⚛️ nuclear theory

Neutrino Induced Charged Current Coherent Pion Production for Constraining the Muon Neutrino Flux at DUNE

This paper proposes using neutrino-induced charged current coherent pion production as a "standard candle" to constrain the muon neutrino flux normalization at DUNE to a few percent, leveraging the Adler relation and potential near-detector measurements of pion-argon elastic scattering.

Original authors: Mun Jung Jung, Vishvas Pandey, Gray Putnam, David W. Schmitz

Published 2026-06-30

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CC BY 4.0

Original authors: Mun Jung Jung, Vishvas Pandey, Gray Putnam, David W. Schmitz

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: The "Standard Candle" for Neutrinos

Imagine you are trying to measure how bright a distant star is. To do that accurately, you need to know exactly how powerful your telescope is. If your telescope’s lens is slightly dirty or its settings are off, your measurement of the star’s brightness will be wrong.

In physics, the Deep Underground Neutrino Experiment (DUNE) is like that telescope. It is a massive experiment designed to study neutrinos—tiny, ghost-like particles that pass through everything, including us, trillions of times a second. DUNE wants to measure how these particles change flavor (oscillate) as they travel 1,300 kilometers from a source to the detector.

To do this, DUNE needs to know exactly how many neutrinos are hitting it and at what energies. This is called the "flux." But just like a telescope, the "detector" has uncertainties. We don’t know the exact number of neutrinos arriving with perfect precision. If we get the flux wrong, our final scientific results about neutrino behavior will also be wrong.

This paper proposes a clever trick to fix this problem: using a specific type of neutrino interaction as a "Standard Candle."

What is a "Standard Candle"?

In astronomy, a "standard candle" is an object with a known, fixed brightness (like a specific type of exploding star). If you know how bright it should be, and you measure how bright it looks, you can calculate the distance or the clarity of the atmosphere between you and the star.

The authors of this paper suggest using a specific particle collision called Charged Current Coherent Pion Production (let’s call it CC-Coh $\pi$ ) as a standard candle for neutrinos.

Why is CC-Coh $\pi$ Special?

Usually, when a neutrino hits an atom (in this case, an Argon atom in the detector), it’s a messy collision. The atom breaks apart, sending out a spray of particles. It’s hard to calculate exactly how likely this is to happen because the math is complex and depends on many unknown factors.

However, CC-Coh $\pi$ is a very clean, rare event. Here’s why it’s useful:

It’s Clean: The neutrino hits the Argon nucleus, but instead of smashing it to bits, the nucleus stays intact in its ground state. It’s like a billiard ball hitting another billiard ball and bouncing off without cracking.
It’s Predictable: Because the nucleus stays whole, physicists can use a mathematical rule called the Adler Relation (based on a theory called PCAC) to predict exactly how often this should happen. This rule links the neutrino collision to something else we can measure: pions bouncing off Argon atoms.
It’s Identifiable: The detector can easily spot this event because it produces exactly two particles: a muon and a pion. If there are any other particles around, we know it’s not this specific event, so we can ignore it. This makes the data very "pure."

The Method: Two Steps to One Answer

The paper proposes a two-step process to pin down the neutrino flux:

Step 1: Measure the "Bounce" (Pion-Argon Scattering)
Inside the DUNE Near Detector, there are millions of pions (particles created by other neutrino collisions) bouncing off Argon atoms. The authors suggest measuring how often these pions bounce elastically (without breaking the atom). This gives us a precise measurement of the "pion-Argon cross-section" (the probability of the bounce).

Step 2: Measure the "Hit" (Neutrino-Argon Collision)
Simultaneously, the detector counts the CC-Coh $\pi$ events (the neutrino hitting the Argon).

The Connection:
The Adler Relation acts like a bridge. It says: "The probability of the neutrino hitting the Argon is directly related to the probability of a pion bouncing off the Argon."

By measuring the pion bounces (Step 1) very precisely, we can calculate exactly what the neutrino hit rate (Step 2) should be. If the actual number of neutrino hits we see is different from what we calculated, we know our estimate of the incoming neutrino flux was wrong. We can then adjust our flux model to match the data.

The Results: How Good Is It?

The authors ran simulations to see how well this method would work. They found:

High Precision: If DUNE measures the pion bounces itself, it can constrain the uncertainty of the neutrino flux to about 1.5% at the peak energy range. This is a huge improvement over the current uncertainty, which is around 10%.
External Data Works Too: Even if DUNE doesn’t measure the pion bounces itself, but uses data from other experiments (like ProtoDUNE or LArIAT) with 1–5% uncertainty, it can still reduce the flux uncertainty to 2–5%.
Robustness: The method is resilient. Even if there are small errors in the theoretical models or if some data is messy, the method still holds up.

The Caveats (What’s Missing?)

The paper is honest about what needs to happen before this can be used in real life:

The "Adler Relation" Needs Validation: We need to be sure that the mathematical rule connecting the neutrino hit to the pion bounce works perfectly in the specific energy ranges DUNE will use. Current experiments (like the Short-Baseline Neutrino program) are helping to check this.
Measuring the Pion Bounce: We need to actually measure the pion-Argon elastic scattering cross-section with high precision. The paper suggests this can be done within DUNE itself or by other dedicated experiments.
Detector Details: The simulation assumes the detector works perfectly. In reality, dead zones in the detector or slight miscalibrations could add small errors, though the authors believe these can be managed.

Summary

Think of the neutrino beam as a rainstorm. DUNE wants to measure how hard it’s raining. But the "umbrella" (the detector) isn’t perfectly calibrated.

This paper says: "Let’s use a specific type of raindrop splash (CC-Coh $\pi$ ) that we understand perfectly. By watching how other droplets (pions) bounce off the ground (Argon), we can calibrate our umbrella. This will let us measure the rainstorm’s intensity with much greater accuracy, improving our ability to study the fundamental nature of neutrinos."

Technical Summary: Neutrino Induced Charged Current Coherent Pion Production for Constraining the Muon Neutrino Flux at DUNE

Problem Statement
The Deep Underground Neutrino Experiment (DUNE) aims to measure charge-parity (CP) violation in the neutrino sector. The precision of these measurements is limited by significant uncertainties in the modeling of the neutrino flux and neutrino-argon cross sections. While DUNE’s near and far detector configuration helps control these uncertainties, further reduction is necessary to enhance sensitivity. Existing methods for in-situ flux constraint, such as neutrino-electron elastic scattering, offer limited statistics and cannot reconstruct the neutrino flavor. The authors propose using neutrino-induced charged current coherent pion production ( $\nu_\mu$ CC-Coh $\pi$ ) as a complementary tool. This process offers high interaction rates in the DUNE Near Detector (ND) and allows for direct reconstruction of the incoming neutrino’s energy and flavor. However, the utility of this process as a flux constraint depends on the ability to determine its cross section in a model-independent way, which relies on the Adler relation and the pion-argon ( $\pi$ -Ar) elastic scattering cross section—a quantity not previously measured on argon.

Methodology
The study develops a procedure to constrain the muon neutrino flux by fitting $\nu_\mu$ CC-Coh $\pi$ events while simultaneously accounting for systematic uncertainties in the cross section model. The core theoretical framework is the Adler relation, derived from the partially conserved axial-vector current (PCAC) theorem, which relates the $\nu_\mu$ CC-Coh $\pi$ cross section to the $\pi$ -Ar elastic scattering cross section.

The methodology involves two primary scenarios for obtaining the $\pi$ -Ar elastic cross section:

DUNE ND Only: Simultaneous measurement of the $\pi$ -Ar elastic cross section using pions produced from neutrino interactions within the DUNE ND.
External $\pi$ Data: Utilizing an external measurement of the $\pi$ -Ar cross section with a defined prior uncertainty.

The analysis employs a template fit approach on the 2D kinematic distribution of reconstructed neutrino energy and $Q^2$ (four-momentum transfer squared). The fit minimizes a combined chi-squared function comprising:

The binned log-likelihood for $\nu_\mu$ CC-Coh $\pi$ data.
The binned log-likelihood for $\pi$ -Ar elastic scattering data (in the DUNE ND scenario).
Priors on the $\pi$ -Ar cross section normalization.
A Gaussian prior on the axial-vector form factor at $Q^2=0$ , fixed by fundamental constants.

The axial-vector form factor is modeled using a $z$ -expansion to allow for a model-independent description of the $Q^2$ dependence. Event selection requires high purity, rejecting backgrounds such as resonant single pion production and deep inelastic scattering. Kinematic cuts are applied to remain within the phase space where the Adler relation is valid (e.g., $Q^2 \lesssim 0.2$ GeV $^2$ , $\nu > 3\sqrt{Q^2}$ ).

Key Contributions

Proposal of In-Situ $\pi$ -Ar Measurement: The authors propose that the DUNE ND can measure the $\pi$ -Ar elastic scattering cross section using the large flux of pions generated from neutrino interactions, covering the kinematic range relevant for $\nu_\mu$ CC-Coh $\pi$ .
Simultaneous Fit Framework: Development of a fitting procedure that extracts the neutrino flux normalization while constraining the $\pi$ -Ar cross section and the axial form factor simultaneously, thereby mitigating systematic uncertainties.
Bias Tests: Demonstration of the method’s resilience against systematic effects, including variations in the axial form factor model (dipole vs. $z$ -expansion) and discrepancies in phase space regions where the Adler relation may not hold.

Results
Using Monte Carlo simulations of the DUNE ND (assuming 5 years of exposure with $1.1 \times 10^{21}$ POT per year), the authors project the constraining power of the method:

DUNE ND Scenario: If the $\pi$ -Ar elastic cross section is measured simultaneously in the DUNE ND (neglecting detector systematics), the uncertainty on the muon neutrino flux normalization at its peak is constrained to approximately 1.5%. This represents a reduction by a factor of ~6 relative to the prior uncertainty.
External Data Scenario: If an external measurement of the $\pi$ -Ar cross section with 1–5% uncertainty is used, the flux normalization uncertainty is constrained to 2–5%.
Statistical Dominance: The large number of $\pi$ -Ar elastic scatters ( $O(10^7)$ ) allows the cross section to be constrained to the sub-percent level statistically. Consequently, the precision of the flux constraint is limited primarily by the precision of the $\pi$ -Ar cross section measurement.
Robustness: Bias tests indicate that the method is robust against variations in the form factor model and systematic shifts in kinematic regions where the Adler relation is less reliable.

Significance and Claims
The paper claims that $\nu_\mu$ CC-Coh $\pi$ has the potential to serve as a "standard candle" for neutrino experiments, specifically for constraining the muon neutrino flux component. The authors emphasize that this method complements neutrino-electron scattering constraints by offering higher statistics and flavor identification. However, the study explicitly states that further work is required to:

Determine the range of validity and precision of the Adler relation at DUNE energies.
Measure the $\pi$ -Ar elastic scattering cross section to the requisite precision, potentially via external experiments like ProtoDUNE or LArIAT, or within DUNE itself.
Address experimental and phenomenological developments necessary to fully unlock this process for flux constraint.

The authors conclude that while the statistical power is sufficient to constrain flux uncertainties to a few percent, the realization of this technique depends on resolving the theoretical and experimental challenges associated with the Adler relation and the $\pi$ -Ar cross section measurement.