Study of High Multiplicity Event Topology by Wavelet Analysis in Heavy Ion Collisions

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• Study of High Multiplicity Event Topology by
  Wavelet Analysis in Heavy Ion Collisions
• V.L. Korotkikh, G.Eiiubova

Scobeltsyn Institute of Nuclear Physics, Moscow
State University
European Workshop on Heavy Ion Physics, JINR,
Dubna March 2006 ?.
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There are many particles in one event in Heavy
Ion Collisions. It is about
in AuAu collision at RHIC
energies. So we can study a structure of event
angular distribution or ET (???) distribution as
function of ? and f . Lets show one example,
but we dont analyze this experiment. Just now
in STAR collaboration in RHIC the angular
correlation of two charge particles in AuAu vs
130 GeV/c(see Fig.) were measured, which show
significant and unexpected fluctuations at low
pT lt 2 GeV/c.
The most power method of study such kind
distributions is Discrete Wavelet
Transformations (DWT).
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Publications with Wavelet analysis in
nuclear-nucleus collisions

• 1) I.M. Dremin et al, Phys. Lett. B499,
  p.97(2001)
• (Discrete Wavelets Transformation (DWT), PbPb,
  158 A GeV, fix target, ring structure in angular
  distribution of particles)
• 2) V.V. Uzhinskii et al., hep-ex/0206003(2002)
• (Continuous Wavelets, OEm, SEm, 60, 200 A GeV,
  ring structure in angular distribution of
  particles)
• 3) I. Berden et al., Phys. Rev C65, 044903(2002)
• (Discrete Haar wavelets, PbPb, 158 A GeV, fix
  target, texture of events)
• 4) M. Kopytin, nucl-ex/0211015(2002) (Discrete
  Haar wavelets, AuAu vs 200 A GeV (RHIC,
  STAR). Study of event texture)
• 5) J. Adams et al., nucl-ex/0407001(2005)
• (Discrete Haar wavelets, AuAu vs 200 A
  GeV (RHIC, STAR). Study of event texture with the
  help of power wavelets as function of
  centralities and pT)
• 6) V.L. Korotkikh, G.Kh.Eiiubova, Preprint ?????
  ??? 2005-21/787
• (Discrete Daubechies wavelets. Study of MC
  simulation of two-dimension angular
  distributions with ring and jet structure of
  event)
• 7) M.V. Altaisky et al, Preprint JINR
  E10-2001-205
• WASP (Wavelet Analysis of Secondary Particles
  Angular Distributions) Package

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Content

• Main notions
• 2-dimension Discrete Wavelet Transformation
• Examples with ring structure
• Jet like structure
• Conclusion

SINP,MSUV.L. Korotkikh, G.Eiiubova
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Main notions

• Analysis decomposition f(x) by the help of basic
  function wavelets
• Synthesis reconstruction of function, using
  wavelet coefficients

Wavelet decomposition has two parameters j
scale parameter, analogous Fourier frequency k
shift parameter, which sets a wavelet location
- oscillator functions, wavelet
- scaling functions
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D8- Daubechies wavelet
scaling functions
oscillator function, wavelet
?.Ma??? ???????? ? ????????? ????????, ?.
???, 2005
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2-dimension Discrete Wavelet Transformation
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Algorithm of Fast wavelet transform is used for
calculation of wavelet coefficientsThe iterative
formulas, so-called pyramid algorithm the
coefficients of scale (j 1) are calculated by
the coefficients of scale j (from small to large
scales)
hn ? gn filter coefficients of the wavelet
?
D8- Daubechies wavelet h0,,h7 ? 0
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• Two dimension wavelets

Here are X, Y, D the directions on the
strings, coulombs and diagonals.
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Algorithm of two dimension analysis
hn
hn
s j1
S j
gn
d x j1
gn
hn
d y j1
gn
d d j1
along strings
along coulombs
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Example with ring structure
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We simulate a two dimension histogram,
corresponding to our example function in order to
test DWT
N10000
If we used all wavelet coefficients then we get
the same exactly distributions after the
synthesis
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• But to reveal structure of histogram on large
  scale
• we put to zero the coefficients at small scales
  j1..5
• and make the synthesis with the coefficients j7,
  j6.

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Original histogram
Final histogram after synthesis with zero d ?j
at j1-5.
You see that a small peak disappears
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WL with d ?j ??0 at j 6,5,4
WL with d ?j ??0 at j 1,2
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Jet like structure
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• HIJING
• Monte Carlo Program for Parton and Particle
  Production in High Energy Hadronic and Nuclear
  Collisions
• (X.N. Wang, M. Gyulassy, Phys.Rev. D44(1991)3501)
• ?s5500 GeV, our event is a sum
• 1)pp?jet1jet2
• 2)PbPb ?particles, no jets. (dN/dy)y0 6000
• Our next histograms are

-5 lt ? lt 5
-3.14 lt f lt 3.14
???0.078 ???0.050
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Algorithm of jet reconstruction

1. Wavelet analysis of an event (Daubechies
   wavelets)
2. Calculation of background with large scale
   coefficients d ?j and subtraction from original
   histogram
3. Selection of coefficients d ?j , which are above
   the certain threshold
4. Synthesis with selected coefficients d ?j

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reconstruction by wavelet analysis
jet background
Jet ET70 GeV
-5 lt ? lt 5
???0.078 ???0.050
-3.14 lt f lt 3.14
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• a)Two jet event
• ET (jet1) 30 GeV
• ET (jet2) 22GeV
• b) this event background

a)
b)
c)
d)
c)Background after wavelet synthesis d)Reconstruct
ion of event
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Event projection on axis f

• Event reconstruction with the help of Daubechies
  wavelets D8 after removing background

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Conclusion

• We demonstrate the using of Discrete Wavelets
  Transformation (DWT) for the analysis of many
  particle events in heavy ion collision
• DWT software for one and two dimension
  distributions was made
• Method is tested on the events which are
  simulated by the event generators PYTHIA and
  HIJING
• It is shown that method works well for the ring
  and jet structure events.
• The event bacground is removed if we select d ?j
  coefficients by the special way
• Wavelet analysis allows to selects the jets with
  ET gt ETmin20 GeV

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Plans for future

• Testify wavelet analysis on simulated and
  reconstructed data on CMS detector
• Testify on real data from RHIC