⚛️ phenomenology

DUNE Beam-Energy Dependence of Sensitivity to the Violation of the Equivalence Principle

This study demonstrates that the Deep Underground Neutrino Experiment (DUNE) achieves superior sensitivity to violations of the Equivalence Principle using a Low-Energy beam configuration compared to a Medium-Energy one, providing tighter constraints on VEP parameters and highlighting the importance of beam-energy optimization and channel-specific analysis.

Original authors: Monjowara Khatun, Debajyoti Dutta

Published 2026-10-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Monjowara Khatun, Debajyoti Dutta

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

Gravity is the most familiar force in our universe, yet it remains the most mysterious in its deepest workings. For over a century, physicists have relied on a cornerstone idea called the equivalence principle. In simple terms, this principle states that gravity treats all objects exactly the same way, regardless of what they are made of or how heavy they are. A feather and a hammer, if dropped in a vacuum, will fall at the exact same speed. This rule is so fundamental that it underpins our entire understanding of space, time, and how the universe holds itself together. However, scientists have long wondered if this rule holds true for the most elusive particles of all: neutrinos. These ghostly particles, which zip through the Earth by the trillions every second, might interact with gravity differently than other matter. If they do, it would signal a crack in the foundation of modern physics, pointing toward new, undiscovered laws of nature.

A recent study by researchers at Bhattadev University in India takes a fresh look at how we might catch a glimpse of such a violation. They focused their attention on the Deep Underground Neutrino Experiment, or DUNE, a massive upcoming project in the United States designed to fire a beam of neutrinos from Illinois to a detector in South Dakota, a distance of 1,300 kilometers. The experiment is already famous for its ability to study how neutrinos change their identity, or "flavor," as they travel. The researchers asked a specific question: does the energy of the neutrino beam matter when trying to detect a violation of the equivalence principle? DUNE has the flexibility to tune its beam to be either low-energy or medium-energy, and the team set out to determine which setting would be the most sensitive tool for this particular hunt.

To answer this, the scientists ran detailed computer simulations of the experiment, modeling how neutrinos would behave if the equivalence principle were indeed broken. In their model, they imagined that different types of neutrinos might couple to the gravitational field with slightly different strengths, a subtle effect that would cause them to oscillate, or change flavors, in a pattern distinct from the standard predictions. They then compared how well the low-energy beam versus the medium-energy beam could spot these subtle deviations. The results were clear and decisive: the low-energy configuration is the superior choice. When the beam is tuned to lower energies, it concentrates its intensity right where the neutrinos are most likely to show the tell-tale signs of a gravitational violation. This configuration allows the experiment to place much tighter limits on the possible size of the effect.

The study found that if the universe behaves according to the standard rules, the low-energy beam can constrain the potential violation to a range between negative 8.47 and positive 8.47 times ten to the power of negative twenty-four for one specific parameter, and a nearly identical range for another. These numbers represent an incredibly small scale, but the low-energy setup achieves this precision with greater certainty than the medium-energy setup. The researchers also discovered that the way the data is collected matters significantly. The experiment has two main ways of observing neutrinos: watching them disappear as they travel (disappearance) or watching them appear as a new type (appearance). The disappearance channels provided a smooth, steady signal that was easy to analyze, while the appearance channels were more complicated, with patterns that shifted depending on other unknown factors.

Furthermore, the team showed that the experiment does not need to rely on both neutrinos and their antimatter counterparts, called antineutrinos, running simultaneously to find these effects. Both modes can independently probe the violation, though their sensitivity depends on the beam energy chosen. In a surprising twist, while the low-energy beam was generally better, the medium-energy beam showed a slight edge in sensitivity when looking specifically at antineutrinos at the highest levels of statistical certainty. This nuance highlights that there is no single "perfect" setting for every question; the best approach depends on exactly what is being measured.

Ultimately, this work serves as a crucial guide for the future of the DUNE experiment. It confirms that by carefully optimizing the energy of the beam, scientists can maximize their chances of detecting a violation of the equivalence principle. If such a violation is found, it would be a monumental discovery, suggesting that gravity does not treat all particles equally and opening a door to physics beyond our current understanding. If no violation is found, as the simulations suggest is the most likely outcome given current constraints, the low-energy beam will have proven its worth by ruling out a vast range of possibilities with unprecedented precision. The study underscores that in the quest to understand the fundamental forces of nature, the details of how we look are just as important as what we are looking for.

Technical Summary: DUNE Beam-Energy Dependence of Sensitivity to the Violation of the Equivalence Principle

Problem Statement
The Weak Equivalence Principle (WEP), a cornerstone of General Relativity, posits that the trajectory of a test particle in a gravitational field is independent of its intrinsic properties. While classical tests have verified this to high precision, many Beyond Standard Model (BSM) theories predict violations of the Equivalence Principle (VEP). In the neutrino sector, VEP can manifest as a non-universal coupling of neutrino propagation eigenstates to the gravitational potential, leading to energy-dependent modifications in oscillation probabilities. While previous studies have established the potential of neutrino oscillations to probe VEP, the specific impact of experimental beam-energy configurations on the sensitivity to these violations at the upcoming Deep Underground Neutrino Experiment (DUNE) has not been systematically investigated. This work addresses the question of how the choice between Low-Energy (LE) and Medium-Energy (ME) beam configurations affects DUNE's ability to constrain VEP parameters.

Methodology
The authors employ a comprehensive simulation framework using the General Long Baseline Experiment Simulator (GLoBES) to model DUNE's 1300 km baseline. The study compares two specific beam flux configurations:

Low-Energy (LE): Optimized for the first oscillation maximum, peaking near 2.5 GeV.
Medium-Energy (ME): A broader spectrum peaking between 3.0 and 5.0 GeV, extending to higher energies.

The theoretical formalism incorporates VEP effects into the standard three-flavor oscillation Hamiltonian. The VEP contribution is parameterized by dimensionless terms $t_1 = \Phi\Delta\gamma_{21}$ and $t_2 = \Phi\Delta\gamma_{31}$ , where $\Phi$ is the gravitational potential and $\Delta\gamma_{ij}$ represents the difference in gravitational coupling between mass eigenstates. The analysis assumes a gravitational mixing matrix restricted to the (2,3) sector, characterized by an exotic mixing angle $\theta_N$ and a CP-violating phase $\Phi_N$ .

The sensitivity analysis involves:

Event Spectra Generation: Simulating reconstructed event spectra for both neutrino ( $\nu_\mu \to \nu_e, \nu_\mu \to \nu_\mu$ ) and antineutrino ( $\bar{\nu}_\mu \to \bar{\nu}_e, \bar{\nu}_\mu \to \bar{\nu}_\mu$ ) channels over a 13-year exposure (6.5 years Forward Horn Current + 6.5 years Reverse Horn Current).
$\chi^2$ Analysis: A statistical evaluation using the $\Delta\chi^2$ test statistic to determine exclusion limits. The analysis marginalizes over standard oscillation parameters (including $\theta_{23}$ , $\delta_{CP}$ , and mass-squared differences) and VEP sector parameters ( $\theta_N, \Phi_N$ ), while accounting for systematic uncertainties via the "pull" method.
Benchmark Scenarios: The study evaluates sensitivity for three true values of the atmospheric mixing angle $\theta_{23}$ (43°, 45°, and 47°) and compares the performance of LE and ME configurations across appearance and disappearance channels.

Key Contributions and Results
The paper provides a detailed comparison of LE and ME configurations, yielding the following primary results:

Superiority of Low-Energy Configuration: The LE configuration generally provides stronger constraints on VEP parameters than the ME configuration. This is attributed to the fact that VEP-induced spectral distortions are most pronounced near the first oscillation maximum (2–3 GeV), where the LE flux concentrates its intensity.
- For $\theta_{23} = 43^\circ$ , the LE configuration constrains $\Phi\Delta\gamma_{21}$ to $8.47 \times 10^{-24}$ and $\Phi\Delta\gamma_{31}$ to $8.53 \times 10^{-24}$ at the 3 $\sigma$ confidence level (CL).
- In contrast, the ME configuration yields weaker bounds (e.g., $1.15 \times 10^{-23}$ for $\Phi\Delta\gamma_{21}$ at 3 $\sigma$ for the same $\theta_{23}$ ).
Channel-Dependent Sensitivity:
- Appearance Channels: These channels exhibit strong phase-dependent degeneracies between the standard CP phase ( $\delta_{CP}$ ) and the exotic VEP phase ( $\Phi_N$ ). This leads to irregular, non-monotonic exclusion contours and reduced sensitivity.
- Disappearance Channels: These channels show smoother exclusion sensitivity with a monotonic rise in $\Delta\chi^2$ . They act as a "magnitude anchor," effectively breaking degeneracies and driving the overall statistical limits down to the $10^{-23}$ scale.
Neutrino vs. Antineutrino Modes: Both neutrino-only (FHC) and antineutrino-only (RHC) running modes can independently probe VEP effects. However, their relative sensitivity depends on the beam energy. While LE is generally superior, the ME configuration demonstrates enhanced sensitivity in the antineutrino mode at the 5 $\sigma$ exclusion threshold.
Parameter Space Constraints: The 2D sensitivity contours in the $\Phi\Delta\gamma_{21}$ – $\Phi\Delta\gamma_{31}$ plane confirm that the LE configuration strictly envelopes the ME configuration, providing tighter simultaneous constraints on the correlated VEP parameter space. The tightest joint constraints are achieved assuming $\theta_{23} = 43^\circ$ .

Significance
The authors conclude that optimizing the beam-energy configuration is critical for exploring possible violations of the equivalence principle at DUNE. The work demonstrates that the Low-Energy beam, by aligning its peak flux with the kinematic window where VEP effects are most distinct from standard oscillations, offers a significant advantage in constraining the VEP parameter space. Furthermore, the study highlights the necessity of channel-wise analysis, noting that while appearance channels are susceptible to degeneracies, disappearance channels provide robust, monotonic constraints. These findings underscore the importance of tailored experimental designs in distinguishing subtle BSM effects from standard neutrino oscillation phenomena.

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