Elliptic Flow Fluctuations with the PHOBOS detector Burak Alver - PowerPoint PPT Presentation

Elliptic Flow Fluctuations with the PHOBOS detector Burak Alver Massachusetts Institute of Technology v 2 fluctuations at PHOBOS Burak Alver - MIT

PHOBOS Collaboration Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek , Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Holynski, Burt Holzman, Aneta Iordanova, Jay Kane,Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith, Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs, Barbara Wosiek, Krzysztof Wozniak, Shaun Wyngaardt, Bolek Wyslouch ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER v 2 fluctuations at PHOBOS 2 Burak Alver - MIT

Motivation High v 2 observed in CuCu can be explained by fluctuations in initial collision region. Can we test the Participant Eccentricity Model? v 2 fluctuations at PHOBOS 3 Burak Alver - MIT

Expected fluctuations Assuming v 2 ∝ε ∝ε part , participant eccentricity model predicts v 2 fluctuations Expected σ v2 from fluctuations in ε part Data MC Au+Au v 2 fluctuations at PHOBOS 4 Burak Alver - MIT

Measuring v 2 Fluctuations • We have considered 3 different methods – 2 particle correlations → <v 2 2 > • c.f. S. Voloshin nucl-th/0606022 • σ v2 2 = <v 2 2 > - <v 2 > 2 • Do systematic errors cancel? – 2 particle correlations → v 2 2 event by event • Mixed event background generation is possible • Reduces fit parameters to 1 (no reaction plane) • Hard to untangle acceptance effects event by event – v 2 event by event • This is the method we are pursuing v 2 fluctuations at PHOBOS 5 Burak Alver - MIT

Measuring v 2 Fluctuations - Today’s Talk • Measuring v 2 event by event • Ongoing analysis on 200GeV Au-Au • Today – How we are planning to make the measurement – Studies on fully simulated MC events • Modified Hijing - Flow • Geant v 2 fluctuations at PHOBOS 6 Burak Alver - MIT

Method Overview - Simplified Example 2 possible v 2 values Event by Event measurement Demonstration Demonstration u =v 2obs. K b ( u ) K a ( u ) or u = v 2 2 obs. or u = q obs. V 2b V 2a V 2a V 2b Relative abundance in sample Observed u distribution in a sample f 1 Demonstration Demonstration g(u) f 2 Question: What is the relative abundance of 2 v 2 ’s in the sample? v 2 fluctuations at PHOBOS 7 Burak Alver - MIT

Method Overview - Simplified Example 2 possible v 2 values Event by Event measurement Demonstration Demonstration u =v 2obs. K b ( u ) K a ( u ) or u = v 2 2 obs. or u = q obs. V 2b V 2a V 2a V 2b Relative abundance in sample Measured u distribution in a sample f 1 Demonstration Demonstration g( u ) f 2 Question: What is the relative abundance of v 2a to v 2b in the sample? v 2 fluctuations at PHOBOS 8 Burak Alver - MIT

Method Overview - Simplified Example 2 possible v 2 values Event by Event measurement Demonstration Demonstration u =v 2obs. K b ( u ) K a ( u ) or u = v 2 2 obs. or u = q obs. V 2b V 2a V 2a V 2b Extracted v 2true distribution from sample Measured u distribution in a sample f a Demonstration Demonstration g( u ) f b V 2a V 2b Question: What is the relative abundance of v 2a to v 2b in the sample? g( u )=f a K a ( u ) + f b K b ( u ) v 2 fluctuations at PHOBOS 9 Burak Alver - MIT

Method Overview Kernel In real life v 2 can take 200 GeV AuAu u =v 2obs. Modified Hijing+Geant a continuum of values K( u ,v 2 ) Extracted v 2true distribution from sample Measured u distribution in a sample 200 GeV AuAu Modified Hijing+Geant f(v 2 ) g( u ) v 2 fluctuations at PHOBOS 10 Burak Alver - MIT

Method Overview • 3 Tasks – Measure u event-by-event g( u ) – Calculate the kernel K( u ,v 2 ) – Extract dynamical fluctuations f(v 2 ) v 2 fluctuations at PHOBOS 11 Burak Alver - MIT

PHOBOS Detector • PHOBOS Multiplicity Array -5.4< η <5.4 coverage -Holes / granularity differences • Idea: Use all available information in event to read off single u value HIJING + Geant dN/d η Hit Distribution 15-20% central Primary particles Hits on detector v 2 fluctuations at PHOBOS 12 Burak Alver - MIT

Measuring u=v 2obs Event by Event I • Probability Distribution Function (PDF) for hit positions: Probability of hit in η Probability of hit in φ PDF u demonstration • Define likelihood of u and φ 0 for an event: v 2 fluctuations at PHOBOS 13 Burak Alver - MIT

Measuring u=v 2obs Event by Event II • Maximize likelihood to find “most likely” value of u • Comparing values of u and φ 0 – In an event, p( η i ) is same for all u and φ 0 . – PDF folded by acceptance must be normalized to the same value for different u and φ 0 ’s Acceptance v 2 fluctuations at PHOBOS 14 Burak Alver - MIT

Measuring u=v 2obs Event by Event II • Maximize likelihood to find “most likely” value of u • Comparing values of u and φ 0 – In an event, p( η i ) is same for all u and φ 0 . – PDF folded by acceptance must be normalized to the same value for different u and φ 0 ’s Acceptance v 2 fluctuations at PHOBOS 15 Burak Alver - MIT

Measuring u=v 2obs Event by Event III Observed u distribution in a sample Mean and RMS of u in slices of v 2 200 GeV AuAu Modified Hijing+Geant g( u ) Error bars show RMS 200 GeV AuAu Modified Hijing+Geant Next Step: Construct the Kernel to unfold g( u ) v 2 fluctuations at PHOBOS 16 Burak Alver - MIT

Calculating the Kernel I • Simple: Measure u distribution in bins of v 2 • 2 small complications – Kernel depends on multiplicity: K( u ,v 2 , n ) • n = number of hits on the detector • Measure u distribution in bins of v 2 and n . – Statistics in bins can be combined by fitting smooth functions 200 GeV AuAu Modified Hijing+Geant v 2 fluctuations at PHOBOS 17 Burak Alver - MIT

Calculating the Kernel II • In a single bin of v 2 and n u distribution with for fixed v 2 and n 200 GeV AuAu Modified Hijing+Geant (a, b) ↔ (< u >, σ u ) • Distribution is not Gaussian • But can be parameterized by < u > and σ u v 2 fluctuations at PHOBOS 18 Burak Alver - MIT

Calculating the Kernel III • Measure < u > and σ u in bins of v 2 and n • Fit smooth functions K( u ,v 2 , n ) 200 GeV AuAu Modified Hijing+Geant 200 GeV AuAu K( u ,v 2 , n ) Modified Hijing+Geant v 2 fluctuations at PHOBOS 19 Burak Alver - MIT

Calculating the Kernel IV • Multiplicity dependence can be integrated out K( u ,v 2 , n ) 200 GeV AuAu Modified Hijing+Geant K( u ,v 2 ) 200 GeV AuAu Modified Hijing+Geant N( n ) = Number hits distribution in sample v 2 fluctuations at PHOBOS 20 Burak Alver - MIT

Extracting dynamical fluctuations known ? v 2 fluctuations at PHOBOS 21 Burak Alver - MIT

Extracting dynamical fluctuations known ? Ansatz with two parameters: Ansatz for f(v 2 ) ansatz Ansatz v 2 fluctuations at PHOBOS 22 Burak Alver - MIT

Extracting dynamical fluctuations known ? Ansatz with two parameters: Ansatz for f(v 2 ) Expected g( u ) for Ansatz ansatz Ansatz 200 GeV AuAu Modified Hijing+Geant integrate v 2 fluctuations at PHOBOS 23 Burak Alver - MIT

Extracting dynamical fluctuations known ? Ansatz with two parameters: Ansätze for f(v 2 ) Expected g( u ) for Ansätze ansatz 200 GeV AuAu Modified Hijing+Geant integrate v 2 fluctuations at PHOBOS 24 Burak Alver - MIT

Extracting dynamical fluctuations known ? Ansatz with two parameters: Ansätze for f(v 2 ) Comparison with sample ansatz 200 GeV AuAu Modified Hijing+Geant integrate Compare expected g(u) for Ansatz with measurement Minimum χ 2 → <v 2 > and σ v2 v 2 fluctuations at PHOBOS 25 Burak Alver - MIT

Method Summary K( u ,v 2 , n ) MC MC Many MC events integration N( n ) K( u ,v 2 ) MC MC A Small Sample measurement l a r g f in (v 2 ) e t n i n i χ 2 χ <v 2 >=0.05 e z i m i n i M σ v2 =0.02 MC MC <v 2 >=0.048 measurement σ v2 = 0.023 g( u ) f out (v 2 ) v 2 fluctuations at PHOBOS 26 Burak Alver - MIT

Verification • Ran this analysis on Modified Hijing – v 2 ( η ) = v 2 (0) • (1-| η |/6) • Same as the assumption in our fit – v 2 (0) given by a Gaussian distribution in each sample • Same as our Ansatz – Analysis done in 10 collision vertex bins • Final results are averaged – 0-40% central events used to construct Kernel – 15-20% central events used as sample v 2 fluctuations at PHOBOS 27 Burak Alver - MIT