Selection and processing of calibration samples to measure the particle identification performance of the LHCb experiment in Run 2

This paper outlines the novel strategy developed by the LHCb experiment during Run 2 to select and process calibration samples using a dedicated online-offline computing model, enabling precise measurement of particle identification performance and data-quality monitoring across various decay channels.

The Gist

Imagine the LHCb experiment at CERN as a massive, high-speed supermarket that is constantly scanning millions of shoppers (particles) every second. The goal isn't to buy groceries, but to find very specific, rare shoppers (like "beauty" or "charm" particles) who might be carrying a secret message about new physics.

However, the supermarket is chaotic. There are millions of people, and many of them look very similar. A "pion" might look like a "kaon," or an "electron" might look like a "muon." If the security guards (the detectors) can't tell them apart, they might let the wrong people through or kick out the VIPs they are actually looking for.

This paper is about how the LHCb team built a super-smart ID system and a quality control lab to make sure their security guards are perfect at their jobs.

Here is the breakdown of their strategy using everyday analogies:

1. The Problem: The "Imposter" Crowd

The LHCb detector sees five main types of charged particles: electrons, muons, pions, kaons, and protons.

• The Challenge: Imagine trying to spot a specific celebrity in a crowd of 100,000 people where everyone is wearing a similar hat. If your security camera (the detector) makes a mistake, you might think a random fan is the celebrity, or miss the celebrity entirely.
• The Solution: They need to know exactly how good their cameras are at telling these people apart. But you can't just ask the cameras, "Are you sure?" because they might be biased. You need a Control Group.

2. The Control Group: The "Calibration Samples"

To test the cameras, the team needs a group of people whose identities are 100% guaranteed without looking at the cameras.

• How they do it: They look for specific "family reunions" (particle decays) where the rules of physics make the identity obvious.
  • Example: If a particle decays into two muons, and we know the math perfectly, we know those two particles must be muons. We don't need the camera to tell us; the math tells us.
• The Result: They have a "Gold Standard" dataset. They can run their ID software on these known muons and see: "Okay, the software correctly identified 99% of them, but it got confused 1% of the time." This tells them exactly how accurate their system is.

3. The New "Turbo" System: Speed vs. Detail

In the past (Run 1), the supermarket had a two-step process:

1. Hardware Trigger: A quick glance to see if something interesting happened.
2. Software Trigger: A deep dive to reconstruct the whole event.

In Run 2 (the focus of this paper), they upgraded to a hybrid system:

• The "Turbo" Stream: For most events, they do the deep analysis instantly while the data is still flowing. They save the "receipt" (the result) but throw away the "raw video footage" to save space.
• The "Full" Stream: For special cases, they keep the raw video footage.
• The Innovation: They created a special "Calibration Stream" (TurboCalib). This is like a double-check station. They take the same event, process it once with the fast "online" method and once with the slow, detailed "offline" method. By comparing the two, they can see if the fast method is missing anything or if the slow method is changing its mind. This ensures that even if they only save the "receipt" later, they know the receipt is accurate.

4. The "Magic Mirror" (Correcting Simulations)

Scientists use computer simulations to predict what should happen. But computers aren't perfect; they are like a cartoon version of reality.

• The Issue: The simulation might think a kaon looks like a pion 5% of the time, but in real life, it's 7%. If they use the simulation to plan their experiment, they will be wrong.
• The Fix: They use their "Gold Standard" calibration data to create a Magic Mirror.
  • They take the cartoon simulation and "paint over" it with the real data.
  • They use a technique called sPlot (think of it as a statistical magic wand) to separate the signal from the background noise.
  • They then "resample" or "transform" the simulation data so that it behaves exactly like the real calibration samples. Now, their computer models are perfectly tuned to reality.

5. Why This Matters for the Future

The paper explains that this system is crucial for Run 3 of the LHC.

• In the future, the data flow will be so fast that they won't be able to save the "raw video footage" for anything except the most interesting events. They will only save the "receipts."
• Because they can't go back and re-analyze the raw footage later, the online analysis must be perfect.
• The calibration samples described in this paper are the training wheels that ensure the online system is so good that they can eventually throw the training wheels away.

Summary

Think of this paper as the User Manual for a High-Tech Security System.

1. We built a test lab using known particles (Calibration Samples) to measure how often our ID system makes mistakes.
2. We built a double-processing machine that checks our work in real-time to ensure speed doesn't sacrifice accuracy.
3. We created a "Magic Mirror" to fix our computer simulations so they match reality perfectly.
4. We are ready for the future, ensuring that even when we have to make split-second decisions without saving all the raw data, we can still trust our results.

This allows physicists to search for the tiniest, rarest particles with the confidence that their "security guards" are telling the truth.

Technical Summary

1. Problem Statement

The LHCb experiment at CERN focuses on heavy flavor physics, requiring precise Particle Identification (PID) to distinguish between electrons, muons, pions, kaons, and protons. The performance of PID detectors (RICH, Calorimeters, Muon systems) and algorithms is critical for:

• Measuring CP violation and rare decays (e.g., $B \to \mu^+\mu^-$).
• Reducing background in trigger selections.
• Correcting systematic biases in physics analyses.

Key Challenges in Run 2 (2015–2018):

• Trigger Evolution: The LHCb trigger shifted to a model relying heavily on online event reconstruction. Most data is processed in real-time, with offline reconstruction reserved for specific cases.
• Bias Avoidance: Traditional offline selection strategies often introduce biases in PID variables. To measure PID efficiency accurately, "calibration samples" are needed that are unbiased by PID requirements.
• Scalability & Precision: Run 2 required significantly larger statistics to measure PID efficiencies across a wide kinematic range and for hundreds of decay channels.
• Data Formats: The introduction of the Turbo stream (storing only reconstructed candidates, not raw data) meant that standard offline reprocessing was impossible for many datasets. A method was needed to validate online PID performance against offline standards without losing raw data for calibration.
• Simulation Mismatch: Simulations often fail to perfectly model detector responses. Reliable data-driven corrections are essential to correct Monte Carlo (MC) simulations.

2. Methodology

The paper outlines a comprehensive framework for selecting, processing, and utilizing calibration samples.

A. Calibration Sample Selection Strategy

• Tag-and-Probe Model: Pure samples of specific particles are selected using decay modes where one particle ("tag") is well-identified, and the other ("probe") is selected without any PID requirements. This ensures the probe sample is unbiased regarding PID variables.
• Decay Modes: Specific channels are used for each particle species to cover various momentum ($p$) and pseudorapidity ($\eta$) ranges:
  • Muons: $J/\psi \to \mu^+\mu^-$ and $B^+ \to J/\psi K^+$ ($J/\psi \to \mu^+\mu^-$).
  • Pions/Kaons: $K_S^0 \to \pi^+\pi^-$, $D^{*+} \to D^0 \pi^+$ ($D^0 \to K^- \pi^+$), and $D_s^+ \to \phi \pi^+$ ($\phi \to K^+ K^-$).
  • Protons: $\Lambda^0 \to p \pi^-$ and $\Lambda_c^+ \to p K^- \pi^+$.
  • Electrons: $B^+ \to J/\psi K^+$ ($J/\psi \to e^+ e^-$).
• Background Subtraction: The sPlot technique is used to statistically subtract residual background. Fits are performed on invariant mass distributions (and mass differences for $D^*$) to assign sWeights to signal candidates.

B. PID Performance Measurement

• Efficiency Calculation: PID efficiency is calculated by weighting the calibration sample to match the kinematic distributions ($p_T, \eta$) and event multiplicity of the target "reference sample" (either data or simulation).
• Correction Techniques: To correct MC simulations, two advanced techniques are employed:
  1. Resampling: Replacing MC PID variables with values sampled from calibration PDFs (Kernel Density Estimation).
  2. Variable Transformation: Transforming MC PID variables so their distribution matches the data while preserving correlations with kinematics. This uses the formula:
     $$PID_{corr} = P^{-1}_{exp}(P_{MC}(PID_{MC} | p_T, \eta, N_{evt}) | p_T, \eta, N_{evt})$$
     where $P$ represents the cumulative distribution function.

C. The TurboCalib Computing Model

To address the challenge of online-only data and the need for offline validation, a new data processing scheme was developed:

• TurboCalib Format: A dedicated data format that stores both the online trigger candidates (Turbo stream) and the raw detector data for specific calibration events.
• Double Reconstruction:
  1. Online: Full reconstruction performed in real-time by the trigger.
  2. Offline: Independent full reconstruction performed later using the stored raw data.
• Matching: Tracks from online and offline reconstructions are matched (using shared clusters or the TisTos algorithm). This allows analysts to compare online PID variables directly with offline "ground truth" variables, enabling the measurement of combined selection efficiencies.
• Distributed sPlot: To handle the massive size of calibration samples, the sPlot background subtraction is implemented in a distributed manner across the LHCb grid, avoiding single-node memory bottlenecks.

D. Multivariate Classifiers (ANNPID)

The paper details the use of ANNPID (Artificial Neural Network PID), a Multi-Layer Perceptron that combines likelihoods from RICH, Calorimeters, and Muon systems with tracking variables (momentum, fit quality, hit multiplicity) to provide a global PID score.

3. Key Contributions

1. Innovative Data Processing Scheme: The introduction of the TurboCalib format and the online-offline double reconstruction strategy. This allows for the validation of online trigger performance against offline standards even when raw data is not typically stored for physics analyses.
2. Unbiased Calibration Strategy: A rigorous "tag-and-probe" selection strategy that avoids PID biases at the trigger level, ensuring the calibration samples are representative of the true detector performance.
3. Advanced Correction Algorithms: Implementation of PID variable transformation and resampling techniques using Kernel Density Estimation (Meerkat library) to correct simulation data, preserving correlations between PID variables and kinematics.
4. Scalable Computing Infrastructure: A distributed implementation of the sPlot technique and the PIDCalib Python package, which standardizes the transfer of PID information from calibration samples to physics analyses.
5. Comprehensive Coverage: The selection of decay modes covers a wide kinematic range (low to high momentum) for all five charged particle species, including specific strategies for high-momentum protons and low-momentum pions.

4. Results

• Performance Validation: The calibration samples successfully provided high-statistics measurements of PID efficiency and misidentification probabilities across the full kinematic acceptance of LHCb.
• Consistency: The comparison between online and offline reconstructions in the TurboCalib samples confirmed that online calibration parameters are of sufficient quality for offline use, ensuring consistency between trigger and analysis.
• Background Subtraction: The distributed sPlot implementation successfully handled large datasets, allowing for precise background subtraction without statistical loss.
• Data Quality Monitoring: The samples are actively used to monitor detector alignment, temperature effects, and aging, triggering alarms if deviations from standard conditions are detected.

5. Significance

• Physics Impact: The methodology ensures that LHCb physics results (CP violation measurements, rare decay searches) are not limited by systematic uncertainties in particle identification. It enables the sub-percent precision required for ambitious CP asymmetry measurements.
• Run 3 Preparation: The computing model (TurboCalib, real-time selection, online-only storage) developed for Run 2 is the blueprint for Run 3, where the LHCb experiment will operate with a fully software-based trigger and store almost exclusively decay candidates (Turbo stream) without raw data.
• General Applicability: While focused on PID, the computing model and selection strategies are being applied to other calibration needs, such as tracking calibration and neutral particle identification, demonstrating the robustness of the framework.

In summary, this paper describes a critical evolution in the LHCb experiment's data handling capabilities, moving from a purely offline-centric model to a sophisticated real-time processing framework that ensures high-precision particle identification in the era of high-luminosity LHC data.