.
The paper warns that these potholes can hide the truth. They can make it look like the laws of physics are working perfectly when they aren't, or they can make it impossible to measure the "spark" (CP violation) that explains our existence.
To get the right answer, future experiments must be designed to untangle these two types of bumps simultaneously.

The paper does not suggest any medical uses or immediate applications; it is purely about understanding the fundamental rules of the universe and ensuring our "map" of reality is accurate.

Technical Summary: Interplay of CPT-Violating and CPT-Conserving Lorentz Invariance Violation at DUNE

Problem Statement
While the Standard Model (SM) successfully describes particle interactions at accessible energies, theoretical arguments suggest that spacetime symmetries, specifically Lorentz and CPT invariance, may be violated at the Planck scale. The Standard Model Extension (SME) provides a systematic effective field theory framework to parameterize these violations. In the context of neutrino oscillations, Lorentz Invariance Violation (LIV) introduces new terms into the propagation Hamiltonian. These terms are categorized into CPT-violating coefficients ( $a_{\alpha\beta}$ ) and CPT-conserving coefficients ( $c_{\alpha\beta}$ ).

Although numerous studies have investigated LIV effects, most have focused exclusively on CPT-violating components or treated CPT-conserving contributions in isolation. A comprehensive analysis of the interplay between both CPT-violating and CPT-conserving isotropic LIV parameters remains largely unexplored. This is critical because the simultaneous presence of these terms can lead to distinct modifications in oscillation probabilities, energy dependencies, and parameter degeneracies that could obscure or mimic standard CP violation (CPV). This paper addresses this gap by investigating the individual and combined impacts of $a_{\alpha\beta}$ and $c_{\alpha\beta}$ on neutrino oscillations, with a specific focus on the Deep Underground Neutrino Experiment (DUNE).

Methodology
The authors employ a hybrid analytical and numerical approach:

Theoretical Framework: The study utilizes the minimal SME framework, incorporating renormalizable operators (mass dimension $\le 4$ ). The effective Hamiltonian for neutrino oscillations is constructed as $H_{eff} = H_{vac} + H_{mat} + H_{LIV}$ , where $H_{LIV}$ contains the diagonal and off-diagonal $a_{\alpha\beta}$ (CPT-odd) and $c_{\alpha\beta}$ (CPT-even) coefficients. The analysis assumes the isotropic limit and utilizes the Sun-centered celestial equatorial frame.
Analytic Formulation: Using a perturbative expansion in terms of small parameters ( $s_{13}$ and $\alpha = \Delta m^2_{21}/\Delta m^2_{31}$ ), the authors derive second-order analytic expressions for the $\nu_\mu \to \nu_e$ transition probability ( $P_{\mu e}$ ) in the presence of LIV. This allows for the isolation of first-order and second-order contributions from $a_{\alpha\beta}$ and $c_{\alpha\beta}$ , clarifying their energy dependence and phase correlations.
Experimental Simulation: The study adopts DUNE as a representative long-baseline experiment (1300 km baseline, 40 kt Liquid Argon TPC). Simulations are performed using GLoBES with a 7-year exposure (3.5 years in $\nu$ -mode and 3.5 years in $\bar{\nu}$ -mode).
Statistical Analysis: A $\chi^2$ minimization technique is employed to assess constraints on LIV parameters and CP violation sensitivity. The analysis includes marginalization over standard oscillation parameters ( $\theta_{23}$ , $\Delta m^2_{31}$ , $\delta_{CP}$ ) and systematic uncertainties. The CPV sensitivity is quantified by the ability to distinguish CP-violating $\delta_{CP}$ values from CP-conserving values ( $0^\circ, 180^\circ$ ).

Key Contributions and Results

Dominance of Specific Coefficients: The analysis identifies that among diagonal LIV coefficients, $a_{ee}$ and $a_{\tau\tau}$ dominate the modification of oscillation probabilities, while $a_{e\mu}$ and $a_{e\tau}$ provide the most significant off-diagonal contributions. In contrast, the corresponding $c_{\alpha\beta}$ coefficients generally exhibit sub-leading effects within the DUNE energy range, though their impact becomes more relevant at higher energies.
Distinct Signatures in Probability and CP Trajectories:
- Energy Dependence: In the neutrino channel, CPT-violating $a_{\alpha\beta}$ and CPT-conserving $c_{\alpha\beta}$ often induce opposing effects (e.g., $a_{ee}$ enhances $P_{\mu e}$ while $c_{ee}$ suppresses it). Conversely, in the antineutrino channel, both types of coefficients tend to exhibit similar behaviors.
- CP Trajectories: In the bi-probability plane ( $P_{\mu e}$ vs. $\bar{P}_{\mu e}$ ), diagonal $a_{\alpha\beta}$ terms primarily displace the standard CP ellipse along its major axis, mimicking a matter-like fake CP asymmetry. Off-diagonal terms ( $a_{e\mu}, a_{e\tau}$ ) cause significant rotation and enlargement of the ellipse, introducing new phase dependencies.
Parameter Correlations and Degeneracies:
- The study reveals strong correlations between paired LIV parameters ( $a_{\alpha\beta}$ and $c_{\alpha\beta}$ ). Heatmap analyses of $\Delta P_{\mu e}$ show linear bands where combinations of $a$ and $c$ yield identical probability shifts, leading to SI-LIV degeneracies.
- A significant degeneracy exists between the standard CP phase $\delta_{CP}$ and the LIV phases ( $\phi^a_{\alpha\beta}, \phi^c_{\alpha\beta}$ ). Specifically, the condition $\delta_{CP} + \phi^a_{\alpha\beta} + \phi^a_{matter} \approx n\pi$ creates diagonal degeneracy bands, complicating the extraction of the true $\delta_{CP}$ .
Impact on CP Violation Sensitivity:
- The presence of LIV parameters significantly degrades DUNE's sensitivity to CP violation.
- Diagonal Terms: The inclusion of $a_{ee}$ , $a_{\tau\tau}$ , and their combinations with $c$ terms reduces the CP discovery potential, often dropping the significance below $3\sigma$ over a substantial fraction of the $\delta_{CP}$ range.
- Off-Diagonal Terms: The presence of $a_{e\mu}$ and $a_{e\tau}$ (and their $c$ counterparts) causes even stronger suppression, frequently reducing sensitivity below $3\sigma$ across the entire $\delta_{CP}$ spectrum.
- Combined Effects: When both CPT-violating and CPT-conserving terms are present simultaneously, they introduce non-trivial interference and degeneracies that further deteriorate CP sensitivity, generally preventing the experiment from achieving the $5\sigma$ discovery potential expected in the absence of LIV.
Projected Constraints: The paper projects that DUNE can provide improved bounds on off-diagonal CPT-violating parameters ( $a_{e\mu}$ and $a_{e\tau}$ ) compared to current limits from Super-Kamiokande and KM3NeT. However, the simultaneous variation of $a$ and $c$ parameters broadens the allowed regions, highlighting the necessity of considering both types of LIV terms in global fits.

Significance and Claims
The authors claim that this work provides a necessary systematic examination of the interplay between CPT-violating and CPT-conserving LIV effects in long-baseline neutrino experiments. The primary significance lies in demonstrating that neglecting the interplay between these terms can lead to incorrect interpretations of experimental data. Specifically:

Degeneracy Management: The study emphasizes that LIV effects can mimic or obscure genuine CP violation, creating degeneracies that reduce the statistical significance of CP discovery.
Precision Necessity: The findings underscore that future precision oscillation studies, particularly at DUNE, must incorporate LIV effects to avoid misinterpreting new physics signals as standard oscillation parameters or vice versa.
Comprehensive Constraints: By analyzing both $a_{\alpha\beta}$ and $c_{\alpha\beta}$ simultaneously, the paper offers a more realistic assessment of DUNE's discovery potential and its ability to constrain Lorentz and CPT violation, revealing that the combined presence of these terms is more detrimental to CP sensitivity than either term alone.

The paper concludes that while DUNE retains the potential to constrain specific LIV parameters, the presence of these effects fundamentally alters the experiment's sensitivity landscape, necessitating a robust theoretical framework that accounts for the full SME parameter space.