Application of the HBOM method

Transkrypt

Correcting for detector effects in high-multiplicity events
with the HBOM method
Piotr Janus, Jakub Kremer
AGH University of Science and Technology in Kraków
Kraków, 8.1.2016
Detector effects
Measurements of particle multiplicities in high energy collisions may be affected by
following detector effects:
inefficiency in the detection of particles,
incorrectly reconstructed tracks (called fakes),
secondary particles created in decays of primary particles or due to their
interactions with the detector material.
In general measurements with a detector can be expressed by:
Z
g (y ) =
A(y , x)f (x)dx,
where:
g (y ) - measured distribution
f (x) - truth distribution
A(y , x) - response function
Discrete form with n bins for x and m bins for y :
y = Ax
y - measured histogram
x - truth histogram
A - response matrix
Piotr Janus, Jakub Kremer (AGH)
Kraków, 8.1.2016
2 / 11
General idea of unfolding
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Response matrix
truth
arb. unit
To correct for detector effects an unfolding method is used which needs to invert the
response matrix:
x = A−1 y
truth
measured
PDF
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observable
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measured
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However unfolding does not work when real data has a wider distribution than
simulation used to obtain the response matrix.
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mc
data
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observable
Kraków, 8.1.2016
3 / 11
HBOM (Hit Backspace Once More) method
First proposed: J. Monk, C. Oropeza-Barrera, Nucl. Instrum. Meth. A 701 (2013) 17-24
Let us consider a detector response described by operator A, then:
X obs = X (0) = AX true = AX (−1)
Operator A can be applied i times:
X (i) = Ai+1 X true
X(i)
Repetition of the above procedure will result in a sequence of values of the observable
X (i).
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Kraków, 8.1.2016
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Observables
To study performance of the HBOM method factorial moments will be used which are
defined as:
+
* B
Y nj !
Fi1 ,...,iB ≡
,
(nj − ij )!
j=1
where B denotes number of pseudorapidity bins and nj is the number of charged
particles emitted into a given pseudorapidity interval. For three pseudorapidity bins, the
above equation can be expressed as:
FiL ,iC ,iR ≡
nL !
nC !
nR !
(nL − iL )! (nC − iC )! (nR − iR )!
In the following we will focus on the four factorial moments:
F100 , F101 , F120 , F111
Factorial moments are extracted in 3 pseudorapidity bins with varying distance between
forward and backward bin.
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η bins
Kraków, 8.1.2016
5 / 11
Correction of the factorial moments I
To correct for track reconstruction inefficiency the following procedure is
applied:
measurement of an observable (in this case: factorial moments) using
all reconstructed tracks satisfying the analysis cuts – 0th iteration,
removal of tracks from the sample according to the detector
inefficiencies (discussed in the next slide),
repeated measurement of the observable – 1st iteration,
removal of further tracks from the sample and measurement of the
observable – 2nd iteration, etc.,
fitting (with exponential or polynomial) the distribution of the
observable as a function of the iteration number,
extrapolation to the iteration -1 should give an estimate of the true
value of the observable.
Secondaries and fakes can be also corrected for.
Kraków, 8.1.2016
6 / 11
Correction of the factorial moments II
counts
Condition for removing tracks takes the form:
eff > r ,
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where eff is the efficiency for a given track and
r is a random number from the uniform
distribution in the interval [0,1].
Non-integer iterations can be introduced. In
general, the rejecting procedure of the n-th
iteration can be done from the 0th iteration
with the following condition:
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eff n > r
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eff (pT , η) =
2 −1
tg
π
pT − 80 MeV
150 MeV
exp −
0-10%
p > 500 MeV
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track multiplicity
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efficiency
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p [GeV]
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For performance studies PbPb collisions at
√
sNN = 2.76 TeV were generated using the
HIJING generator. As a track reconstruction
efficiency function was taken:
HIJING PbPb sNN = 2.76 TeV
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η
Kraków, 8.1.2016
7 / 11
Closure test I
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To correct factorial moments for detector inefficiencies the HBOM method
was used. For the fitting function ax 3 + bx 2 + cx + d was chosen.
HIJING PbPb s=2.76 TeV
Iterations
Extrapolation
Truth MC
Iterations
Extrapolation
Truth MC
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|η|<0.1 -0.3<η<-0.1
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Iterations
Extrapolation
Truth MC
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Iterations
Extrapolation
Truth MC
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×103
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Iteration
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Iteration
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Iteration
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Iteration
In the central rapidity bins the HBOM method reproduces truth value very
well.
Kraków, 8.1.2016
8 / 11
Closure test II
F101
F100
Factorial moments as a function of distance between bin centers corrected with
ax 3 + bx 2 + cx + d
d.
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truth MC
extrapolation
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[0]+[1]*x+[2]*x*x+[3]*x*x*x
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truth MC
extrapolation
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truth MC
extrapolation
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[0]+[1]*x+[2]*x*x+[3]*x*x*x
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Iterations
Extrapolation
Truth MC
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Iteration
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∆η
Factorial moments of rank 2 and 3 are significantly shifted with respect to the truth
value.
Kraków, 8.1.2016
9 / 11
Closure test III
F101
F100
Factorial moments as a function of distance between bin centers corrected with
exp(ax 2 + bx + c) + dd.
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truth MC
extrapolation
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exp([0]+[1]*x+[2]*x*x)+[3]
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truth MC
extrapolation
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exp([0]+[1]*x+[2]*x*x)+[3]
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truth MC
extrapolation
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exp([0]+[1]*x+[2]*x*x)+[3]
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truth MC
extrapolation
exp([0]+[1]*x+[2]*x*x)+[3]
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Exponential function reproduces truth value very well in the whole pseudorapidity range.
Kraków, 8.1.2016
10 / 11
Summary
The general problem of correcting for detector effects in HEP
measurements was discussed.
The HBOM method was studied on high track multiplicity events
generated with HIJING.
Factorial moments were choosen as an example observable.
Presented method gives promising results.
More studies of the fitted function are needed.
Kraków, 8.1.2016
11 / 11

Application of the HBOM method

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