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

1. 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 г.

2. There are many particles in one event in Heavy Ion Collisions. It is about in Au+Au collision at RHIC energies. So we can study a structure of event angular distribution or ET () distribution as function of η and φ . Lets show one example, but we don’t analyze this experiment. Just now in STAR collaboration in RHIC the angular correlation of two charge particles in Au+Au √s =130 GeV/c(see Fig.) were measured, which show significant and unexpected fluctuations at low pT < 2 GeV/c. The most power method of study such kind distributions is Discrete Wavelet Transformations (DWT).

3. Publications with Wavelet analysis in nuclear-nucleus collisions • 1) I.M. Dremin et al, Phys. Lett. B499, p.97(2001) (DiscreteWavelets Transformation (DWT),Pb+Pb, 158 A GeV, fix target, ring structure in angular distribution of particles) • 2) V.V. Uzhinskii et al., hep-ex/0206003(2002) (Continuous Wavelets, O+Em, S+Em, 60, 200 A GeV, ring structure in angular distribution of particles) • 3) I. Berden et al., Phys. Rev C65, 044903(2002) (DiscreteHaar wavelets,Pb+Pb, 158 A GeV, fix target, texture of events) • 4) M. Kopytin, nucl-ex/0211015(2002) (DiscreteHaar wavelets, Au+Au √s = 200 A GeV (RHIC, STAR). Study of event texture) • 5) J. Adams et al., nucl-ex/0407001(2005) (DiscreteHaar wavelets, Au+Au √s = 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 НИИЯФ МГУ 2005-21/787 (DiscreteDaubechies wavelets. Study of MC simulation of two-dimension angular distributions with ring and jet structure of event) 7) M.V. Altaisky et al, Preprint JINRE10-2001-205 WASP (Wavelet Analysis of Secondary Particles Angular Distributions) Package

4. Content • Main notions • 2-dimension Discrete Wavelet Transformation • Examples with ring structure • Jet like structure • Conclusion SINP,MSUV.L. Korotkikh, G.Eiiubova

5. Main notions Analysis— decompositionf(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

6. D8- Daubechies wavelet scaling functions oscillator function, wavelet С.Maлла «Вейвлеты в обработке сигналов», М. «Мир», 2005

7. 2-dimension Discrete Wavelet Transformation

8. 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) h[n] и g[n]— filter coefficients of the waveletψ D8- Daubechies wavelet: h[0],…,h[7]  0

9. Two dimension wavelets : Here areX, Y, D —the directions on the strings, coulombs and diagonals.

10. Algorithm of two dimension analysis h[n] h[n] S j s j+1 g[n] d x j+1 g[n] h[n] d y j+1 g[n] d dj+1 along strings along coulombs

11. Example with ring structure

12. We simulate a two dimension histogram, corresponding to our example function in order to test DWT N=10000 If we used all wavelet coefficients then we get the same exactly distributions after the synthesis

13. But to reveal structure of histogram on large scale we put to zero the coefficients at small scales j=1..5 and make the synthesis with the coefficients j=7, j=6.

14. Original histogram Final histogram after synthesis with zero d λj at j=1-5. You see that a small peak disappears

15. WL with d λj0 at j = 6,5,4 WL with d λj0 at j = 1,2

16. Jet like structure

17. 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) s=5500 GeV, our event is a sum : 1)p+p→jet1+jet2 2)Pb+Pb→particles, no jets. (dN/dy)y=0 = 6000 Our next histograms are -5 < η < 5 -3.14 < φ < 3.14 0.078 0.050

18. Algorithm of jet reconstruction • Wavelet analysis of an event (Daubechies wavelets) • Calculation of background with large scalecoefficients d λjand subtraction from original histogram • Selection of coefficientsd λj , which are above the certain threshold • Synthesis with selected coefficientsd λj

19. reconstruction by wavelet analysis jet + background JetET=70 GeV -5 < η < 5 0.078 0.050 -3.14 < φ < 3.14

20. 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)Reconstruction of event

21. Event projection on axis φ Event reconstruction with the help ofDaubechies waveletsD8after removing background

22. Conclusion • We demonstrate the using of DiscreteWavelets 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 testedon 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 λjcoefficients by the special way • Wavelet analysis allows to selects the jets with ET > ETmin=20 GeV

23. Plans for future • Testify wavelet analysis on simulated and reconstructed data on CMS detector • Testify on real data from RHIC