Measurement of the Muon Flux at SND@LHC: Results from the 2023-2025 Proton and Heavy-Ion Periods

This paper presents the precise measurement of muon fluxes in the forward pseudorapidity region of the SND@LHC experiment using 2023–2025 proton and heavy-ion collision data, reporting values that agree with Monte Carlo predictions and are dominated by systematic uncertainties.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed train station where particles are the trains. Usually, scientists are interested in the "passengers" (neutrinos) that get off at a very specific, hard-to-reach platform called IP1. However, to catch these elusive passengers, they have to build a detector called SND@LHC about 480 meters down the tunnel.

The problem? The station is incredibly crowded with "noise"—specifically, a flood of muons (a type of heavy electron) that are just passing through. These muons are like a constant, roaring waterfall of rain. If you are trying to hear a whisper (a neutrino interaction) in the middle of that waterfall, you need to know exactly how loud the rain is.

This paper is essentially the "weather report" for that waterfall, measured over three years (2023–2025). Here is the breakdown in simple terms:

1. The Detective's Toolkit (The Detector)

The SND@LHC detector is like a multi-layered security checkpoint:

• The Veto System: Think of this as a motion sensor at the door. It tags anyone entering from the main collision point so the scientists know who is who.
• The Target (The Emulsion): This is the "trap" where they hope to catch neutrinos. It's made of special film (like high-tech photographic paper) sandwiched between heavy tungsten plates.
• The Tracker (SciFi & DS): These are the eyes of the operation. They are made of glowing fibers and scintillating bars that light up when a particle zips through, telling the computer exactly where the particle went.
• The Muon System: This is the final gate at the end of the tunnel, designed specifically to catch the muons that made it all the way through.

2. The Mission: Counting the Raindrops

The main goal of this paper is to count exactly how many muons hit the detector every second. Why?

• Noise Cancellation: If you know the background noise (muons) is X, and you see a signal of X+1, you know you found something new (a neutrino).
• Film Protection: The special photographic film inside the detector gets "fogged" or ruined if too many muons hit it. Knowing the muon count tells the scientists exactly when to swap out the film, like changing a camera roll before it gets overexposed.

3. The Results: A Changing Weather Pattern

The scientists took measurements over three years, and the "weather" changed significantly:

• The "Proton" Years (The Light Rain):
  When the LHC smashes protons (light particles), the muon rain is light but steady.

  • 2023: A steady drizzle.
  • 2024: Double the rain! Why? The scientists flipped the magnetic switches in the tunnel (like changing the direction of a river current). This accidentally funneled more muons toward the detector.
  • 2025: The rain slowed down a bit as they adjusted the settings again, but it was still heavier than in 2023.

• The "Heavy-Ion" Years (The Tsunami):
  When the LHC smashes heavy lead nuclei (heavy particles), the muon rain is a massive tsunami. The numbers here are 1,000 times higher than the proton years.

  • The scientists found that most of these muons aren't actually coming from the main collision point (IP1). Instead, they are coming from a "side door" about 400 meters up the tunnel (near a magnet called MQ.11R1).
  • Analogy: Imagine you are standing in a hallway. You think the wind is coming from the front door (IP1), but you realize the real wind is actually blowing in from a window 400 feet away, channeled by the hallway's shape. The paper maps out exactly where this "wind" is coming from.

4. The "Guessing Game" vs. Reality

Scientists use super-computers (Monte Carlo simulations) to predict how many muons should be there.

• The Verdict: The computer predictions were pretty good, usually within 10–20% of the real numbers.
• The Surprise: In 2024, the real rain was heavier than the computer predicted because the magnetic "river current" was flipped, and the computer models hadn't fully accounted for that specific change yet.

5. Why This Matters

This paper is the "User Manual" for the background noise.

• Before this, scientists had to guess how much "static" was on their radio.
• Now, they have a precise map. They know exactly how much "rain" is falling so they can subtract it from their data to find the rare, precious "whispers" (neutrinos) they are hunting for.
• It also tells them exactly when to change the photographic film so they don't waste money or time on ruined data.

In a nutshell: The SND@LHC team spent three years counting the "background noise" of muons in a giant underground tunnel. They discovered that the noise level changes drastically depending on how the magnets are set up and that a lot of the noise is actually coming from a side door rather than the main entrance. This map allows them to tune their instruments perfectly to catch the rare neutrinos hiding in the chaos.

Technical Summary

1. Problem Statement and Motivation

The SND@LHC (Scattering and Neutrino Detector at the Large Hadron Collider) experiment is designed to detect high-energy neutrinos in the forward pseudorapidity region ($7.2 < \eta < 8.4$) produced by proton collisions at Interaction Point 1 (IP1).

• Primary Challenge: The vast majority of events recorded by the detector are caused by muons originating from the IP1 or upstream beam interactions. These muons constitute the primary background for Charged Current (CC) neutrino interactions.
• Operational Impact: The detector utilizes an Emulsion Cloud Chamber (ECC) target. Excessive muon exposure degrades the emulsion films, necessitating frequent target replacements. The frequency of these replacements is directly dependent on the muon rate.
• Objective: A precise characterization of the muon flux is essential for background subtraction, neutrino signal extraction, and optimizing the operational schedule (target replacement frequency) of the experiment.

2. Methodology

2.1 Experimental Setup

The SND@LHC detector is located ~480 m downstream from the ATLAS interaction point (IP1) in the TI18 tunnel. It consists of:

• Veto System: Parallel planes of scintillator bars to tag charged particles. A third veto plane was added in 2024 to reduce inefficiency.
• Target: Tungsten plates interleaved with nuclear emulsion films and electronic trackers (acting as an electromagnetic calorimeter).
• Scintillating Fiber (SciFi) Tracker: Interleaved with the target, providing precise position measurements.
• Muon System: Located downstream, comprising iron blocks (HCAL) and alternating scintillator planes (Upstream and Downstream) for muon identification.
• Coordinate System: A right-handed system with the origin 480 m from IP1.

2.2 Data Sample

The analysis covers data collected during the 2023, 2024, and 2025 LHC runs for both:

• Proton Collisions: High-energy proton beams.
• Heavy-Ion Collisions: Fully stripped lead nuclei ($^{208}\text{Pb}^{82+}$).
• Selection: The study utilized full track reconstruction for specific LHC fills (runs) and a sampling approach for others to manage statistics, as systematic uncertainties dominate the total error budget.

2.3 Reconstruction and Analysis Techniques

• Track Finding: A Hough transform algorithm maps detector hits to parameter space to identify candidate tracks.
• Track Fitting: A Kalman filter (via the Genfit package) reconstructs 3D tracks by combining independent XZ and YZ plane reconstructions.
• Efficiency Estimation: Tracking efficiency is calculated using a "tag-and-probe" method. A track found in one subsystem (e.g., SciFi) is extrapolated to the other (e.g., Downstream scintillators). If the crossing points match within 3 cm, it is considered a successful match.
• Flux Calculation: The muon flux ($\Phi_\mu$) is calculated using the formula:
  $$\Phi_\mu = \frac{N_{\text{tracks}}}{A \cdot L_{\text{int}} \cdot \epsilon}$$
  Where $N_{\text{tracks}}$ is the number of muon tracks, $A$ is the fiducial area ($31 \times 31 \text{ cm}^2$), $L_{\text{int}}$ is the integrated luminosity, and $\epsilon$ is the tracking efficiency.

2.4 Monte Carlo Simulations

Simulations were performed using FLUKA (for hadron collisions and particle transport through rock/tunnel) and Geant4 (for detector response).

• Heavy-Ion Modeling: Combined Nuclear Interactions (NI) and Electromagnetic Dissociation (EMD) components.
• Source Identification: Simulations identified that a significant portion of muons in heavy-ion runs originate not from IP1, but from pion/kaon decays at the LEHR.11R1 site (~415 m upstream), directed by the MQ.11R1 quadrupole magnet. These muons are synchronous with collisions and cannot be temporally separated from IP1 muons.

3. Key Contributions

• First Multi-Year Flux Measurement: Provides the first comprehensive muon flux measurements for SND@LHC covering three consecutive years (2023–2025) for both proton and heavy-ion collisions.
• Unified Fiducial Area: Unlike the 2022 analysis, this work adopted a unified fiducial area for both SciFi and Downstream (DS) subsystems, eliminating detector subsystem choice as a source of systematic uncertainty.
• LHC Configuration Impact: The study quantifies the impact of specific LHC machine configuration changes (e.g., IR1 triplet polarity reversal in 2024, crossing angle adjustments in 2025) on the muon background.
• Background Characterization: Detailed identification of non-IP1 muon sources (specifically from LEHR.11R1) which contribute significantly to the heavy-ion flux.

4. Results

4.1 Measured Muon Fluxes

The fluxes were measured in the central $31 \times 31 \text{ cm}^2$ fiducial area.

Proton Collisions (Units: $10^{-2} \text{ nb/cm}^2$):

• 2023: $1.90 \pm 0.04$
• 2024: $3.74 \pm 0.06$ (Significant increase due to LHC configuration changes)
• 2025: $2.48 \pm 0.04$

Heavy-Ion Collisions (Units: $10^4 \text{ nb/cm}^2$):

• 2023: $3.13 \pm 0.11$
• 2024: $5.54 \pm 0.17$
• 2025: $3.60 \pm 0.13$

4.2 Uncertainty Analysis

• Dominance of Systematics: Uncertainties are dominated by systematic effects (luminosity and efficiency).
  • Proton Data: Statistical contribution is $\approx 1\%$; Systematics (Luminosity $\approx 2\%$, Efficiency $\approx 30-36\%$) dominate.
  • Heavy-Ion Data: Statistical contribution is $< 0.1\%$; Systematics (Luminosity $\approx 3.5\%$, Efficiency $\approx 8-22\%$) dominate.
• Comparison with Simulation:
  • Proton: Data agrees with Monte Carlo predictions within 10–20%. The 2024 flux was higher than predicted due to the polarity reversal of the IR1 triplet (FDF to DFD), which optimized machine lifetime but increased muon transmission.
  • Heavy-Ion: Simulations (based on 2022 configurations) agree with 2023 data within $\sim 5\%$.

4.3 Angular Distribution

• Most tracks exhibit minimal slopes.
• A secondary peak at $\theta_{XZ} \approx 45 \text{ mrad}$ (horizontal) and a plateau near $110 \text{ mrad}$ were observed, attributed to low-energy muons from upstream decays (LEHR.11R1), particularly prominent in heavy-ion runs.

5. Significance

• Neutrino Physics: These precise flux measurements are critical for reducing background uncertainties in the search for neutrino oscillations and interactions at the LHC.
• Detector Operation: The data directly informs the replacement schedule for the emulsion target, ensuring optimal detector performance and data quality.
• Machine-LHC Interaction: The results highlight the sensitivity of forward particle fluxes to LHC magnet configurations (triplet polarity, crossing angles), providing valuable feedback for future LHC operations and machine protection strategies.
• Validation of Simulations: The agreement between data and FLUKA/Geant4 simulations validates the models used for forward particle production and transport through the LHC tunnel and rock shielding.