Wire-by-Wire Tracking Efficiency Plots: A New Diagnostic for the Belle~II Central Drift Chamber

This paper introduces a wire-by-wire tracking efficiency diagnostic for the Belle~II Central Drift Chamber, which extrapolates reference tracks to individual wires to identify localized tracking failures that remain invisible to conventional channel-level monitoring.

The Gist

Imagine the Belle II Central Drift Chamber (CDC) as a massive, high-tech stadium filled with thousands of individual security cameras (wires) designed to track the path of every particle speeding through it.

For a long time, the engineers managing this stadium only checked the main power switches for each section of cameras. They asked: "Is the power on? Is the camera getting electricity?" If the answer was yes, they assumed the whole section was working perfectly.

The Problem: The "Silent" Failure
The paper explains that this "power switch" check is like checking if a security camera is plugged in, but not checking if the lens is cracked or if the image is blurry.

• The Flaw: Sometimes, a specific camera (or a whole row of them) might be broken or "dead," but the rest of the stadium is so good at its job that it can guess the path of the particle anyway. The system thinks, "Oh, we missed a few pictures, but we still have a good enough guess, so everything is fine."
• The Consequence: This creates a false sense of security. The system looks healthy on the big charts, but it's actually missing details that could ruin the scientific "movie" being filmed.

The New Solution: "Wire-by-Wire" Tracking
The author, Suryanarayan Mondal, introduces a new diagnostic tool borrowed from a neutrino observatory in India. Instead of just checking the power, this new method acts like a super-precise GPS.

Here is how it works, using a simple analogy:

1. The Prediction: Imagine a particle is a runner on a track. The computer calculates exactly where the runner should be at every single moment, drawing a perfect line (a "helix") through the stadium.
2. The Check: The system then looks at the specific camera (wire) that the runner should have passed right in front of.
3. The Verdict:
   • Did that specific camera take a picture? Yes = The wire is healthy.
   • Did that specific camera stay silent? No = The wire is broken, even if the power switch says it's on.

What This Reveals
By checking every single wire against the predicted path, the new method found "blind spots" that the old method missed.

• The "Dead Zones": The paper shows that when a whole board of wires fails (like a section of the stadium losing power), the old charts looked okay because the system compensated. The new charts, however, show a clear "hole" in the data, revealing exactly where the failure is.
• The Domino Effect: The paper notes that when these wires fail, the computer tries to fix the missing data using other detectors (like the Silicon Vertex Detector). While this saves the physics data, it creates a "patched-up" track that might get rejected later by other parts of the system (like the Calorimeter), causing good data to be thrown away unnecessarily.

Why It Matters for the Team
This new tool is now part of the daily monitoring system (DQM). It helps the team in three practical ways:

1. Spotting Immediate Breaks: If a whole board dies, they see a big red spot on the map immediately, rather than waiting for a slow decline.
2. Smarter Data Selection: Instead of throwing away an entire day's worth of data because of a small broken section, they can just ignore the specific broken angles (like ignoring a specific corner of the stadium) and keep the rest.
3. Long-Term Health: By watching these maps over years, they can see which wires are slowly getting "tired" or degrading, allowing them to fix problems before they become total failures.

In Summary
This paper presents a smarter way to check the health of the Belle II detector. It moves from asking "Is the power on?" to "Did the camera actually see the runner?" This simple shift allows scientists to find hidden broken parts, fix them faster, and ensure they aren't throwing away good data just because a few wires are silent.

Technical Summary

Technical Summary: Wire-by-Wire Tracking Efficiency Plots for the Belle II Central Drift Chamber

Problem Statement
Large detector systems are frequently monitored at the channel level (e.g., drift time, collected charge, hit maps). While these metrics validate hardware functionality, they do not directly assess tracking performance. This limitation creates two specific diagnostic blind spots:

1. Localised Failures: A localized hardware failure can be absorbed into the global acceptance, leaving no clear signature in standard monitoring plots.
2. Silent Compensation: In multi-detector systems, one sub-detector (such as the Silicon Vertex Detector, SVD) can silently compensate for inefficiencies in another (the Central Drift Chamber, CDC), creating false confidence in overall performance while the root cause remains undetected.

The Belle II experiment's CDC, a primary charged-particle tracking detector, is subject to these issues. Standard CDC Data Quality Monitoring (DQM) confirms hardware limits but fails to determine if the detector is successfully finding the tracks it should.

Methodology
The paper presents a wire-by-wire tracking efficiency diagnostic adapted from the extrapolation-based efficiency measurement standard used in Resistive Plate Chamber (RPC) stacks for the India-based Neutrino Observatory (INO).

• Core Principle: A reference track (helix) is reconstructed using standard Belle II algorithms. This helix is extrapolated to each wire layer within the CDC.
• Efficiency Calculation: For each layer, the sense wire nearest to the extrapolated crossing point is identified as the "expected hit." If the reconstructed track has an associated hit on that specific wire, the crossing is counted as "observed." The per-wire efficiency ($\varepsilon$) is calculated as the ratio of observed hits to expected crossings ($N_{observed} / N_{expected}$).
• Implementation Differences: Unlike the strict RPC procedure where the layer under test is excluded from the track fit, this method includes all layers in the fit. Given the CDC's 56 wire layers, the gain in fit independence from excluding a single layer is marginal, and the added complexity is not justified.
• Visualization: Results are accumulated in a two-dimensional histogram of wire index versus layer index (or azimuthal angle $\phi$), providing a geometric view of the full CDC acceptance.
• Integration: The method is implemented within the Belle II DQM framework, running both online and offline, and requires no external reference detector or baseline run.

Key Contributions

• Adaptation of RPC Diagnostics: Successfully transfers the extrapolation-based efficiency method from RPC stacks to the wire-based geometry of the Belle II CDC.
• Revealing Invisible Failures: The method exposes localized tracking failures that are invisible to conventional channel-level diagnostics (hit maps, drift time, collected charge) because the SVD often compensates for CDC gaps in standard reconstruction.
• Direct Feedback Mechanism: Provides a direct metric for run selection and operational decisions without relying on aggregate performance metrics.

Results
The method was validated using Monte Carlo simulations of $e^+e^- \to B^0\bar{B}^0$ events with controlled "dead-wire" conditions. The simulation included scattered genuine dead wires and two injected full-depth board failures (one in superlayer 2 and one in superlayer 4).

• Detection of Localised Drops: The efficiency map successfully identified efficiency drops at specific azimuthal locations corresponding to the disabled boards: a pronounced drop near $\phi \approx +135^\circ$ (inner superlayer 2) and a less severe drop near $\phi \approx +42^\circ$ (outer superlayer 4).
• Quantitative Metrics: In the simulation, 83.29% of wires showed efficiency above 0.72, 14.11% fell in an intermediate range, and 2.59% were effectively dead ($\varepsilon < 0.08$). The mean wire efficiency was 77.9%. The 2.59% dead-wire fraction matched the injected conditions (371 out of 14,336 wires).
• Downstream Impact Analysis: The study demonstrated that when a full axial superlayer is missing, CDC tracking produces incomplete tracks. The MVA-based track quality estimator rejects these as poorly formed. Consequently, the SVD-to-CDC Combinatorial Kalman Filter (CKF) attaches hits only up to the gap, preventing the track from reaching outer layers and failing to extrapolate to the Electromagnetic Calorimeter (ECL). This breaks calorimeter association, which is critical for electron and photon analyses. The efficiency map alone was sufficient to localize this failure and reveal these downstream consequences.

Significance and Claims
The paper claims that this wire-by-wire efficiency method provides immediate, wire-resolved feedback for operations and physics analysis. Its significance lies in three operational areas:

1. Immediate Failure Detection: Disabled boards or high-voltage channels produce drops over contiguous wire regions visible within a single run.
2. Granular Run Selection: Analysts can exclude or down-weight specific $\phi$ regions with reduced efficiency rather than rejecting entire runs based on global flags.
3. Long-term Studies: Accumulated per-wire efficiency trends serve as a sensitive probe for wire ageing, gas gain evolution, and detector degradation.

The authors conclude that this approach generalizes to any tracking detector with individually instrumented channels, enabling reconstruction-level quality monitoring that goes beyond standard channel-level plots. Additionally, the identified failure modes motivate retraining the MVA-based CDC track quality estimator to better handle partially missing axial superlayers.