Application of multi-resolution method on flow measurement in CBM Vojtech Petracek GSI – CBM week

Outline Motivation – event-by-event reaction plane & v2 & fluct. Motivation – event-by-event reaction plane & v2 & fluct. Fluctuations in event shape – statistics, fireball instability and granularity, jets... Fluctuations in event shape – statistics, fireball instability and granularity, jets... Event-by-event fluctuation in particle density in 1D and 2D Event-by-event fluctuation in particle density in 1D and 2D Multi-resolution analysis of particle density fluctuations Multi-resolution analysis of particle density fluctuations Strategy of domain analysis Strategy of domain analysis Reaction plane and v2 parameters Reaction plane and v2 parameters Summary & outlook Summary & outlook

Elliptic flow measurement & background ? Elliptic flow reflects the original geometry of the collision zone We measure azimuthal anisotropy in Pt,y slice of the phase space Background : stat. fluctuations, fireball granularity, jets Apart of statistical fluctuations even the background is an interesting signal

Can we detect the critical point from fluctuations? Onset of spinodal instability for larger  ? Source structure in crossover region (bags) ? Source structure in crossover region (bags) ? B. Tomasik CBM

Fireball instability Fast cooling can bring the system to the unstable configuration Fast cooling can bring the system to the unstable configuration Fireball decomposes as it reaches the spinodal point Fireball decomposes as it reaches the spinodal point Cooling must be fast bubble nucleation rate < expansion rate Cooling must be fast bubble nucleation rate < expansion rate V B. Tomasik

Granular fireball Fireball can decompose to spherical droplets Fireball can decompose to spherical droplets Or to objects with more complicated shapes with larger surface/volume ratio Or to objects with more complicated shapes with larger surface/volume ratio Or nothing like that happens Or nothing like that happens Can we distinguish between these options -> MRA Can we distinguish between these options -> MRA Can we eliminate jet background -> MRA Can 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)‏ MRA method uses 2D Cauchy-Lorentz function We can observe  -  particle density distribution with different resolution We can observe  -  particle density distribution with different resolution We can characterize fluctuation between different resolutions We can characterize fluctuation between different resolutions

Example - MRA in 1D This method can isolate large scale structures which would be otherwise hidden in noise which would be otherwise hidden in noise Jets, DCC, elliptic flow pattern, reaction plane.. If 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 distribution recursively the original density distribution like in wavelet transform like in wavelet transform Compared to the discrete wavelet transformation method this approach transformation method this approach doesn’t have problem with domain splitting doesn’t have problem with domain splitting

Mother & Father functions Mother functions L smooth the high freq. noise Mother functions L smooth the high freq. noise Father functions F determine the fluctuation between the two resolution scales Father functions F determine the fluctuation between the two resolution scales Original domain is optimally reproduced when its characteristic scale coincide with resolution Original domain is optimally reproduced when its characteristic scale coincide with resolution L1L2F12

Event-by-event fluctuation domain detection Events with isotropic particle distribution are used for the detection threshold calibration Events with isotropic particle distribution are used for the detection threshold calibration Threshold is set to 2 , so that ~5% of random signal is above it Threshold is set to 2 , so that ~5% of random signal is above it Events containing non-statistical local fluctuations in particle density will have the fraction of signal above the threshold significantly higher Events containing non-statistical local fluctuations in particle density will have the fraction of signal above the threshold significantly higher When we Pt weight the MF, this way the jet area can be When we Pt weight the MF, this way the jet area can be detected as area of higher than average Pt detected as area of higher than average Pt

Example of droplet reconstruction in MF 2D analysis Characteristic droplet dimensions dimensions ~ 0.5y x Pi/4 For small number of droplets (<20) is possible droplets (<20) is possible direct droplet counting direct droplet counting For larger numbers droplets merge droplets merge

Individual droplet FF 2D analysis When the direct droplet counting is possible, the counting is possible, the best estimate is the # best estimate is the # of maxima in FF over of maxima in FF over certain threshold certain threshold

Droplets & the event fluctuation Distribution of fraction of the area covered by detected domain Distribution of fraction of the area covered by detected domain Red : 100% particles from droplets Red : 100% particles from droplets Green : 0% particles from droplets Green : 0% particles from droplets Scale 2 Scale 2

Jet reconstruction Example of jet reconstruction using the described MRA method Pt weighting – necessary !! Pt*N ~ Et-Jet Mean Pt map <Pt>(eta,phi)=<Pt*N>(eta,phi)/<N>(eta,phi)‏

Strategy of event analysis Compare  P in domains to surrounding => identify jet Compare  P in domains to surrounding => identify jet Check the charge symmetry. Asymmetry => DCC Check the charge symmetry. Asymmetry => DCC Density fluctuation due to the droplet Density fluctuation due to the droplet Eliminate jet – replace by surrounding background Eliminate jet – replace by surrounding background Analyze event shape for reaction plane & v2 Analyze event shape for reaction plane & v2

What v2 we want to measure Expected elliptic flow in CBM NA49 – PRC 68, (2003)‏ A. Wetzlar 2005 Below 10% for high Pt particles Complicated event-by-event but when reaction plane is determined events can be combined CBMCBM

Examples of reaction plane and v2 reconstruction event-by-event Reaction plan 300 tracks, v2 =0.1 Reconstruction of reaction plane angle easy and stable at all scales precission of RP estimate from spread between fits at different scales v2 can be reconstructed

Examples of reaction plane and v2 reconstruction event-by-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 and v2 reconstruction event-by-event Reaction plan 500 tracks v2=0.02 In this case is the statistical fluctuation comparable to the signal RP estimate less precise but still stable v2 ? RP reconstruction is stable -> events can be combined for v2 measurement

Examples of reaction plane and v2 reconstruction event-by-event Reaction plan 1000 tracks v2=0.02 RP reconstruction stable on most scales v2 in single event not reliable -> combine events when RP is reconstructed consistently on all scales

Summary & outlook Area of the ,  plane covered by domains with non-statistically high particle density fluctuation is a robust measure which can be used for detection of events with granular source responsible at least for 20% of particle production (for 100 fm 3 droplets)‏ Area of the ,  plane covered by domains with non-statistically high particle density fluctuation is a robust measure which can be used for detection of events with granular source responsible at least for 20% of particle production (for 100 fm 3 droplets)‏ For small number of droplets the direct droplet counting is possible For small number of droplets the direct droplet counting is possible Dijet reconstruction using the Pt weight works reliably in HI environment for jets with Et>~30 GeV Dijet reconstruction using the Pt weight works reliably in HI environment 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-event event-by-event Deflection of fragmentation products by the radial and longitudinal flow and resulting medium response need more study => Mach cone ! Deflection of fragmentation products by the radial and longitudinal flow and resulting medium response need more study => Mach cone ! Jet can be decoupled from underlying flow pattern Jet can be decoupled from underlying flow pattern Reaction plane and v2 can be estimated for v2>=0.02 and multiplicities >500 Reaction plane and v2 can be estimated for v2>=0.02 and multiplicities >500