Measurements of differential charged-current cross sections on argon for electron neutrinos with final-state protons in MicroBooNE

The MicroBooNE collaboration presents the first single-differential electron-neutrino charged-current cross-section measurements on argon with final-state protons, reporting a total cross section of $[4.1 \pm 0.3 \text{ (stat.)} \pm 1.1 \text{ (syst.)}] \times 10^{-39} \mathrm{cm}^{2}/\mathrm{nucleon}$ that shows good agreement with standard neutrino event generator predictions.

The Gist

Imagine you are a detective trying to figure out how a specific type of invisible ghost (a neutrino) interacts with a very dense, frozen block of ice (liquid argon).

This paper is the report from the MicroBooNE team, a group of scientists who built a giant, high-tech camera inside a tank of liquid argon at Fermilab (a massive particle accelerator in Illinois). Their goal was to catch these ghosts in the act of bumping into the argon atoms and to measure exactly how often and how hard they hit.

Here is the breakdown of their investigation, explained with everyday analogies:

1. The Setup: The Ghost Hunting Ground

Think of the NuMI beam as a giant, high-powered flashlight shooting a stream of these invisible ghosts toward the detector.

• The Detector (MicroBooNE): Imagine a massive, 170-ton tank filled with liquid argon (like super-cold, super-clear ice). Inside, there are thousands of wires acting like a 3D spiderweb.
• The Trigger: When a ghost hits an argon atom, it creates a tiny spark of light and a trail of electric charge. The wires catch this charge, and cameras catch the light. It's like a snow globe where a single snowflake hitting a wall creates a visible, glowing trail.

2. The Crime Scene: What They Were Looking For

The scientists weren't looking for just any ghost interaction. They were hunting for a very specific "signature":

• The Victim: An electron neutrino (a specific type of ghost).
• The Aftermath: The ghost hits an argon atom, knocks out an electron (which creates a shower of energy) and kicks out at least one proton (a piece of the atom's core).
• The "No Pions" Rule: They specifically wanted cases where no pions (another type of particle) were created. Think of it like looking for a car crash where only the bumper and a headlight broke off, but the rest of the car stayed intact. This makes the crash easier to study.

3. The Investigation: Sorting the Noise

The detector is like a busy city street. It sees everything: the ghosts they want, other types of particles (muons, pions), and even random noise from cosmic rays (space dust hitting the detector).

To find the specific "electron neutrino + proton" crashes, the team used a digital sieve (a computer algorithm called a Boosted Decision Tree or BDT):

• The Filter: They taught the computer to ignore anything that looked like a muon (a heavier cousin of the electron) or a pion.
• The "Proton" Clue: They specifically looked for events where a proton was kicked out. This is a clever trick because it helps filter out "anti-neutrinos" (the ghost's evil twin), making their sample much cleaner.
• The Result: Out of thousands of events, they found about 203 that fit their perfect description.

4. The Measurement: Counting the Hits

Once they had their clean list of 203 events, they started measuring:

• How much energy did the electron have?
• How much total energy was visible?
• What angle did the electron and proton fly off at?
• How many protons were kicked out?

They turned these raw counts into a Cross Section.

• Analogy: Imagine throwing darts at a wall. The "cross section" is the size of the bullseye. If the bullseye is huge, you hit it often. If it's tiny, you rarely hit it. They measured the "size" of the target that the electron neutrino sees when it hits an argon atom.

5. The Results: Did the Theories Hold Up?

The scientists compared their real-world measurements against computer simulations (the "theories"). These simulations are like video game physics engines that try to predict how ghosts should behave.

• The Verdict: The real data matched the computer predictions very well!
• The Total Hit Rate: They calculated that the "bullseye" size (cross section) is roughly 4.1 (in very small scientific units).
• The Uncertainty: Like any measurement, there was a little bit of guesswork involved (about 10-15% uncertainty), mostly because it's hard to know exactly how many ghosts were in the flashlight beam to begin with.

6. Why Does This Matter?

You might ask, "Why do we care about neutrinos hitting argon?"

• The Big Picture: These measurements are crucial for the future of neutrino physics. Scientists are trying to solve the mystery of why the universe has more matter than antimatter (why we exist at all).
• The Future: The next big experiment, DUNE (Deep Underground Neutrino Experiment), will use a much bigger version of this liquid argon tank. To make DUNE accurate, scientists need to know exactly how neutrinos behave in argon right now. This paper provides that essential "rulebook" for the future.

Summary

In short, the MicroBooNE team acted like high-tech detectives. They caught a rare type of particle interaction in a giant tank of liquid argon, filtered out the noise, and confirmed that our current computer models of the universe are doing a pretty good job predicting how these elusive particles behave. It's a small step for a neutrino, but a giant leap for understanding the fundamental building blocks of our universe.

Technical Summary

Here is a detailed technical summary of the paper "Measurements of differential charged-current cross sections on argon for electron neutrinos with final-state protons in MicroBooNE."

1. Problem Statement and Motivation

• Scientific Context: Precise measurements of electron-neutrino ($\nu_e$) charged-current (CC) cross-sections on nuclei are critical for next-generation long-baseline neutrino oscillation experiments (e.g., DUNE) and searches for sterile neutrinos. Current models often extrapolate from muon-neutrino ($\nu_\mu$) data or rely on limited direct $\nu_e$ measurements.
• The Gap: While inclusive $\nu_e$ cross-sections on argon have been measured, exclusive final states with specific topologies remain under-constrained. Specifically, the channel $\nu_e$ CC with no pions and one or more protons ($\nu_e$ CC0$\pi$Np) is a dominant contribution to event rates at $\sim$1 GeV. This channel probes quasi-elastic-like processes and nuclear effects (such as final-state interactions) that alter proton kinematics and multiplicities.
• Specific Challenge: Measuring this channel requires high-purity separation of $\nu_e$ from $\bar{\nu}_e$ and $\nu_\mu$ backgrounds, as well as precise reconstruction of low-energy protons in Liquid Argon Time Projection Chambers (LArTPCs).

2. Methodology

Experimental Setup:

• Detector: MicroBooNE, a 170-ton LArTPC located at Fermilab.
• Beam: The Neutrinos at the Main Injector (NuMI) beam, operating in two modes:
  • Run 1 (FHC): Forward Horn Current (neutrino mode), $2.0 \times 10^{20}$ Protons on Target (POT).
  • Run 3 (RHC): Reverse Horn Current (antineutrino mode), $5.0 \times 10^{20}$ POT.
• Flux: The analysis utilizes a flux prediction constrained by the PPFX framework and Geant4 simulations, accounting for off-axis geometry ($\approx 8^\circ$).

Event Selection:

• Signal Definition: Events with exactly one electron-like shower ($E_{kin} > 20$ MeV), at least one proton-like track ($E_{kin} > 40$ MeV), and zero pions (charged or neutral) in the final state.
• Background Rejection:
  • $\nu_\mu$ CC: Rejected using a log-likelihood test on the $dE/dx$ profile of the longest track (proton vs. muon) and a Pandora shower score.
  • $\pi^0$ Background: Rejected by requiring the distance between the interaction vertex and the shower start to be $< 12$ cm (electrons start at the vertex; photons convert after a gap) and using Molière angle and $dE/dx$ cuts.
  • $\bar{\nu}_e$ Contamination: This is an irreducible background ($\bar{\nu}_e + ^{40}\text{Ar} \to e^+ + Np + 0\pi$) indistinguishable from signal in LArTPC. It is estimated via simulation and subtracted.
• Multivariate Analysis: A Boosted Decision Tree (BDT) using XGBoost was trained on seven variables (including track PID, shower score, subcluster counts, and vertex-shower distances) to optimize signal purity.
  • BDT Cut Thresholds: $>0.55$ for FHC and $>0.575$ for RHC.
  • Resulting Purity: $\approx 78.5\%$ (FHC) and $74.0%$ (RHC).

Cross-Section Extraction:

• Unfolding: To correct for detector resolution and selection efficiency, the authors used the Wiener-Singular Value Decomposition (Wiener-SVD) method. This technique regularizes the unfolding to prevent noise amplification while preserving the $\chi^2$ consistency between data and prediction.
• Variables: Differential cross-sections were measured as a function of:
  1. Outgoing electron energy ($E_e$).
  2. Total visible energy ($E_{visible}$).
  3. Cosine of the opening angle between the electron and the leading proton ($\cos \theta_{ep}$).
• Total Cross-Section: Calculated using the formula $\sigma = (N - B) / (\epsilon \times N_{target} \times \Phi_{\nu_e})$.

3. Key Contributions

• First Exclusive Measurement with NuMI: This is the first measurement of exclusive $\nu_e$ CC0$\pi$Np cross-sections on argon using the higher-energy NuMI beam, complementing previous results from the lower-energy Booster Neutrino Beam (BNB).
• High-Purity Sample: The analysis successfully isolated a sample of 155 background-subtracted events from 203 total selected events, achieving a signal purity of $\sim 74-78\%$.
• Comprehensive Uncertainty Budget: The paper provides a detailed breakdown of systematic uncertainties, identifying neutrino flux (dominated by hadron production modeling) as the leading systematic source ($\sim 26-27\%$), followed by detector response ($10%$) and cross-section model uncertainties.
• Model Validation: The results provide a rigorous testbed for neutrino event generators (GENIE, NEUT, NuWro, GiBUU) in the $\nu_e$ sector, which is less constrained than the $\nu_\mu$ sector.

4. Key Results

• Total Cross-Section:
  $$\sigma = [4.1 \pm 0.3 \text{ (stat.)} \pm 1.1 \text{ (syst.)}] \times 10^{-39} \text{ cm}^2/\text{nucleon}$$
• Differential Distributions:
  • The unfolded differential cross-sections for $E_e$, $E_{visible}$, and $\cos \theta_{ep}$ were compared against five major event generators: NEUT v5.4.0.1, NuWro v.21.09.2, GiBUU 2025, GENIE v03.4.2 AR23, and the MicroBooNE-tuned GENIE v03.0.6 G18.
  • Agreement: All generators show good agreement with the data within $2\sigma$ across all variables.
  • $\chi^2$ Metrics:
    • Electron Energy ($E_e$): $\chi^2/n$ ranges from 5.6/5 to 6.6/5.
    • Visible Energy: $\chi^2/n$ ranges from 11.5/7 to 13.8/7 (slightly higher tension, but still consistent).
    • Opening Angle: $\chi^2/n$ ranges from 3.7/5 to 5.7/5.
• Comparison to Previous Work: Unlike the earlier BNB measurement which observed model overprediction, this NuMI analysis observes a slight model underprediction in electron energy. However, the differences are not statistically significant, and both measurements agree within $1\sigma$.

5. Significance

• Validation of Models: The results confirm that current neutrino event generators can effectively model $\nu_e$ interactions on argon within the current experimental uncertainties, providing confidence for future DUNE analyses.
• Flux Constraints: The dominant uncertainty remains the neutrino flux prediction. The paper highlights the need for off-axis hadron production data to further reduce systematic errors in future measurements.
• Statistical Limitations: The analysis is currently statistics-limited. The authors note that future MicroBooNE runs (leveraging $\sim 3\times$ more data) will allow for separate measurements of $\nu_e$ and $\bar{\nu}_e$ cross-sections and potentially more complex topologies (e.g., proton multiplicity unfolding).
• Methodological Benchmark: The successful application of Wiener-SVD unfolding to exclusive $\nu_e$ channels on LArTPC data sets a standard for future high-precision neutrino cross-section measurements.

In summary, this work represents a significant step forward in understanding electron-neutrino interactions on argon, providing essential data to refine interaction models for the upcoming era of precision neutrino physics.