⚛️ phenomenology

RG Running of Multiple Neutrino Mixing Parameters at Oscillation Experiments

This paper investigates how a new physics scale within the energy range of neutrino oscillation experiments can induce renormalization group running effects between production and detection, demonstrating that combining data from upcoming experiments like DUNE-ND, JUNO-TAO, and FASER $\nu$ 2 offers strong sensitivity to disentangle these running parameters and resolve non-trivial degeneracies.

Original authors: Peter B. Denton, Shao-Feng Ge, Chui-Fan Kong, Pedro Pasquini

Published 2026-06-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Peter B. Denton, Shao-Feng Ge, Chui-Fan Kong, Pedro Pasquini

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 Idea: Neutrinos Changing Their "Outfit" on the Journey

Imagine neutrinos as travelers going on a trip. In the Standard Model of physics (our current best rulebook), these travelers wear a specific "outfit" (their mixing parameters) when they leave home, and they wear the exact same outfit when they arrive at their destination.

However, this paper suggests that if there is some "New Physics" (a hidden force or particle we haven't found yet) operating at a specific energy scale, these travelers might change their outfits while they are in transit.

In the language of physics, this is called Renormalization Group (RG) Running. It means the properties of the neutrinos (how they mix and oscillate) depend on the energy of the interaction. If the neutrino is produced at one energy level and detected at another, the "outfit" it wears at the start might be slightly different from the one it wears at the end.

The Problem: The "Blind Spot"

The authors of this paper are trying to catch these outfit changes. But there is a tricky problem: Degeneracy.

Think of it like trying to figure out how much sugar and how much salt are in a soup. If you only taste the soup once, you might think, "Maybe it's a little sugar and a lot of salt," or "Maybe it's a lot of sugar and a little salt." Both combinations could taste the same. You can't tell which is which just by looking at one spoonful.

In the paper, the "sugar and salt" are the different physics parameters (like the angles of mixing and the CP phase). If you only look at one experiment (one spoonful of soup), the math allows for many different combinations of these parameters to look identical. This is called a degeneracy, and it makes it impossible to pin down the true values of the new physics.

The Solution: A Trio of Detectors with Different "Eyes"

To solve this puzzle, the paper proposes using three specific future experiments that act like three different people tasting the soup at different temperatures and with different palates. Because they see the world differently, they can break the "blind spot" and figure out exactly what the parameters are.

JUNO-TAO (The Reactor):
- The Analogy: This is like a detector looking at very low-energy neutrinos (from nuclear reactors), similar to looking at the soup in a cool, calm room.
- What it does: It looks at electron neutrinos disappearing. Because of the low energy, the math here is very clean. It doesn't have the confusing "sugar-salt" mix-up that the other experiments have. It gives a perfect circle of possibilities, meaning it can measure two specific parameters very well on its own, but it misses the third one entirely.
DUNE-ND (The Accelerator):
- The Analogy: This is a detector near a massive particle accelerator (DUNE), looking at medium-energy neutrinos. It's like tasting the soup while it's steaming hot.
- What it does: It looks at muon neutrinos turning into electron neutrinos. However, this experiment has a strong "correlation" problem. If you try to measure the two main parameters here, they get tangled up. If one goes up, the other must go down to keep the math working. This creates a long, narrow "blind spot" where the true answer could be hiding.
FASERν2 (The LHC):
- The Analogy: This detector is at the Large Hadron Collider, looking at extremely high-energy neutrinos (trillions of electron volts). It's like tasting the soup while it's boiling violently.
- What it does: It can detect all three flavors of neutrinos, including the rare "tau" neutrino. Crucially, the way its parameters tangle together is the opposite of DUNE-ND. Where DUNE-ND has a positive correlation (both go up), FASERν2 has a negative one.

The Magic of Combining Them

The paper's main discovery is that if you combine the data from all three experiments, the "blind spots" cancel each other out.

DUNE-ND says: "The answer is somewhere along this long, tilted line."
FASERν2 says: "The answer is somewhere along this different tilted line."
JUNO-TAO says: "The answer is in this specific circle."

Where these three shapes overlap, the area becomes tiny. Instead of a long, confusing line where the answer could be anywhere, the combination of all three experiments narrows it down to a tiny, precise point.

The Results

By simulating data from these three experiments, the authors found that:

They can break the "degeneracy" (the confusion between parameters) that plagues single experiments.
They can measure the "running" of the neutrino mixing parameters with high precision.
Specifically, they can constrain the size of these new physics effects to be very small (less than 0.015 for some parameters), which keeps the physics in a "linear" regime where the math is reliable and easy to interpret.

Summary

In short, the paper argues that while looking for new physics in neutrinos is like trying to solve a puzzle with missing pieces, using three different experiments (JUNO-TAO, DUNE-ND, and FASERν2) that operate at vastly different energy levels provides enough unique perspectives to solve the puzzle. They act as a team, where the weaknesses of one are covered by the strengths of the others, allowing scientists to finally see if neutrinos are changing their "outfits" as they travel through the universe.

Technical Summary: RG Running of Multiple Neutrino Mixing Parameters at Oscillation Experiments

Problem Statement
The neutrino sector remains a primary frontier for physics beyond the Standard Model (BSM). While oscillation parameters are being measured with increasing precision, the origin of neutrino masses and potential new physics (NP) scales remain unresolved. If new physics arises at an intermediate scale—specifically within the energy range of neutrino oscillation experiments (MeV to TeV)—it manifests not only as effective operators but also through Renormalization Group (RG) running of the effective parameters between the production and detection processes.

Conventionally, the neutrino mixing matrix $U$ is assumed to be identical at production ( $Q_p^2$ ) and detection ( $Q_d^2$ ). However, if NP exists below the characteristic scales of these processes, $U(Q_p^2)$ and $U(Q_d^2)$ may differ due to RG running. This mismatch, $\delta U = U_d - U_p$ , alters oscillation probabilities. While previous studies focused on single parameters (e.g., the Dirac CP phase), a more natural scenario involves the simultaneous RG running of multiple parameters (three mixing angles and the CP phase). This introduces complex degeneracies where different combinations of running parameters ( $\beta_X$ ) yield identical oscillation probabilities in a single experiment, making it difficult to disentangle the underlying physics.

Methodology
The authors investigate this phenomenon in a model-independent framework, treating the RG running of mixing parameters as a phenomenological effect governed by $\beta$ -functions ( $\beta_X$ ). They utilize the linear approximation for the running of parameters $X$ above a new physics scale $Q_0^2$ :
$X(Q^2) \approx X(Q_0^2) + \beta_X \ln\left(\frac{Q^2}{Q_0^2}\right)$
In the zero-distance limit ( $L \ll 2E_\nu/\Delta m_{ij}^2$ ), relevant for short-baseline (SBL) experiments, the oscillation probability $P_{\alpha\beta}$ depends quadratically on the logarithm of the momentum transfer ratio, parametrized by effective coefficients $B_{\alpha\beta}$ which are functions of the $\beta_X$ parameters.

To address the degeneracies inherent in single-channel measurements, the paper proposes a combined analysis of three upcoming or ongoing experiments spanning a vast energy range and diverse flavor combinations:

JUNO-TAO: A reactor-based SBL experiment (MeV scale) measuring $\bar{\nu}_e \to \bar{\nu}_e$ disappearance.
DUNE-ND: The near detector of the DUNE long-baseline experiment (GeV scale), measuring $\nu_\mu \to \nu_e$ appearance and $\nu_\mu \to \nu_\mu$ disappearance.
FASER $\nu$ 2: A forward detector at the LHC (TeV scale), capable of detecting all three neutrino flavors ( $\nu_e, \nu_\mu, \nu_\tau$ ) from various parent particle decays.

The methodology involves calculating the expected event rates for these experiments, incorporating the RG running effects into the transition probabilities. The authors construct $\chi^2$ functions for each experiment, accounting for statistical uncertainties and systematic nuisance parameters (flux normalization and tilt). Crucially, they analyze the correlation structures of the $\beta_X$ parameters in each channel. For instance, the $\nu_\mu \to \nu_e$ channel at DUNE-ND exhibits a positive correlation between $\beta_{12}$ and $\beta_{13}$ , while the $\nu_e \to \nu_\tau$ channel at FASER $\nu$ 2 exhibits a negative correlation. JUNO-TAO, measuring electron disappearance, shows no correlation between these specific parameters.

Key Contributions

Identification of Degeneracies: The paper demonstrates that in a single experiment, multiple RG running parameters are highly correlated (degenerate), significantly reducing sensitivity. For example, in DUNE-ND, a positive correlation between $\beta_{12}$ and $\beta_{13}$ creates a "blind spot" where large values of these parameters can mimic the standard model.
Strategy for Degeneracy Breaking: The authors show that combining experiments with different energy scales and flavor channels breaks these degeneracies. The distinct correlation patterns (positive, negative, or null) across JUNO-TAO, DUNE-ND, and FASER $\nu$ 2 allow for the simultaneous constraint of multiple $\beta_X$ parameters.
Comprehensive Sensitivity Analysis: The study provides a detailed numerical sensitivity analysis for the combination of these three experiments, moving beyond single-parameter studies to a multi-parameter global fit.

Results
The combined analysis yields projected sensitivities at the 68% Confidence Level (C.L.) that are well within the linear regime of the RG running approximation:

Mixing Angles: $|\beta_{12}|, |\beta_{13}| \lesssim 0.015$ .
Third Angle: $|\beta_{23}| \lesssim 0.01$ .
CP Phase: $|\beta_{\delta}| < 0.045$ .

The results highlight that while individual experiments struggle with degeneracies (e.g., JUNO-TAO is insensitive to $\beta_{23}$ , and DUNE-ND suffers from strong correlations), the combination of all three experiments significantly tightens the bounds. Specifically, the combination reduces the allowed parameter space for $\beta_{12}$ and $\beta_{13}$ from a range of $\sim \pm 0.14$ (in the DUNE-ND blind spot) to $\sim \pm 0.015$ . The analysis also confirms that the variation of the Dirac CP phase $\delta_D$ has a negligible effect on these sensitivity curves.

Significance
The paper claims that if new physics exists at intermediate scales, its effects on neutrino mixing can be probed through RG running. The primary significance of this work is the demonstration that no single short-baseline experiment can independently and model-independently constrain multiple RG running parameters due to intrinsic degeneracies. However, by leveraging the complementary nature of JUNO-TAO, DUNE-ND, and FASER $\nu$ 2—specifically their differences in energy scales (MeV to TeV) and accessible flavor channels—these degeneracies can be resolved. This approach offers a robust, model-independent method to test for new physics in the neutrino sector using upcoming experimental data, potentially revealing the scale and nature of interactions beyond the Standard Model.