Transcript A New Approach to Cluster Finding and Hit Reconstruction

VIII INTERNATIONAL WORKSHOP ON ADVANCED
COMPUTING AND ANALYSIS TECHNIQUES IN
PHYSICS RESEARCH (ACAT'2002)
24-28 June, 2002, Moscow, Russia
A New Approach to Cluster Finding and
Hit Reconstruction in Cathode Pad
Chambers and its Development for the
Forward Muon Spectrometer of ALICE
A.Zinchenko, G.Chabratova
JINR, Dubna. Russia
A New Approach to Cluster Finding and Hit Reconstruction
in Cathode Pad Chambers and its Development for the
Forward Muon Spectrometer of ALICE
Overview
The ALICE Experiment & MUON Spectrometer
Physical Tasks & Requirements to MUON Tracking
Basic Ideas of Bayesian Unfolding
Application to MUON Cluster Finding
Results & Discussion
Conclusion
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction
in Cathode Pad Chambers and its Development for the
Forward Muon Spectrometer of ALICE
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
General overview of Muon
Spectrometer
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction
in Cathode Pad Chambers and its Development for the
Forward Muon Spectrometer of ALICE
Physical Tasks & Requirements to MUON Tracking
U (1S)
Mass (MeV)
U (2S)
9460.37±0.21
Difference
A.Zinchenko, G.Chabratova
560 MeV
10023.3±0.31
U (3S)
10355.3±0.5
330 MeV
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction
in Cathode Pad Chambers and its Development for the
Forward Muon Spectrometer of ALICE
Physical Tasks & Requirements to MUON Tracking
Requirement to the tracking and reconstruction
efficiency: mass resolution has to be < 100 MeV
Requirement to the detector response reconstruction:
a reconstruction algorithm has to reduce the statistical noise
and does not introduce excessive smothing.
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction
in Cathode Pad Chambers and its Development for the
Forward Muon Spectrometer of ALICE
Basic Ideas of Bayesian Unfolding
Bayer' theorem: G.D. Agostini NIM A362(1995)487
If anybody observes a single event E(effect), the probability
that it has been due to the i th cause of Ci, i=1,2,..,nc is
proportional to the probability of cause P(Ci) times the
probability of the cause to produce the effect P(E|Ci).
P(Ci | E ) 
P( E | Ci ) P(Ci )
ni
 P( E | C ) P(C )
i 1
A.Zinchenko, G.Chabratova
i
i
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction
in Cathode Pad Chambers and its Development for the
Forward Muon Spectrometer of ALICE
Basic Ideas of Bayesian Unfolding (cont)
Maximum Likelihoods - Expectation Maximization (MLEM):
L.A. Shepp and Y. Vard IEEE Trans.Med.Im.v.1(1982)113
An application to the positron
emission tomography.
Pairs of photons are registered in coincidence by
pairs of detectors. The region, where the image is
reconstructed is subdivided into pixels and
different pairs of detectors. Since the number of
emissions inside pixels and number of of photon
coincidences are described by the Poisson
statistics, the likelihood function can be written
L ( ) 
j 1,...,n p

i 1,...,nt
A.Zinchenko, G.Chabratova
e
 ij
ij
nij
nij !
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Basic Ideas of Bayesian Unfolding (cont)
where   (1,...,n ) -vector of pixel activities ,
ij - the mean number of emissions from the pixel j
contributing to the tube i, n ij is the number of
photon pairs counted in the tube i from the pixel j.
n i is the number of detectors , n j - number of
pixels. The Expectation step of the EM algorithm
is done by taking a conditional expectation of log
likelihood with a respect of parameter estimates
n
 at the nth iteration and measured counts ni   nij
The new value for the jth component of the vector j
p
nj1 
nj
c
ij
i
 cij
i
ni
n
c
 ij k
k
where c ij - the jth pixel visibility from the detector i.
The results of reconstruction is shown at picture.
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Application to MUON Cluster Finding
Detector: Cathod Pad Chamber (CPC).
Sizes of pads vary from (0.4x0.6)cm2 to (10.x0.7143)cm2
Old method: The pad charge distribution is described by twodimensional integral of the Mathieson function and coordinates of a
single track is extracted from the fit of pad charge distributed by this
function. The number of track candidates is estimated from the number
of local maxima in the pad charge distribution. An amount of events with
significant overlapping of signal and background induced pad charges is
not negligible. An estimation of the number of track candidates from the
local maxima is not sufficiency accurate and results in deterioration of
coordinate resolution.
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Application to MUON Cluster Finding
¥
New method:transform the "twocathode fixed pad size" problem into the
"one-anode plane variable pixel size"
one.
¥ Find a groups of adjacent pads on
one cathode and overlap with its
pads on the other cathode
precluster
¥ Precluster
array of pixels in
the anode plane with size defined by
the overlap of pads on both cathodes.
¥ It is assumed that each pixel contains
a track
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Application to MUON Cluster Finding(cont)
New method(cont):
0
Iterative procedure: Track j has an initial value p j of
energy release . Usually all
p
k 1
j

p kj
N pads
N pads
c
i 1
p j 0 's are set to 1.
qi
cij k

fi
i 1
ij
with
fi k 
N trsck
k
c
p
 ij i
j 1
where f i k - the expected signal on pad i with track energy
releases
at the kth iteration,
p jk
c ij - the track-to-pad coupling(signal on pad i from track j given
N track
by Mathieson) and
- the number of tracks in the
array.
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Application to MUON Cluster Finding(cont)
New method (cont):
after several iterations (10-15) the pixel size is decreased by two;
track candidates with the lowest energy releases are removed, if the
total number of candidates exceeds the number of pads;
interactive procedure is repeated;
Algorithm stops when the pixel size becomes sufficiently small
(1mm)
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Results:
A.Zinchenko, G.Chabratova
residuals in the non bending plane
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Results(cont): residuals in the bending plane
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia
A New Approach to Cluster Finding and Hit Reconstruction in
Cathode Pad Chambers and its Development for the Forward
Muon Spectrometer of ALICE
Conclusion:
New method of Cluster Finding and Hit Reconstruction
improves essentially the space resolution of CPC chambers for
the Forward Muon Spectrometer of ALICE
A.Zinchenko, G.Chabratova
ACAT 2002, Moscow, 24-28 June, 2002, Russia