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Transcript
Particle Identification
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 z2
All these informations may be combined to identify low energy
particles
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
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,...
Particle identification techniques and detector
geometries have to take into account the usual
penetration capabilities of the different species.
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.
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.
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
Landau distribution
Mean
energy loss
Most
probable
energy loss
Long tail in the high energy side, asymmetric
distribution
Simulation of dE/dx in keV and MIP
units for pions of 830-930 MeV/c in
a silicon detector
ΔE1
ΔE5 ΔE
6
ΔE2 ΔE3 ΔE4
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.
ΔE-p plot for pions, kaons and protons in the
ALICE ITS (6 layers).
The truncated mean approach is used.
Distribution of truncated
mean energy loss in the ALICE
ITS for pions, kaons and
protons of 400 MeV/c
Separation between particle species is made,
for each given momentum interval, by the PID
probability for each type of particle.
(PID probability)i = gi/Σgi
gi = gaussian value for each species
(centroid from Bethe-Bloch function, with a σ
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 Ci (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?)
PID results
Define
PID Efficiency
= Ncorr/Ntrue
PID Contamination = Nincorr/(Nincorr+Ncorr)
Ncorr = No. of correctly identified particles
Nincorr = No. of misidentified particles
Ntrue
= True number of particles of that species
Momentum dependence of PID
efficiency and contamination for
pions, kaons and protons in the
ALICE ITS.
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.
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
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
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)
TRD may contribute also to pion,
kaon and proton PID
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 (MultigapResistive-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.
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,
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
Items not covered in detail:
Neutral particle identification: especially
neutral pions and photons
Principal-ComponentAnalysis (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.
Principal-Component-Analysis of
showers in a photon detector
Neural-network approach
Several applications exist for particle
identification with neural network algorithms
Just one example: π0 / 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)
Training with 2 event samples:
1) Clusters with single photons
2)
Clusters with overlapped photons (from π0 decay)
Typical results in ALICE with the
PHOS (Photon Spectrometer)
Probability of true
photon identification
Probability of
misidentification of a π0
as a photon