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Tracking performance study of the LHCb UP Detector

This paper presents the design of the LHCb UP MAPS-based pixel tracker and demonstrates that its dedicated standalone reconstruction algorithms achieve high efficiency (~98%) and low ghost rates (<4%), offering a robust solution for future high-luminosity tracking challenges.

Original authors: Yisheng Fu, Jianchun Wang, Xuhao Yuan

Published 2026-06-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yisheng Fu, Jianchun Wang, Xuhao Yuan

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 Large Hadron Collider (LHC) as a massive, high-speed particle racetrack. The LHCb detector is like a specialized camera positioned at one end of the track, designed to take incredibly sharp photos of heavy particles as they zoom by.

As the racetrack gets upgraded to handle even more traffic (higher "luminosity"), the camera needs a better lens to keep up. This paper introduces a new piece of hardware called the UP Detector (Upstream Pixel Tracker) and explains how to teach computers to "see" the paths of these particles through it.

Here is the breakdown of the paper's work in simple terms:

1. The New "Eye" (The UP Detector)

Currently, the LHCb detector uses a system called the UT, which is like a set of four sheets of graph paper with long, thin lines (strips) on them. It's good, but it's getting crowded.

For the next big upgrade (Upgrade II), they are replacing this with the UP Detector.

The Change: Instead of long strips, imagine replacing those sheets with four layers of high-resolution digital camera sensors (pixels).
The Layout: It's a box with four layers. Inside, there are 40 long, thin "staves" (like wooden slats) holding 320 tiny sensor modules.
The Goal: These sensors sit before the magnet bends the particles. By seeing the particles early, the system can figure out their paths much better, especially for slow-moving particles or those that break apart quickly.

2. The Challenge: Finding a Needle in a Haystack

When the machine runs at full speed, the detector gets flooded with data. It's like trying to find a few specific people walking through a stadium during a massive concert where everyone is moving at once.

The Problem: With so many particles hitting the sensors, the computer has to figure out which "dots" (hits) belong to the same person (particle) and which are just random noise or "ghosts" (fake tracks).
The Old Way: The current system (UT) is too simple to do this on its own; it needs help from other parts of the detector.
The New Way: Because the UP detector uses 2D pixels (like a photo) instead of 1D strips, it has enough detail to find the paths all by itself (standalone reconstruction).

3. The "Software" Solution: The Seed-Forward Algorithm

The authors first tested a software method to find these paths. Think of this like a detective solving a mystery:

The Seed: The detective picks a starting clue (a "seed" hit) on the first layer of sensors.
The Search: They look at the next layer for a matching clue that fits the angle.
The Chain: They keep connecting the dots layer by layer.
The Fix: Sometimes, two different paths might try to claim the same dot. The authors added a rule: "If a dot fits two paths, give it to the path that already has the most matches." This prevents fake paths from forming.

The Result: This software method is very good. It successfully finds about 98% of the real paths and creates very few fake ones (less than 4% "ghosts"). This gives the main computer system high-quality data to work with.

4. The "Hardware" Solution: The FPGA (RETINA)

The paper also looks at a faster, more specialized way to do this: using FPGAs (Field-Programmable Gate Arrays).

What is an FPGA? Imagine a standard computer processor as a single chef who can only chop one vegetable at a time. An FPGA is like a kitchen with 1,000 chefs, all chopping different vegetables simultaneously. It's designed for speed and parallel processing.
The Method (RETINA): Instead of connecting dots one by one, this method uses a mathematical trick called the Hough Transform.
- Analogy: Imagine you have a bunch of scattered dots on a piece of paper. Instead of drawing lines between them, you ask, "If I drew a line through any two dots, what would the angle and position be?" You create a giant map of all possible lines. Where many dots agree on the same line, a "peak" appears on the map. The computer just looks for the highest peaks.
The Result: This hardware method is almost as good as the software method. It finds the paths just as well, especially for slower particles. It is slightly less perfect for very fast particles right now, but the authors say this is just because the software version has been tweaked more often. The hardware version is promising because it can do this incredibly fast, which is necessary for the real-time data of the future.

Summary

The paper shows that the new UP Detector (a 4-layer pixel camera) works great.

Software can find the particle paths with high accuracy (98% efficiency) by connecting the dots smartly.
Hardware (FPGA) can do the same thing using a "map of possibilities" method, which is fast enough to handle the massive data flood of the future.

This proves that the LHCb detector will be able to keep taking clear photos of the universe's smallest building blocks, even when the traffic on the racetrack gets ten times heavier.

Technical Summary: Tracking Performance Study of the LHCb UP Detector

Problem Statement
The LHCb experiment is preparing for its Upgrade II phase in the 2030s, which targets an instantaneous luminosity of up to $1.0 \times 10^{34} \text{ cm}^{-2}\text{s}^{-1}$ . This increase in luminosity will result in significantly higher detector occupancy and data rates, posing severe challenges for track reconstruction, particularly regarding pattern recognition in dense environments. A critical component of this upgrade is the replacement of the current silicon-strip Upstream Tracker (UT) with a new four-plane pixel detector, the Upstream Pixel Tracker (UP). While the UT, based on one-dimensional strip sensors, renders standalone track reconstruction impractical, the UP's use of two-dimensional Monolithic Active Pixel Sensors (MAPS) offers the potential for efficient standalone reconstruction. The primary challenge addressed in this work is developing algorithms capable of reconstructing tracks within the UP detector alone with high efficiency and low ghost rates, to serve as inputs for global reconstruction and to address real-time processing requirements under high-luminosity conditions.

Methodology
The paper outlines the design of the UP detector and evaluates two distinct approaches for standalone track reconstruction:

Detector Design: The UP detector consists of four detection planes located upstream of the magnet. Each plane covers an active area of approximately $1400 \times 1200 \text{ mm}^2$ with a central beam pipe opening. The detector is constructed from lightweight support staves holding modules composed of 14 MAPS chips arranged in a $7 \times 2$ configuration on flexible circuits. The pixel size is $50 \times 150 \text{ \mu m}^2$ , with an estimated material budget of $1.2\% X_0$ per plane in the range $2 < \eta < 4.5$ .
Software Algorithm (Seed-Forward with Optimization):
- The authors adapted a "seed-forward" strategy, similar to that used in the VELO detector.
- Process: Seed hits are selected from a reference layer. Search windows are opened in subsequent layers to identify compatible hit pairs, which are then extrapolated to remaining layers.
- Optimization: To address the issue of "ghost tracks" caused by overlapping modules and extra hits, a "hit-sharing optimization" was implemented. When a hit is compatible with multiple track candidates, it is preferentially assigned to the candidate with the highest number of matched hits.
- Iterative Refinement: The search window size is optimized iteratively to balance reconstruction efficiency against ghost rate suppression.
Hardware Algorithm (FPGA-based RETINA):
- To address the projected online data throughput of 200 Tbit/s, the authors investigated an FPGA-based implementation using the RETINA algorithm, originally developed for the VELO.
- Process: The algorithm utilizes a Hough transformation to map the track-finding problem into a four-dimensional parameter space $(r_0, \phi_0, r_1, \phi_1)$ defined by two reference planes at the detector entrance and exit.
- Implementation: The parameter space is discretized into bins (currently $150^4$ cells, reduced to $\sim 6\text{M}$ active cells via phase-space constraints). Detector hits increment corresponding cells, and track candidates are identified as cells containing at least three hits. A $\chi^2$ -based linear regression is then applied to refine the candidates.

Key Contributions and Results
The study presents performance metrics for both reconstruction methods based on Monte Carlo simulations:

Software Algorithm Performance:
- The initial seed-forward algorithm achieved an overall efficiency of 82.1% with a ghost rate of 11.5%.
- After applying the hit-sharing optimization, the overall efficiency improved to 91.4% (rising to 97.7% for tracks with momentum $p > 5 \text{ GeV}/c$ ), while the ghost rate was reduced to 3.9%.
- The authors note that tracks with $p > 1.5 \text{ GeV}/c$ generally follow straight lines, facilitating the seed-forward approach.
FPGA/RETINA Performance:
- The FPGA-based RETINA algorithm demonstrated tracking performance comparable to the conventional seed-forward approach in terms of overall efficiency.
- It showed a noticeable improvement in reconstruction efficiency in the low-momentum region, attributed to the Hough-transform strategy's effectiveness in pattern recognition within the track-parameter space.
- However, the current FPGA implementation exhibited a slightly higher ghost rate and lower efficiency in the high-momentum region compared to the optimized software algorithm. The authors attribute this discrepancy to the fact that the software algorithm has undergone extensive optimization (including hit-sharing and iterative reconstruction) that has not yet been fully incorporated into the RETINA implementation.

Significance and Claims
The paper claims that the UP detector, combined with these reconstruction algorithms, offers a viable solution for the challenges of the LHCb Upgrade II. Specifically:

High-Purity Inputs: The optimized standalone tracks provide high-quality inputs for global LHCb reconstruction, improving the association between upstream and downstream track segments and enhancing momentum resolution, particularly for low- $p_T$ particles and displaced tracks from long-lived particles.
Real-Time Viability: The FPGA-based RETINA approach demonstrates the potential for low-latency, highly parallelized tracking, which is essential for real-time event reconstruction and triggering in high-occupancy environments.
Future Outlook: The results suggest that UP standalone tracking is a robust component for future real-time tracking systems, providing a foundation for handling even higher luminosity conditions where hardware-accelerated tracking will be critical.

The work does not claim that the FPGA solution is currently superior to the software solution in all metrics, but rather that it achieves comparable performance with the added benefit of hardware acceleration, with further optimization expected to close the remaining performance gaps.

1. The New "Eye" (The UP Detector)

2. The Challenge: Finding a Needle in a Haystack

3. The "Software" Solution: The Seed-Forward Algorithm

4. The "Hardware" Solution: The FPGA (RETINA)

Summary

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