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Muon Track Reconstruction Procedures at the Baikal-GVD Neutrino Telescope

This paper presents the track reconstruction methods developed by the Baikal-GVD collaboration for analyzing muon events, including direction and energy reconstruction techniques and candidate selection criteria, along with preliminary results from the 2019–2021 data-taking seasons.

Original authors: Grigory Safronov

Published 2026-05-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Grigory Safronov

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

Imagine the Baikal-GVD as a massive, underwater "net" cast into the deepest, darkest part of Lake Baikal in Russia. Its job isn't to catch fish, but to catch ghosts—specifically, cosmic particles called neutrinos that zip through the Earth without stopping.

Here is how the paper explains the process of catching these ghosts and figuring out where they came from, using simple analogies:

1. The Setup: A Giant Underwater Forest

The telescope isn't a single machine; it's a forest of 14 separate "trees" (called clusters) standing on the lake floor, about 1.3 kilometers deep. Each tree is a long string holding 36 glass "eyes" (optical modules). These eyes are incredibly sensitive cameras that can see a single spark of light.

The goal is to spot a specific type of ghost: a muon. When a high-energy neutrino smashes into something near the detector, it creates a muon. This muon zooms through the water, leaving a trail of blue light (like a jet plane leaving a white contrail in the sky). The detector's job is to see that trail and figure out exactly where the muon (and the original neutrino) came from.

2. The Problem: The Lake is Noisy

The biggest challenge isn't the ghosts; it's the background noise. Lake Baikal is alive. Tiny bits of algae and decaying organic matter float down, glowing faintly like fireflies. To the detector's sensitive eyes, this looks like static on an old TV.

The Analogy: Imagine trying to hear a whisper in a crowded, noisy stadium. The "whisper" is the muon's light trail, and the "stadium noise" is the glowing algae. The paper explains that the detector has to filter out thousands of these "fireflies" to find the one clear "whisper."

3. The Solution: Finding the Trail

The scientists developed a smart algorithm (a set of computer rules) to separate the signal from the noise.

Step 1: The Time Check. Light travels at a specific speed. If the detector sees flashes of light in different "eyes" that arrive at times that make sense for a straight line moving at light speed, it's likely a real muon. If the flashes are random (like the algae), they get ignored.
Step 2: Drawing the Line. Once the computer finds a group of flashes that fit together, it draws a line through them. This line tells them the direction the muon was traveling.
The Result: They can pinpoint the direction of the muon with incredible accuracy—within 0.2 degrees. That's like looking at a coin from a football field away and knowing exactly which side is up.

4. Guessing the Energy: How Fast Was It?

Once they find the trail, they want to know how much energy the muon had.

The Analogy: Think of a car driving through a field of tall grass. A slow car barely disturbs the grass. A fast, heavy truck knocks down a lot of grass and leaves a big mess.
The Method: The muon knocks electrons loose in the water, creating light. The scientists count how much light is produced along the track. More light means a more energetic muon. They use a "median" (the middle value) of these light measurements to estimate the energy. They admit this isn't perfect (it has a margin of error of about 2.5 times the actual value), but it's good enough for their purposes.

5. The Filter: Sorting the Good from the Bad

Even after finding trails, most of them are still "fake" neutrinos. They are actually muons created by cosmic rays hitting the atmosphere above the lake (muon bundles). These are the "background noise" the scientists want to remove.

The Tool: They used a "Machine Learning" tool called a Boosted Decision Tree (BDT).
The Analogy: Imagine a bouncer at a club. The bouncer has a checklist (variables like the shape of the trail, how many lights were hit, etc.). If the event looks like a "party crasher" (a background muon), the bouncer says "No." If it looks like a VIP (a real neutrino), they get in.
They trained two different bouncers: one for low-energy events and one for high-energy events. By using these bouncers, they managed to filter out 97% of the fake muons while keeping 70% of the real neutrinos.

6. The Results: What They Found

The team tested this entire process on data collected between 2019 and 2021.

They found 1,189 potential neutrino candidates.
They compared their findings to computer simulations. The data matched the simulations pretty well, with one small surprise: they found about 30% more events than the computer predicted. They are currently investigating why the real world is slightly "noisier" or more active than their models expected.

Summary

In short, this paper describes how the Baikal-GVD team built a sophisticated "noise-canceling" system for their underwater telescope. They taught the computer to ignore the glowing algae, trace the path of cosmic muons with extreme precision, and use smart algorithms to filter out the fake signals, leaving them with a clean list of potential neutrino discoveries.

Technical Summary: Muon Track Reconstruction Procedures at the Baikal-GVD Neutrino Telescope

Problem Statement
The Baikal-GVD (Gigaton Volume Detector) is the largest neutrino telescope in the Northern Hemisphere, designed to study the TeV–PeV cosmic neutrino flux. While the detector's cascade channel offers precise energy reconstruction, the track channel is superior for identifying astrophysical point sources due to its superior angular resolution. The primary challenge in analyzing track-like events in Lake Baikal is the high rate of ambient optical background noise caused by the luminescence of sinking organic matter and algae. This background produces a non-uniform noise rate (ranging from tens to hundreds of kHz) that can generate hundreds of spurious hits within the detector's 5 µs readout window, complicating the identification of genuine Cherenkov light from muons produced by neutrino interactions.

Methodology
The paper details a reconstruction pipeline specifically developed for single-cluster data processing (where multiple clusters are not yet fully integrated for track analysis). The methodology proceeds through three main stages:

Muon Hit Finding and Noise Suppression:
- Two-Step Criteria: The algorithm first identifies Cherenkov pulses by suppressing background using time-correlation criteria. A simple time-difference condition ( $\Delta t < \Delta R n/c + \delta$ ) filters hits, followed by a "directional causality" criterion that connects hits based on strict requirements relative to a track direction.
- Graph Theory: The collection of hits forming the largest fully-connected clique is identified using the Bron–Kerbosch algorithm.
- Direction Scanning: A scan is performed over a $60^\circ \times 60^\circ$ grid around a preliminary track direction to find the direction yielding the largest fully-connected hit cliques.
- Hit Purity: This procedure achieves a hit collection purity of approximately 95% while maintaining a 95% probability of capturing Cherenkov hits for atmospheric neutrino spectra.
Track Reconstruction and Energy Estimation:
- Direction and Position: The track direction and position are determined by minimizing a two-term loss function. The first term is a $\chi^2$ based on the time difference between measured hits and the expected Cherenkov arrival time (assuming direct emission). The second term penalizes offset tracks based on the distance from the track and the deposited charge, weighted to remain effective across a wide energy range (TeV to PeV).
- Energy Reconstruction: Muon energy is estimated using a "median energy estimator." The energy loss rate is calculated for optical modules within 40 m of the track, accounting for light absorption and geometric factors. The median of these elementary energy losses serves as a proxy for the true muon energy ( $E_{true}$ ), which is mapped via polynomial fits. Corrections are applied to account for biases related to the number of hits and zenith angle.
Neutrino Candidate Selection:
- Background Rejection: The reconstructed event sample is dominated by misreconstructed atmospheric muon bundles. To isolate neutrino candidates (specifically upgoing events with zenith angles $>100^\circ$ ), the authors employ Boosted Decision Trees (BDTs).
- BDT Training: Two separate BDTs are trained: one for low-energy neutrinos ( $E_\mu < 10$ TeV) and one for high-energy neutrinos ( $E_\mu > 10$ TeV). These utilize approximately 20 quasi-independent variables, including fit quality and event topology.
- Signal vs. Background: The BDTs are trained on atmospheric neutrino and astrophysical neutrino spectra (based on Bartol and IceCube models) against a background of atmospheric muon bundles (simulated via CORSIKA).

Key Results
The analysis pipeline was applied to data collected during the 2019–2021 seasons, corresponding to a total livetime of 14.4 years in single-cluster mode.

Angular Resolution: The reconstruction procedure achieves a median angular resolution of $0.2^\circ$ for sufficiently long tracks (length $>500$ m).
Energy Resolution: For muons with energies above $\sim10$ TeV, an energy resolution factor of 2.5 is attained.
Selection Efficiency: Applying a cut of BDT response $>0.25$ (for either low or high-energy BDT) results in a sample where the contribution from misreconstructed muon bundles is estimated at $\sim3\%$ , while maintaining a neutrino event selection efficiency of approximately 70%.
Data-MC Comparison: A sample of 1,189 neutrino candidates was selected. The observed event rate in the data was found to be 30% higher than expected from the simulation of atmospheric neutrinos using the Bartol flux. Consequently, a normalization factor of 1.32 was applied to the Monte Carlo (MC) for further comparison. The distributions of track hits and reconstructed muon energy show acceptable agreement between data and MC expectations after this scaling.

Significance and Claims
The paper claims to present the status of the track-like event analysis pipeline for the Baikal-GVD telescope. Its primary significance lies in demonstrating the capability to reconstruct muon directions with high precision ( $\sim0.2^\circ$ ) and estimate muon energy with a factor of 2.5 resolution in the challenging environment of Lake Baikal. The work validates the use of specific noise suppression techniques and machine learning (BDTs) to effectively separate neutrino signals from the dominant atmospheric muon background. The authors note that the analysis was performed without further cut optimization, serving as a demonstration of the pipeline's performance on the 2019–2021 dataset. The discrepancy in the event rate (data exceeding MC by 30%) is noted as an area for further investigation, but the overall agreement in distributions supports the validity of the reconstruction and selection methods.