1. Particle Identification

2. Particle identification: an important task for nuclear and particle physics Usually it requires the combination of informations from several detectors Example: a charged particle in a magnetic field Under suitable conditions, the radius R of the trajectory is related to the momentum and charge R =p/z The velocity  may be obtained from a time-of-flight measurement, since it is proportional to 1/  The energy loss E of a charged particle may be described by the Bethe-Block formula, where dE/dx is proportional to z 2 All these informations may be combined to identify low energy particles

3. At low energies there is need to identify and discriminate ● particles with different Z (protons, He, Li, light nuclei,…) ● different isotopes of the same Z (p/d/t, 3He/4He,…) This is usually accomplished by combined dE/E and TOF techniques

4. At high energies particles have all Z=1 and most of them have relativistic speed There is need to identify and discriminate ● electrons/muons/pions/kaons/protons ● electrons/photons/neutral pions This is usually accomplished by different techniques tuned to the different momentum ranges: dE/dx, TOF, Cherenkov, TRD,...

5. Particle identification techniques and detector geometries have to take into account the usual penetration capabilities of the different species.

6. Large experiments wish to detect and identify as much as possible all the particles produced in each event. To this aim, a combination of different detectors and tehniques is used, to have good reconstruction efficiency in a large momentum range (0.1 – few GeV/c). For instance, in ALICE, a combination of the information from ITS (silicon), TPC, TOF, TRD and RHIC detectors is used. When the track is identified in more than one detector, the combined information is taken into acount.

7. Particle identification in the silicon detectors The measurement of energy loss in thin silicon layers may be used for PID in the non-relativistic region.

9. Previous equation only gives the average value of the energy loss. However, the energy loss is a statistical process with fluctuations. Two cases: a)Thick absorbers (large number of collisions): Gaussian distribution b)Thin absorber (small number of collisions): extremely difficult to evaluate. Approximation: Landau distribution

10. Landau distribution Long tail in the high energy side, asymmetric distribution Most probable energy loss Mean energy loss

11. Simulation of dE/dx in keV and MIP units for pions of 830-930 MeV/c in a silicon detector

12. The truncated mean approach: in a multi-layer detector, evaluate the mean excluding one or more values, especially the largest ones which may come from the high energy tail. ΔE1ΔE1 ΔE2ΔE2 ΔE3ΔE3 ΔE4ΔE4 ΔE5ΔE5 ΔE6ΔE6

13. ΔE-p plot for pions, kaons and protons in the ALICE ITS (6 layers). The truncated mean approach is used. How to identify such particles? Distribution of truncated mean energy loss in the ALICE ITS for pions, kaons and protons of 400 MeV/c

14. Separation between particle species is made, for each given momentum interval, by the PID probability for each type of particle. (PID probability) i = g i /Σg i g i = gaussian value for each species (centroid from Bethe-Bloch function, with a σ

15. The Bayesian approach The probability to be a particle of type i if a signal s is observed - w(i | s) – depends on the conditional probability - r(s | i) - to observe a signal s if a particle i crosses the detector and on the “a priori” probabilities C i (how often such particle species are detected). A priori probabilities may be estimated from simulations through event generators or from other detectors. W(i | s) = PID weights Identify the particle according to the largest PID weight (with some threshold?)

16. PID results Define PID Efficiency = N corr /N true PID Contamination = N incorr /(N incorr +N corr ) N corr = No. of correctly identified particles N incorr = No. of misidentified particles N true = True number of particles of that species

17. Momentum dependence of PID efficiency and contamination for pions, kaons and protons in the ALICE ITS.

18. Particle identification with TPC Again, the Bethe-Bloch function is used to describe the energy loss of particles as a function of their momentum, especially in the relativistic rise region.

19. The mean value (truncated mean) of the energy loss is gaussian, with a standard deviation determined by the detector properties. dE/dx distribution for various particles of p=0.5 GeV/c

20. The general way to quantify the separation power between particles A and B is to consider the difference in energy loss compared to standard deviation Typical examples of separation power as a function of momentum

21. Particle identification with TRD and RHIC Such detectors are used for TRD: Improve electron/pion separation by a large factor (pion rejection of 100 for large momenta) RHIC: Improve the overall PID at very large momenta (See specific lectures on the working principle of such devices)

22. TRD may contribute also to pion, kaon and proton PID

23. Particle identification with the TOF (Time-Of-Flight) The time-of-flight technique may be used to separate particles with intermediate momenta (a few GeV/c), depending on the time resolution. In ALICE, the TOF system is built with MRPC (Multigap- Resistive-Plate-Chambers), with a time resolution around 80 ps. In such conditions, a pion/kaon separation better than 3 σ is achieved up to 2.5 GeV/c, and kaon/proton up to 4 GeV/c.

25. The combined PID The method can be applied to combine PID information from several detectors Consider the whole detector of N different detectors: Vector of PID signals in N detectors If the PID measurements are uncorrelated over the different detectors,

26. The PID weights combined over the whole system of detectors will be -If a detector is not able to provide PID, its PID weights are set equal, and its contribution cancels out in the product -When several detectors may provide PID, they contribute together, improving the overall information

28. Items not covered in detail: Neutral particle identification: especially neutral pions and photons

29. Principal-Component- Analysis (PCA) of showers A shower in a calorimeter may be characterized by different parameters: Lateral dispersion, two ellipse axes, sphericity parameter, core energy, largest fraction of energy deposited in a single crystal, … Instead of working in a multidimensional space to find the cuts (which is not an easy task), the principal components may be obtained by diagonalization of the covariance matrix of the original parameters. The two most significant components (largest eigenvalues) allow to work in a 2-D space to find selection criteria.

30. Principal-Component-Analysis of showers in a photon detector

31. Neural-network approach Several applications exist for particle identification with neural network algorithms Just one example: π 0 / γ discrimination in ALICE Neural network structure: 3 Layers: 1 input (N nodes = features vector) 1 hidden (2 N + 1 nodes) 1 output (1 node: 0 or 1)

32. Training with 2 event samples: 1)Clusters with single photons 2) Clusters with overlapped photons (from π 0 decay) Typical results in ALICE with the PHOS (Photon Spectrometer) Probability of true photon identification Probability of misidentification of a π 0 as a photon