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Measurement of the $\bar \nu_\mu-$ Hydrogen Charged-Current Quasi-Elastic Cross Section using the NOvA Near Detector

Using the NOvA near detector, researchers achieved the most precise measurement to date of the muon antineutrino charged-current quasi-elastic cross section on hydrogen at an average energy of 1.9 GeV, obtaining a value of $0.538 \pm 0.009 ({\rm stat}) \pm 0.010 ({\rm syst}) \pm 0.055 ({\rm flux}) \times 10^{-38}$ cm $^2$ with sufficiently low non-flux uncertainties to enable future constraints on the absolute antineutrino flux.

Original authors: The NOvA Collaboration

Published 2026-08-13

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: The NOvA Collaboration

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 Ghostly Dance of Invisible Particles

Imagine a world where particles are like shy ghosts that can pass through entire planets without bumping into anything. These are neutrinos, the most abundant matter particles in the universe, yet they are so elusive that trillions of them zip through your body every second without you ever feeling a thing. Scientists are obsessed with catching these ghosts because they hold secrets about how the universe began and why there is more matter than antimatter. To study them, researchers fire beams of these particles from giant accelerators toward massive detectors. But here's the tricky part: when a neutrino hits a target, it doesn't just bounce off a single, lonely atom. Usually, it smashes into a crowded nucleus—a cluster of protons and neutrons stuck together like a messy pile of marbles. This "crowd" makes the crash messy and hard to understand, blurring the details of the interaction.

To get a clear picture, scientists need to see what happens when a neutrino hits a single, lonely proton, free from the chaos of a crowded nucleus. It's the difference between watching a single dancer in an empty room versus trying to figure out their moves while they are part of a chaotic mosh pit. By understanding how a neutrino interacts with a single proton, physicists can build better models to decode the messy data from the big detectors. This is crucial for the next generation of experiments that hope to unlock the deepest mysteries of the cosmos. Without this clean reference point, the "mosh pit" data remains too fuzzy to interpret accurately.

The NOvA Experiment: Catching Ghosts in a Plastic Ocean

In this new study, the NOvA collaboration has taken a giant leap forward in this quest. They used a massive detector called the "Near Detector," located just a few miles from where the neutrino beam is created at Fermilab in Illinois. Think of this detector as a giant, high-tech swimming pool filled not with water, but with a special liquid plastic (scintillator) that glows when particles pass through it. While most of this plastic is made of carbon and other heavy elements, about 10.8% of it is pure hydrogen. This hydrogen is the gold mine of the experiment.

The researchers were looking for a very specific type of "ghostly handshake" called Charged-Current Quasi-Elastic (CCQE) scattering. In this scenario, an antineutrino (the antimatter cousin of the neutrino) smacks into a single hydrogen proton, turns into a positive muon (a heavy, unstable cousin of the electron), and kicks out a neutron. It's a clean, two-body collision: one in, two out. The challenge is that the detector is mostly made of heavier stuff, so for every time a neutrino hits a lonely hydrogen atom, it hits a heavy nucleus hundreds of times. It's like trying to hear a single violin solo in the middle of a roaring rock concert.

To solve this, the team developed a clever "filter" to separate the solo violin from the noise. They used two main tools:

Topological Filters (HitID): They looked at the shape of the glow in the detector. A clean hydrogen hit looks like a single track (the muon) and a small, isolated spark (the neutron). A messy nuclear hit looks like a chaotic explosion of sparks.
Kinematic Filters (KineID): They checked the math of the crash. If the neutrino hit a lonely proton at rest, the energy and momentum of the outgoing particles must balance perfectly. If it hit a crowded nucleus, the math gets messy because the other particles in the nucleus steal some energy.

By combining these filters, the team managed to sift through a massive dataset collected between June 2016 and July 2019. They were looking at a beam containing about 1.2 × 10²¹ protons hitting a target (a number so huge it's hard to imagine). From this ocean of data, they successfully identified 35,509 events that looked like the clean hydrogen collisions they were hunting for. This is the largest collection of such events ever recorded, dwarfing previous attempts that relied on just a handful of observations.

The Results: A Sharper Lens on the Invisible

After carefully subtracting the "noise" from the heavy nuclei and correcting for the quirks of their detector, the team calculated the probability of this specific interaction happening. They found that the total cross section (a fancy way of saying the "target size" or probability of the collision) for the reaction $\bar{\nu}_\mu H \to \mu^+ + n$ is 0.538 ± 0.009 (stat) ± 0.010 (syst) ± 0.055 (flux) × 10⁻³⁸ cm².

This measurement was taken at an average energy of 1.9 GeV. The precision here is remarkable. The uncertainty from the data itself (statistics) and the detector (systematics) is incredibly small—only about 2.5% combined. However, the biggest source of uncertainty comes from knowing exactly how many neutrinos were in the beam in the first place (the flux), which contributes a 10.2% uncertainty.

Why does this matter? Because the measurement of the interaction itself is now so precise that it is more than four times more accurate than our current knowledge of the beam's intensity. This flips the script on how these experiments are usually done. Instead of using the beam to measure the interaction, scientists can now use this incredibly precise measurement of the hydrogen interaction to measure the beam itself. It's like having a ruler so perfect that you can use it to measure how fast a car is moving, rather than using a speedometer to measure the ruler.

The paper confirms that their models for how these particles behave are on the right track, though it also highlights that the "flux" (the number of particles in the beam) remains the biggest hurdle to even greater precision. By providing this high-statistics, clean dataset, the NOvA team has handed future experiments a powerful new tool. They have effectively turned a blurry snapshot of the subatomic world into a high-definition image, allowing physicists to finally see the "solo violin" clearly amidst the cosmic noise.

Technical Summary: Measurement of the $\bar{\nu}_\mu$ -Hydrogen Charged-Current Quasi-Elastic Cross Section using the NOvA Near Detector

Problem and Motivation
Current and future long-baseline neutrino experiments aim to measure neutrino mixing parameters with high precision. However, extracting oscillation parameters requires a robust understanding of neutrino-nucleus cross-sections, which are complicated by nuclear effects such as Fermi motion and final-state interactions (FSI). These effects "smear" the interaction kinematics, making it difficult to disentangle the intrinsic neutrino flux and energy scale from the nuclear physics.

Measurements of neutrino interactions on hydrogen (free protons) provide a critical reference free of nuclear effects, offering a direct probe of the structure of free nucleons. While previous measurements of charged-current quasi-elastic (CCQE) scattering on hydrogen exist, they are historically limited by low statistics. Specifically, the first observation by the BNL 7-foot bubble chamber relied on only $13 \pm 6$ events, and more recent measurements by MINERvA on hydrogen within plastic scintillator have focused on constraining nucleon form factors rather than providing a high-statistics total cross-section measurement.

Methodology
The NOvA collaboration utilized the NOvA Near Detector (ND) to measure the total cross-section for the exclusive process $\bar{\nu}_\mu H \to \mu^+ n$ (note: the paper title and text refer to antineutrinos, $\bar{\nu}_\mu$ , interacting with hydrogen to produce a muon and a neutron). The data corresponds to an exposure of $1.2 \times 10^{21}$ protons-on-target (POT) in the NuMI antineutrino beam mode, collected between June 2016 and July 2019. The average neutrino energy at the detector is approximately 1.9 GeV.

Detector and Target: The ND is a tracking calorimeter filled with liquid scintillator (95% mineral oil, 5% pseudocumene) contained in PVC cells. The fiducial volume contains 116.7 tons of material, of which 12.5 tons is hydrogen (10.8% by mass).
Event Signature: The signal is characterized by a single reconstructed muon track and an isolated cluster of hits from the daughter neutron interacting in the detector.
Event Selection:
- Samples: Events were divided into "contained" (muon stops within the detector) and "uncontained" (muon exits) samples.
- Discriminants: Two multivariate discriminants based on Boosted Decision Trees (BDT) were employed:
  - HitID: A topological classifier using 14 variables (e.g., hit energy depositions, isolation of clusters, distance between neutron candidate and muon track).
  - KineID: A kinematic classifier using 7 variables (e.g., transverse momenta, opening angles, missing transverse momentum) to distinguish interactions on free protons from those on bound nucleons.
- Signal and Control Regions: A Signal Region (SR) was defined in the two-dimensional plane of HitID and KineID. Control Regions (CRs) were established to constrain backgrounds and correct for Monte Carlo (MC) simulation limitations.
Background Estimation and Corrections: Backgrounds from interactions on heavier nuclei (Carbon, Chlorine, etc.) and other interaction channels (NC, RES, DIS) were estimated using MC simulations (GENIE v3.0.6). To mitigate MC model dependence, data-driven corrections were applied:
- $k_{nc}$ : Corrects for differences in neutron interaction rates and detection efficiency between data and MC.
- $k_{cut}$ : Corrects for the efficiency of the sequential HitID and KineID cuts using the CRs.
- These corrections ensure the background predictions are largely insensitive to MC details, limited primarily by the statistics of the control samples.
Simulation: The NuMI flux was predicted using PPFX reweighted Geant4 simulations. Neutrino interactions were simulated with GENIE, utilizing the Llewellyn-Smith model for QEH (with a $z$ -expansion axial form factor) and the Valencia local Fermi gas model for nuclear effects.

Key Contributions

Highest Statistics Measurement: This analysis yields 35,509 signal events after background subtraction, representing the highest statistics sample of (anti)neutrino-hydrogen interactions measured to date.
Data-Driven Background Control: The use of dedicated control regions and data-driven correction factors ( $k_{nc}$ , $k_{cut}$ ) significantly reduces systematic uncertainties related to background modeling, making the result robust against variations in neutrino interaction and neutron propagation models.
Precision Cross-Section: The analysis provides the most precise measurement of the total $\bar{\nu}_\mu$ -hydrogen CCQE cross-section to date.

Results
The flux-averaged total cross-section at an average energy of 1.9 GeV was measured to be:
$\sigma(\bar{\nu}_\mu H \to \mu^+ n) = 0.538 \pm 0.009(\text{stat}) \pm 0.010(\text{syst}) \pm 0.055(\text{flux}) \times 10^{-38} \text{ cm}^2$

Uncertainty Breakdown: The combined statistical and non-flux systematic uncertainty is approximately 2.5% ( $0.013 \times 10^{-38} \text{ cm}^2$ ). This is more than four times smaller than the flux uncertainty (10.2%).
Comparison: The result is consistent with the only previous measurement from the BNL 7-foot bubble chamber (which had large statistical errors) and aligns with GENIE predictions using the Llewellyn-Smith model with the $z$ -expansion form factor.
Systematics: The dominant systematic uncertainty remains the integrated flux. Non-flux systematics (including background estimation, QEH modeling, neutron detection, and detector response) are well-controlled, with the total non-flux uncertainty at 1.9%.

Significance
The paper claims that this measurement provides the most precise total cross-section for this process to date. Due to the high precision of the cross-section measurement relative to the flux uncertainty, the author states that this result can be used in the future to constrain the absolute $\bar{\nu}_\mu$ flux. Furthermore, by providing a clean reference for free-proton interactions, the data offers essential input for modeling neutrino-nucleus cross-sections, which is critical for the extraction of oscillation parameters in long-baseline experiments. The measurement fills a gap in energy coverage between the BNL and MINERvA experiments.

The Ghostly Dance of Invisible Particles

The NOvA Experiment: Catching Ghosts in a Plastic Ocean

The Results: A Sharper Lens on the Invisible

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