Data Analysis Histograms Overview

This document provides a detailed explanation of the histograms used in the data analysis of pp LHC23zzh pass4 (LHC23g3) MC anchored data, including their classification into Reconstructed Histograms and Simulated (MC Truth) Histograms.

Dataset Information

Analysis performed on:

• AO2D file from 2024 MC production
• Anchored to pp LHC23zzh pass4 (LHC23g3) dataset
• Uses both reconstructed tracks and MC truth information

Reconstructed Histograms:

These histograms correspond to the reconstructed tracks from the detector, filled with track-level information:

• eventCounter: Number of processed events
• etaHistogram: η distribution of selected tracks
• ptHistogram: Transverse momentum ($p_T$) of selected tracks
• ptResolution: $p_T$ resolution (reconstructed vs generated)
• tpcDedxVsPt: TPC $dE/dx$ vs $p_T$ correlation
• nSigmaPiVsPt, nSigmaKaVsPt, nSigmaPrVsPt, nSigmaElVsPt: $n\sigma$ distributions for pions, kaons, protons, and electrons vs $p_T$
• nSigmaPiVsP: $n\sigma(\pi)$ vs $p$ distribution
• ptSpectrumPion, ptSpectrumKaon, ptSpectrumProton, ptSpectrumElectron: $p_T$ spectra using configurable $n\sigma$ PID cuts
• Combined PID histograms (TPC + TOF):
  • ptSpectrumPionCombinedPID
  • ptSpectrumKaonCombinedPID
  • ptSpectrumProtonCombinedPID
  • ptSpectrumElectronCombinedPID
• Bayesian PID histograms (TPC + TOF, probabilistic assignment):
  • ptSpectrumPionBayesianPID
  • ptSpectrumKaonBayesianPID
  • ptSpectrumProtonBayesianPID
  • ptSpectrumElectronBayesianPID
• Particle-specific histograms:
  • ptHistogramPion/Kaon/Proton/Electron: Reconstructed $p_T$ for each species
  • dEdxPion/Kaon/Proton/Electron: $dE/dx$ vs $p_T$ for identified particles

New Kinematic Histograms (Run 3 PID Upgrade):

• thetaHistogram: Polar angle ($\theta$) computed from pseudorapidity
• betaHistogram: Velocity $\beta$ from TOF
• massHistogram: Mass estimation using TOF beta and momentum
• chargeHistogram: Distribution of track charge

All Tracks vs Selected Tracks Comparison:

These histograms capture the full population of tracks (before any selection cuts) and allow comparison with selected-track distributions:

• ptHistogramAllTracks: $p_T$ of all reconstructed tracks
• etaHistogramAllTracks: η of all reconstructed tracks
• chargeHistogramAllTracks: Charge distribution before cuts

Per-Collision Particle Statistics:

New histograms added to inspect particle production per collision:

• nTracksPerCollision: Total number of selected tracks per collision
• nPionsPerCollision, nKaonsPerCollision, nProtonsPerCollision, nElectronsPerCollision: Number of matched physical primaries (|y| < 0.5) per reconstructed collision, for each of the four most common species

Simulated (MC Truth) Histograms:

These histograms use MC particle-level information:

• ptGeneratedPion/Kaon/Proton/Electron: Generated $p_T$ of true MC particles
• numberOfRecoCollisions: Number of reconstructed collisions per MC collision
• multiplicityCorrelation: Track multiplicity correlation between reconstructed collisions

Analysis Task Features:

The associated analysis task (myExampleTaskPID.cxx) includes:

1. Track selection with DCA cut (< 0.2 cm) and configurable η cut
2. PID validation using:
   • TPC signal ($dE/dx$) vs momentum
   • $n\sigma$ separation for pions, kaons, protons, electrons (TPC and TOF)
   • Configurable PID cuts for flexibility (via JSON)
   • Bayesian PID using combined detector response and species priors
3. Extended physics observables:
   • $\beta$ and mass via TOF-based PID
   • $\theta$ from $\eta$, charge histograms
4. MC truth matching for:
   • $p_T$ resolution studies
   • Physical primary identification ($|y| &lt; 0.5$)
5. Collision-track association and multiplicity studies
6. All-track histograms for comparison with selected populations
7. Per-collision particle yields for physics performance validation

Summary of Histogram Classification:

Reconstruction Histograms	MC Truth Histograms
eventCounter	ptGenerated*
etaHistogram, thetaHistogram	numberOfRecoCollisions
ptHistogram*, ptHistogramAllTracks	multiplicityCorrelation
dEdx*, tpcDedxVsPt
nSigma*VsPt, nSigma*VsP
betaHistogram, massHistogram
chargeHistogram, chargeHistogramAllTracks
nTracksPerCollision, nPionsPerCollision
nKaonsPerCollision, nProtonsPerCollision
nElectronsPerCollision
ptSpectrum*BayesianPID

Key Notes:

• The analysis is structured using O2Physics PID helpers (pidTPC, pidTOF, pidTOFmass, pidTOFbeta, pidBayesian)
• Supports both single-detector and combined (TPC + TOF) PID
• Mass estimation relies on TOF-based $\beta$ with momentum using $m = p\sqrt{1/\beta^2 - 1}$
• Histogram binning and selection cuts are configurable using Configurable<> settings in JSON
• Full-track vs selected-track histograms aid in assessing the effect of selection criteria
• Per-collision particle statistics allow monitoring particle production per event for performance studies
• Bayesian PID enables probabilistic species assignment using detector response functions and user-defined priors

Summary Table: nσ vs Bayesian PID

Method	What it does	Pros/Cons
nσ cut	Selects if $n\sigma$ is within PID threshold	Simple and fast, but only uses one detector
Bayesian (max)	Uses all detectors, selects highest probability species	Higher purity, combines detector information
Bayesian (weighted)	Fills histograms with posterior probability as weight	For advanced/statistical analyses

Bayesian PID: Key Formula

For each species $H_i$ (e.g., $\pi$, K, p, e), the Bayesian posterior probability is given by:

$P(H_i \mid \vec{S}) = \dfrac{P(\vec{S} \mid H_i) \cdot C(H_i)}{\sum_k P(\vec{S} \mid H_k) \cdot C(H_k)}$

Where:

• $\vec{S}$ is the vector of detector PID signals (e.g., TPC $dE/dx$, TOF time)
• $P(\vec{S} \mid H_i)$ is the likelihood of observing the signals given species $H_i$
• $C(H_i)$ is the prior probability for species $H_i$

Assuming Gaussian detector responses, the likelihood for each detector $\alpha$ (TPC or TOF) is:

$P(S_\alpha \mid H_i) \propto \exp\left(-\frac{1}{2} n\sigma_{i,\alpha}^2\right)$

Thus, the combined likelihood (assuming independence) becomes:

$P(\vec{S} \mid H_i) \propto \exp\left(-\frac{1}{2} \left[n\sigma_{i,\text{TPC}}^2 + n\sigma_{i,\text{TOF}}^2\right]\right)$

These $n\sigma$ values are computed by O2Physics and used directly in the Bayesian PID calculation.