🔬 physics

Model-Independent Determination of Intrinsic Leptonic CP Violation

This paper proposes a model-independent method using Gaussian Process regression to infer neutrino oscillation probabilities at DUNE and Hyper-Kamiokande, demonstrating that combining data from these experiments can establish intrinsic leptonic CP violation at a 3σ significance level for over 60% of the possible values of the CP-violating phase $\delta_{\mathrm{CP}}$ .

Original authors: Ting Cheng, Kevin J. Kelly, Max Knobbe, Pedro A. N. Machado

Published 2026-10-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ting Cheng, Kevin J. Kelly, Max Knobbe, Pedro A. N. Machado

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

Deep in the subatomic world, a fundamental mystery connects the smallest particles we know to the vast existence of everything around us. Neutrinos are ghostly particles that zip through the universe almost entirely unnoticed, yet they hold the key to understanding why the cosmos is made of matter rather than being an empty void of antimatter. For decades, physicists have searched for a specific kind of imbalance in how these particles behave, a phenomenon called Charge-Parity violation. This imbalance would explain why the Big Bang produced more matter than antimatter, allowing stars, planets, and people to exist. While we know this imbalance exists in other contexts, proving it for neutrinos has remained elusive. The next generation of massive experiments, designed to fire beams of neutrinos through the Earth, aims to catch this elusive difference, but the path to discovery is complicated by the very rock and soil the particles travel through.

The challenge lies in distinguishing between two types of effects that look identical to our detectors. When a neutrino beam travels hundreds of kilometers through the Earth, it interacts with the matter inside the planet. This interaction creates an artificial difference between how neutrinos and their antimatter counterparts, antineutrinos, behave. This is an "extrinsic" effect, caused by the environment, not by the particles themselves. To find the "intrinsic" violation—the genuine difference in the nature of the particles—scientists usually have to assume a specific mathematical model of how neutrinos work. They assume the standard three-neutrino framework is correct and then try to subtract the environmental noise to see if a signal remains. This approach, however, ties the discovery of a fundamental phenomenon to the validity of a specific model. If the model is slightly wrong, the conclusion about the phenomenon could be wrong too.

A new approach, proposed by researchers at Fermi National Accelerator Laboratory and Texas A&M University, seeks to observe this intrinsic difference without relying on any pre-set model. Instead of forcing the data into a specific equation, the team treated the probability of a neutrino changing its identity as a free-floating function, a shape that could take any form the data suggested. They used a statistical tool known as Gaussian process regression, which acts like a flexible ruler that learns the shape of a curve directly from the measurements rather than assuming the curve is a straight line or a specific wave. By applying this method to data from two major experiments, DUNE in the United States and Hyper-Kamiokande in Japan, they could reconstruct the behavior of neutrinos and antineutrinos as they travel, letting the numbers speak for themselves.

The two experiments are perfectly suited for this task because they look at the particles from different angles. DUNE sends a beam 1,300 kilometers through the Earth, while Hyper-Kamiokande sends a beam 295 kilometers. Because the Earth's matter affects the particles differently depending on the distance traveled and the density of the rock, the "noise" created by the environment is different for each experiment. The researchers combined the results from both locations using a clever mathematical trick. By comparing the differences in behavior between the two distances, they could cancel out the environmental effects almost entirely. This left behind only the intrinsic difference between neutrinos and antineutrinos, the genuine signature of the violation they were hunting for. It is similar to listening to two different recordings of the same song played in rooms with different echoes; by comparing the two, you can isolate the original sound of the singer from the room's acoustics.

The team tested this method by simulating what the experiments would see if the standard model of physics were true. They found that by combining the data from both facilities, they could identify the intrinsic difference with high confidence for a wide range of possible scenarios. Specifically, their model-independent approach could confirm the existence of this violation at a level of certainty that physicists call three standard deviations for more than 60 percent of the possible values for the particle's behavior. For about 30 percent of those values, the certainty would rise to five standard deviations, the gold standard for a discovery in particle physics. This means that even without assuming the standard model is perfect, the combined power of these two experiments is sufficient to prove that neutrinos and antineutrinos are fundamentally different.

This work represents a shift in how we might confirm the deepest secrets of the universe. Rather than waiting for a model to be proven correct before claiming a discovery, this method allows scientists to observe the phenomenon directly. The researchers showed that the data itself, when treated with the right statistical tools, can reveal the intrinsic nature of matter and antimatter. While the results presented here are based on simulations of future data, the method provides a robust roadmap for the coming decade. When the DUNE and Hyper-Kamiokande experiments begin collecting real data, this approach will offer a way to establish the existence of leptonic Charge-Parity violation as a fact of nature, independent of the theoretical frameworks we currently use to describe it.

Technical Summary: Model-Independent Determination of Intrinsic Leptonic CP Violation

Problem Statement
Establishing leptonic Charge-Parity (CP) violation is a primary objective of next-generation long-baseline neutrino experiments, specifically DUNE and Hyper-Kamiokande (HK). Current experimental analyses typically operate within the standard three-neutrino framework, focusing on excluding specific values of the CP-violating phase, $\delta_{CP} \in \{0, \pi\}$ . This approach conflates intrinsic CP violation (a fundamental property of neutrino oscillations in vacuum) with extrinsic CP violation induced by matter effects as neutrinos propagate through the Earth. Furthermore, standard analyses rely on specific parametrizations of the neutrino mixing matrix. The authors argue that a more fundamental goal is to observe intrinsic leptonic CP violation—the difference between $\nu_\mu \to \nu_e$ and $\bar{\nu}_\mu \to \bar{\nu}_e$ appearance rates in vacuum—as a phenomenon, independent of any specific oscillation model or matter density assumptions.

Methodology
The paper proposes a novel, model-independent framework to reconstruct neutrino oscillation probabilities directly from data without assuming a functional form (e.g., polynomial or three-flavor fit).

Gaussian Process (GP) Regression: The core methodology employs Gaussian Process regression to treat the oscillation probabilities $P(\nu_\mu \to \nu_e)$ and $P(\bar{\nu}_\mu \to \bar{\nu}_e)$ as unknown functions of the variable $u = L/E$ (baseline over energy).
- Prior: The probabilities are governed by a prior distribution $P_0 \sim \mathcal{N}(\mu_0, K)$ , where the covariance kernel $K$ (specifically a Matérn-5/2 kernel) correlates probabilities based on the distance in $L/E$ space.
- Hyperparameters: The kernel hyperparameters (length scale $\ell$ and amplitude $a$ ) are marginalized over using a Bayesian approach, allowing the data to determine the functional complexity rather than fixing it a priori.
- Uncertainty Propagation: Statistical and systematic uncertainties (normalization, spectral tilt, energy scale) are incorporated into the noise covariance matrix $\Sigma_n$ , ensuring they are naturally propagated to the reconstructed probabilities.
Experimental Inputs: The study simulates combined data from DUNE (1300 km baseline, broad-band beam) and HK (295 km baseline, narrow-band off-axis beam).
- DUNE exposure: 624 kt-MW-yr (10 years, split FHC/RHC).
- HK exposure: 2431 kt-MW-yr (10 years, single tank, 1:3 FHC/RHC split).
Extracting Intrinsic CP Violation:
- Matter effects introduce an extrinsic asymmetry between neutrino and antineutrino channels. The authors assume that, beyond the dominant $L/E$ dependence, matter effects can be expanded in terms of the product of matter density $\rho$ and baseline $L$ .
- By combining the reconstructed probabilities from DUNE ( $P_D$ ) and HK ( $P_H$ ), they construct a linear combination that cancels the leading-order matter contribution:
  $P_{CPV} \equiv \frac{\lambda_D (P_H - \bar{P}_H) - \lambda_H (P_D - \bar{P}_D)}{2(\lambda_D - \lambda_H)}$
  where $\lambda_x = \rho_x L_x$ . This quantity $P_{CPV}$ represents the intrinsic CP-violating term in vacuum, robust against non-standard matter effects.

Key Results

Reconstruction Capability: The GP regression successfully reconstructs the appearance probabilities for both experiments. The posterior bands are unbiased, containing the true three-flavor oscillation curves within $\pm 2\sigma$ .
Information Content: DUNE resolves approximately 12 functional degrees of freedom ( $\langle N_{eff} \rangle \approx 12$ ) with a mutual information of $\approx 20$ nats, while HK resolves $\approx 7$ degrees of freedom with $\approx 12$ nats.
Intrinsic CPV Sensitivity: Using the standard three-neutrino framework as a benchmark for "truth," the combined analysis of DUNE and HK can establish model-independent intrinsic CP violation at the $3\sigma$ confidence level for over 60% of true $\delta_{CP}$ values. For 30% of the $\delta_{CP}$ values, the sensitivity reaches $5\sigma$ .
Robustness: The linear combination method effectively removes matter-induced asymmetries, even when $\delta_{CP} = 0$ (where intrinsic CPV is zero), demonstrating that the observed asymmetry in the reconstructed $P_{CPV}$ is a genuine measure of the intrinsic effect.

Significance and Claims
The authors claim that this work shifts the paradigm of CP violation searches from a model-specific parameter exclusion (ruling out $\delta_{CP} = 0, \pi$ ) to a direct, model-independent observation of the phenomenon itself. By treating probabilities as free functions and combining baselines to cancel matter effects, the method isolates the intrinsic CP-odd probability $P_{CPV}$ .

The paper emphasizes that this is a "much harder question" to answer than standard three-flavor analyses because it makes no assumptions about the mixing matrix unitarity or the specific form of the oscillation probability. The results demonstrate that the combined capabilities of DUNE and HK are sufficient to achieve this ambitious goal, establishing intrinsic CP violation at high significance for a majority of the parameter space without relying on the standard oscillation framework for the extraction itself. The authors note that while they used the standard framework as a benchmark to validate the method, the conclusions hold for any source of CP violation in the neutrino sector.

More like this