Charged-lepton identification at Belle~II

Technical Summary: Charged-lepton identification at Belle II

Problem
The Belle II experiment, operating at the SuperKEKB $e^+e^-$ collider, aims to achieve high-precision measurements of CP violation, CKM matrix elements, and searches for physics beyond the Standard Model. A critical requirement for these physics goals is robust particle identification (PID), specifically the ability to distinguish charged leptons (electrons and muons) from charged hadrons (pions, kaons, protons). While previous experiments (BABAR and Belle) established strong PID capabilities, the higher instantaneous luminosity and harsher background conditions at SuperKEKB present significant challenges to both hardware and reconstruction software. The paper addresses the need to characterize and optimize the algorithms used to identify electrons and muons and separate them from hadrons using data collected during Run 1 (2019–2022, 428 fb$^{-1}$).

Methodology
The study utilizes control samples derived from specific physics processes to measure PID efficiency and mis-identification rates without applying biasing selection criteria to the "probe" tracks. The methodology relies on two primary techniques:

1. Tag-and-Probe: Used for samples lacking peaking structures (e.g., $e^+e^- \to e^+e^-(\gamma)$, $e^+e^- \to \mu^+\mu^-\gamma$, and two-photon fusion e^+e^- \to e^e^-\ell^+\ell^-). One track ("tag") is selected with strict PID criteria to define the sample, while the other ("probe") is used to measure performance unbiasedly.
2. Peak Fitting and sWeights: Used for samples with clear invariant mass peaks ($J/\psi \to \ell^+\ell^-$) and hadron control samples ($K_S^0 \to \pi^+\pi^-$, $D^{*+} \to D^0\pi^+$, $\Lambda \to p\pi^-$). Signal yields are extracted via fitting, and sWeights are employed to subtract background contributions when calculating efficiencies.

The PID algorithms combine information from multiple subdetectors:

• Local Likelihoods: Individual subdetectors (SVD, CDC, TOP, ARICH, ECL, KLM) provide likelihoods based on specific observables (e.g., $dE/dx$, Cherenkov photon timing, energy deposition $E/p$, and penetration depth).
• Global Probabilities: Local likelihoods are combined using Bayes' theorem to form global species-dependent probabilities.
• Boosted Decision Trees (BDT): To address limitations in simple likelihood combinations (such as neglecting correlations and suboptimal handling of low-momentum regions), the authors employ BDT classifiers. These utilize additional Electromagnetic Calorimeter (ECL) variables (e.g., cluster shape moments) and waveform pulse shape discriminants to enhance lepton/hadron separation, particularly for electrons at low momentum ($p \le 1$ GeV/c).

Key Contributions

• Performance Characterization: The paper presents a comprehensive evaluation of electron and muon identification efficiencies and hadron-to-lepton mis-identification rates across the full momentum and polar angle range accessible in Run 1.
• Algorithm Comparison: It provides a direct comparison between "simple" probability methods (based on global likelihood ratios) and BDT-based multivariate approaches.
• Data/Simulation Corrections: The authors compile correction tables (scale factors) to align simulation performance with observed data, accounting for discrepancies in efficiency and mis-ID rates. These are provided for various working points ($P > 0.5, 0.9, 0.95, 0.99$) and charge states.
• Identification of Systematic Effects: The study explicitly identifies and quantifies the impact of beam-injection backgrounds on the Central Drift Chamber (CDC) $dE/dx$ measurements, which degrades performance in data compared to simulation, particularly for low-momentum particles.

Results

• Electron Identification:
  • The BDT-based selection significantly outperforms the simple probability method, particularly in the low-momentum region ($0.5 < p < 1.0$ GeV/c) and the barrel region ($32^\circ < \theta < 128^\circ$).
  • Electron ID efficiencies range from 50% to 98% for pion mis-identification rates between 0.1% and 1%.
  • Data performance is generally lower than simulation, with discrepancies attributed largely to CDC $dE/dx$ biases caused by beam-injection backgrounds.
• Muon Identification:
  • For momenta below 1 GeV/c, achieving efficiencies above 80% requires accepting pion mis-identification rates above 18%.
  • Contrary to the electron case, the simple probability method often performs better than the BDT approach in data for muons, particularly at low momenta where the BDT relies on ECL information that is less effective for muons than for electrons.
  • In the intermediate momentum range ($1.0 < p < 3.0$ GeV/c) studied via $J/\psi$ decays, both methods show stable performance, with efficiencies generally exceeding 90%.
• Mis-identification Rates:
  • $\pi$-as-$e$: Data rates are 2–3 times higher than simulation predictions across most of the phase space.
  • $\pi$-as-$\mu$: Data rates are generally lower than simulation, particularly at higher momenta.
  • $p$-as-$e$: The simple probability method significantly outperforms the BDT method, which was optimized for $\pi$ separation and struggles to distinguish protons from electrons in the $1.0 < p < 1.5$ GeV/c range where $dE/dx$ values are similar.

Significance
The paper establishes that effective lepton identification is achievable at Belle II despite the challenging background conditions of Run 1. The results demonstrate that while simple likelihood-based methods remain robust (and sometimes superior for muons and protons), multivariate techniques (BDT) offer substantial improvements for electron identification, particularly in low-momentum regions where traditional variables lose discrimination power. The provided correction tables and performance metrics are essential for physics analyses requiring precise flavor tagging, full reconstruction of B mesons, and searches for rare decays. The authors note that future improvements will likely involve extending neural network approaches (previously successful for $K$ vs. $\pi$ separation) to leptons and refining calibration procedures to mitigate the effects of beam-injection backgrounds on the CDC.