New method for clustering thresholds determination in Microstrip Silicon Detector

This paper proposes a new method to independently determine clustering thresholds for the Microstrip Silicon Detector in the FOOT experiment, providing reference values to evaluate single-ion detection efficiency and guide tracking-based clustering analysis.

The Gist

Imagine you are trying to listen to a single person whispering in a crowded, noisy room. That person is a tiny particle of energy (like a proton) zipping through a detector, and the room is the Microstrip Silicon Detector (MSD). The detector is made of thousands of tiny "ears" (called strips) waiting to hear the whisper.

The problem? The room is full of static noise (electronic glitches), and sometimes the whisper is so faint that it sounds just like the noise. If you turn your volume up too high, you'll hear the whisper clearly, but you'll also hear every cough and rustle in the room as if it were a shout (false alarms). If you turn the volume down too low, you'll miss the whisper entirely.

This paper is about a clever new way to find the perfect volume setting (the "threshold") so the detector can hear the particles without getting confused by the noise.

Here is the breakdown of their method using simple analogies:

1. The Setup: A Grid of Ears

The detector isn't just one big sensor; it's a grid of 1,920 tiny strips per sensor, arranged in layers. When a particle flies through, it doesn't just hit one "ear"; it usually brushes past a few neighbors. The detector needs to group these neighbors together into a single "cluster" to say, "Hey, a particle went through here!"

To do this, the computer needs two rules:

• The "Seed" Rule: How loud does a single strip have to be before we say, "Okay, something interesting is happening here"?
• The "Fired" Rule: How loud do the neighboring strips have to be before we include them in the group?

2. The Old Problem: Guessing in the Dark

Usually, scientists have to guess these volume settings based on how other detectors in the experiment are working. But in the FOOT experiment (which studies how particles break apart when they hit targets), the data comes in fast and furious. They can't wait for other detectors to tell them what to do. They need a way to set the volume just for this specific detector instantly.

3. The New Method: The "Silent Room" vs. The "Party"

The authors came up with a brilliant two-step comparison, like testing a microphone in two different scenarios:

• Scenario A: The Silent Room (Calibration Run)
  They turn off the particle beam. The room is empty. The detector listens to nothing but its own internal static noise. They record every little "pop" and "crackle" the electronics make on their own.

  • Analogy: This is like recording the background hiss of a radio when no one is talking.

• Scenario B: The Party (Physics Run)
  They turn the particle beam back on. Now, real particles are flying through, creating real signals on top of the background noise.

  • Analogy: This is like turning on the music and having people talk. Now you hear the music (particles) mixed with the same background hiss.

4. The Magic Trick: Subtracting the Noise

The team takes the data from the "Party" and subtracts the data from the "Silent Room."

• The Result: The background hiss cancels out. What's left is the pure sound of the particles.

They then look at the "loudest" signals in the data. They ask: "At what volume level does the signal stop being just random noise and start being a real particle?"

• Finding the "Seed" Threshold: They look for the point where the "real particle" signals start to appear clearly above the noise. They decided that to be safe, they only want to trust a signal if they are 85% sure it's a real particle and not a glitch. This gave them a specific volume number (e.g., 3.9).
• Finding the "Fired" Threshold: They also checked the neighbors. They wanted to make sure they weren't accidentally grouping in too much noise. They decided that if more than 5% of the "hits" were just noise, the volume was too high. This gave them a lower volume number for the neighbors (e.g., 1.8).

5. Why This Matters

The authors tested this with high-energy protons. These are the "whisperers" of the particle world—they leave the faintest trail of energy. If the detector can hear them clearly without getting confused by noise, it will definitely be able to hear the louder, heavier particles (like Oxygen or Carbon) that leave bigger trails.

The Bottom Line:
This paper introduces a "self-check" system. Instead of relying on a manager (other detectors) to tell the sensor how loud to listen, the sensor listens to itself in silence, then listens with the beam on, compares the two, and figures out the perfect volume setting all by itself. This ensures that when the FOOT experiment is racing against the clock to catch rare particles, the detector won't miss a thing or get fooled by static.

Technical Summary

1. Problem Statement

The FOOT (FragmentatiOn Of Target) experiment aims to measure double differential nuclear fragmentation cross-sections for applications in particle therapy and space radioprotection. A critical subsystem is the Microstrip Silicon Detector (MSD), which consists of six 150 $\mu$m-thick silicon sensors arranged in three X-Y planes for particle tracking and energy loss ($dE/dx$) measurement.

The core challenge addressed in this work is the determination of optimal clustering thresholds for the MSD.

• Context: The FOOT experiment operates with short data-taking periods and diverse beam configurations, limiting the time available for detector performance evaluation.
• The Issue: Clustering algorithms require two specific thresholds: a Seed Threshold (to identify the presence of a cluster) and a Fired Threshold (to determine the cluster size).
  • Thresholds too low: Introduce noise, creating false clusters and degrading track reconstruction.
  • Thresholds too high: Miss true particle signals, reducing detection efficiency and losing physical data.
• Limitation of Previous Methods: Traditional approaches often rely on the alignment of the entire experimental setup or the performance of other detectors, which is not always feasible or efficient during short beam campaigns. The authors sought a method to determine these thresholds independently of the global alignment and other subsystems.

2. Methodology

The authors propose a novel, data-driven algorithm to set thresholds by analyzing the statistical behavior of signals in "Calibration Runs" (no beam) versus "Physics Runs" (beam present).

A. Data Pre-processing and Calibration

Before threshold determination, raw signals undergo standard calibration:

1. Pedestal Subtraction: Removal of the average baseline signal.
2. Common Noise (CN) Subtraction: Removal of collective noise variations per ASIC chip (every 64 strips).
3. Noise Normalization: The processed signal ($Signal_i$) is normalized by the Single Strip Noise (SSN) to create a dimensionless quantity: $Signal_i / SSN_i$.

B. The "Potential Seed Strip" Algorithm

To identify true signal peaks without prior knowledge of particle tracks, the authors implemented a three-point algorithm:

1. Identification: Locate strips where the signal is a relative maximum compared to its two immediate neighbors.
2. Sorting: Sort these candidates by ADC value in descending order.
3. Filtering: Remove candidates that are too close in position (defined by a "strip distance" parameter) to avoid double-counting the same cluster.

C. Threshold Determination Strategy

The method compares cumulative histograms of these relative maxima from Calibration Runs ($CAL$) and Physics Runs ($PHY$).

1. Seed Threshold Determination:

   • A difference distribution is calculated: $DIFF = PHY - CAL$.
   • Purity ($Pur$) is defined as the ratio of true particle interactions to total events at a given threshold $N_{thr}$:
     $$Pur(x) = \frac{DIFF(x)}{PHY(x)}$$
   • The Seed Threshold is set at the point where Purity reaches a target value (chosen as 85%). This ensures that 85% of identified seeds are true particle interactions.

2. Fired Threshold Determination:

   • This threshold defines the cluster size (how many strips are included).
   • The authors analyze the fraction of strips in a Calibration Run (noise only) that exceed a threshold $N_{thr}$.
   • The Fired Threshold is set to limit "Fake Fired Strips" (noise strips falsely included in a cluster) to 5%.

3. Key Contributions

• Independence: The method determines thresholds without relying on the global alignment algorithm or data from other detectors (e.g., Time-of-Flight or Calorimeters).
• Robustness: It utilizes the "worst-case scenario" for detection: 230 MeV protons with no target. These particles produce the minimum energy deposition (minimum ionization) in the detector. If thresholds work for these, they are safe for heavier ions or higher energy depositions.
• Systematic Framework: It provides a reproducible, statistical framework (Purity vs. Fake Rate) applicable to various beam configurations and facilities.

4. Results

The method was applied to data collected at the CNAO facility in 2024 using 230 MeV protons. The analysis focused on MSD Sensor 4 as a case study, with results extrapolated to all six sensors.

• Optimal Thresholds for Sensor 4:
  • Seed Threshold: 3.9 (corresponding to 85% Purity).
  • Fired Threshold: 1.8 (corresponding to 5% Fake Fired Strips).
• Full Sensor Array: The study generated specific Seed and Fired thresholds for all six sensors, ranging from:
  • Seed Thresholds: 3.5 (Sensor 2) to 5.9 (Sensor 5).
  • Fired Thresholds: 1.6 (Sensors 1 & 2) to 1.9 (Sensor 0).
• Performance: The resulting thresholds provide a conservative "safe starting point" for clustering analysis. Because the thresholds were optimized for minimum ionization (protons), they are expected to yield high efficiency for heavier fragments ($Z > 1$) which deposit more energy.

5. Significance

• Operational Efficiency: This method allows for rapid threshold optimization during short beam times, a critical requirement for the FOOT experiment's multi-facility campaign (GSI, HIT, CNAO).
• Tracking Precision: By minimizing false clusters and maximizing true signal detection, the method directly improves the single-ion detection efficiency and the accuracy of momentum reconstruction via track fitting.
• Scientific Impact: Improved tracking and $Z$-identification accuracy are essential for achieving the FOOT experiment's goal of measuring nuclear fragmentation cross-sections with <5% accuracy, which is vital for optimizing particle therapy treatments and designing space radiation shielding.
• Generalizability: The approach is not limited to the FOOT experiment; it offers a generalizable solution for clustering in silicon microstrip detectors across various particle physics and medical physics applications.