12.4.201012.4.2010

Application of multi-Application of multi-resolution method on flow resolution method on flow

measurement in CBMmeasurement in CBM

Vojtech PetracekVojtech Petracek

GSI – CBM weekGSI – CBM week

OutlineOutline

Motivation – event-by-event reaction plane & v2 Motivation – event-by-event reaction plane & v2 & fluct.& fluct.

Fluctuations in event shape – statistics, fireball Fluctuations in event shape – statistics, fireball instability and granularity, jets ...instability and granularity, jets ...

Event-by-event fluctuation in particle density in Event-by-event fluctuation in particle density in 1D and 2D1D and 2D

Multi-resolution analysis of particle density Multi-resolution analysis of particle density fluctuationsfluctuations

Strategy of domain analysisStrategy of domain analysis Reaction plane and v2 parametersReaction plane and v2 parameters Summary & outlookSummary & outlook

Elliptic flow measurement & Elliptic flow measurement & backgroundbackground

?

Elliptic flow reflects the original geometry of thecollision zone

We measure azimuthal anisotropy in Pt,y slice of the phase space

Background : stat. fluctuations, fireball granularity, jets

Apart of statistical fluctuationseven the background is an interesting signal

Can we detect the critical pointCan we detect the critical pointfrom fluctuations? from fluctuations?

• Onset of spinodal instability for larger Onset of spinodal instability for larger ? ?• Source structure in crossover region (bags) ?Source structure in crossover region (bags) ?

B. Tomasik

CBM

Fireball instabilityFireball instability

Fast cooling can bring Fast cooling can bring the system to the the system to the unstable configurationunstable configuration

Fireball decomposes Fireball decomposes as it reaches the as it reaches the spinodal pointspinodal point

Cooling must be fast Cooling must be fast bubble nucleation rate bubble nucleation rate < expansion rate< expansion rate

V

B. Tomasik

Granular fireballGranular fireball

Fireball can decompose to spherical dropletsFireball can decompose to spherical droplets Or to objects with more complicated shapes with Or to objects with more complicated shapes with

larger surface/volume ratiolarger surface/volume ratio Or nothing like that happensOr nothing like that happens Can we distinguish between these options -> MRACan we distinguish between these options -> MRA Can we eliminate jet background -> MRACan we eliminate jet background -> MRA BUT we need to work on different scales (resolutions) BUT we need to work on different scales (resolutions)

Multi-resolution analysis (MRA)Multi-resolution analysis (MRA)

• MRA method uses 2D Cauchy-Lorentz functionMRA method uses 2D Cauchy-Lorentz function• We can observe We can observe -- particleparticle densitydensity distribution with different resolutiondistribution with different resolution• We can characterize fluctuation between different resolutionsWe can characterize fluctuation between different resolutions

Example - MRA in 1D Example - MRA in 1D This method can isolate large scale structuresThis method can isolate large scale structures which would be otherwise hidden in noisewhich would be otherwise hidden in noiseJets, DCC, elliptic flow pattern, reaction plane..Jets, DCC, elliptic flow pattern, reaction plane..

If we define a set of resolutions, it is possibleIf we define a set of resolutions, it is possible to reconstruct from L and F functions to reconstruct from L and F functions recursively the original density distributionrecursively the original density distribution like in wavelet transformlike in wavelet transform

Compared to the discrete wavelet Compared to the discrete wavelet transformation method this approachtransformation method this approach doesn’t have problem with domain splittingdoesn’t have problem with domain splitting

Mother & Father functionsMother & Father functions

Mother functions L smooth the high freq. noiseMother functions L smooth the high freq. noise Father functions F determine the fluctuation between the two Father functions F determine the fluctuation between the two

resolution scalesresolution scales Original domain is optimally reproduced when its characteristic Original domain is optimally reproduced when its characteristic

scale coincide with resolutionscale coincide with resolution

L1L1

L2L2

F12F12

Event-by-event fluctuation Event-by-event fluctuation domain detectiondomain detection

Events with isotropic particle distribution are used for Events with isotropic particle distribution are used for the detection threshold calibrationthe detection threshold calibration

Threshold is set to 2Threshold is set to 2, so that ~5% of random signal , so that ~5% of random signal is above itis above it

Events containing non-statistical local fluctuations in Events containing non-statistical local fluctuations in particle density will have the fraction of signal above particle density will have the fraction of signal above the threshold significantly higher the threshold significantly higher

When we Pt weight the MF, this way the jet area can When we Pt weight the MF, this way the jet area can bebe

detected as area of higher than average Pt detected as area of higher than average Pt

Example of droplet Example of droplet reconstruction in MF 2D reconstruction in MF 2D

analysisanalysisCharacteristic droplet Characteristic droplet dimensionsdimensions~ 0.5y x Pi/4~ 0.5y x Pi/4

For small number of For small number of droplets (<20) is possible droplets (<20) is possible direct droplet countingdirect droplet counting

For larger numbers For larger numbers droplets merge droplets merge

Individual droplet FF 2D Individual droplet FF 2D analysisanalysis

When the direct dropletWhen the direct droplet counting is possible, thecounting is possible, the best estimate is the #best estimate is the # of maxima in FF overof maxima in FF over certain thresholdcertain threshold

Droplets & the event Droplets & the event fluctuationfluctuation

Distribution of fraction Distribution of fraction of the area covered by of the area covered by detected domaindetected domain

Red : 100% particles Red : 100% particles from dropletsfrom droplets

Green : 0% particles Green : 0% particles from dropletsfrom droplets

Scale 2Scale 2

Jet reconstructionJet reconstruction

Example of jet reconstruction using the described MRA methodExample of jet reconstruction using the described MRA method

Pt weighting – necessary !! Pt*N ~ Et-JetPt weighting – necessary !! Pt*N ~ Et-JetMean Pt map Mean Pt map <Pt>(eta,phi)=<Pt*N>(eta,phi)/<N>(eta,phi)<Pt>(eta,phi)=<Pt*N>(eta,phi)/<N>(eta,phi)

Strategy of event analysisStrategy of event analysis

Compare Compare P in domains P in domains to surrounding => to surrounding => identify jetidentify jet

Check the charge Check the charge symmetry. Asymmetry symmetry. Asymmetry => DCC=> DCC

Density fluctuation due Density fluctuation due to the dropletto the droplet

Eliminate jet – replace Eliminate jet – replace by surrounding by surrounding backgroundbackground

Analyze event shape Analyze event shape for reaction plane & v2for reaction plane & v2

What v2 we want to measureWhat v2 we want to measure

Expected elliptic flow Expected elliptic flow in CBMin CBM

NA49 – PRC 68, 034903 (2003)

A. Wetzlar 2005

Below 10% for high Pt particlesComplicated event-by-eventbut when reaction plane is determinedevents can be combined

CBM

Examples of reaction plane Examples of reaction plane and v2 reconstruction event-and v2 reconstruction event-

by-eventby-event

Reaction plan

300 tracks, v2 =0.1

Reconstruction of reaction plane angle easy and stable at all scales

precission of RP estimatefrom spread between fits at different scales

v2 can be reconstructed

Examples of reaction plane Examples of reaction plane and v2 reconstruction event-and v2 reconstruction event-

by-eventby-event

Reaction plan

500 tracks v2 = 0.05

with 500 tracks is statistical fluctuation still weaker then signal

RP reconstruction stable

v2 can be reconstructed

Examples of reaction plane Examples of reaction plane and v2 reconstruction event-and v2 reconstruction event-

by-eventby-event

Reaction plan

500 tracks v2=0.02

In this case is the statisticalfluctuation comparable to the signal

RP estimate less precisebut still stable

v2 ?

RP reconstruction is stable-> events can be combined for v2 measurement

Examples of reaction plane Examples of reaction plane and v2 reconstruction event-and v2 reconstruction event-

by-eventby-event

Reaction plan

1000 tracks v2=0.02

RP reconstruction stable on most scales

v2 in single event not reliable

-> combine eventswhen RP is reconstructedconsistently on all scales

Summary & outlookSummary & outlook

Area of the Area of the ,, plane covered by domains with non-statistically plane covered by domains with non-statistically high particle density fluctuation is a robust measure which can be high particle density fluctuation is a robust measure which can be used for detection of events with granular source responsible at used for detection of events with granular source responsible at least for 20% of particle production (for 100 fmleast for 20% of particle production (for 100 fm3 3 droplets)droplets)

For small number of droplets the direct droplet counting is possibleFor small number of droplets the direct droplet counting is possible

Dijet reconstruction using the Pt weight works reliably in HI Dijet reconstruction using the Pt weight works reliably in HI environment for jets with Et>~30 GeVenvironment for jets with Et>~30 GeV

Reconstruction of jet parameters (Pt symmetry in Phi, y.....)Reconstruction of jet parameters (Pt symmetry in Phi, y.....) event-by-eventevent-by-event Deflection of fragmentation products by the radial and Deflection of fragmentation products by the radial and

longitudinal flow and resulting medium response need more study longitudinal flow and resulting medium response need more study => Mach cone ! => Mach cone !

Jet can be decoupled from underlying flow patternJet can be decoupled from underlying flow pattern

Reaction plane and v2 can be estimated for v2>=0.02 and Reaction plane and v2 can be estimated for v2>=0.02 and multiplicities >500multiplicities >500