1. RHIC results on cluster production in pp and heavy ion George S.F. Stephans Massachusetts Institute of Technology For the Collaboration

2. Workshop at RHIC&AGS Users’ Meeting 20091-June2George S.F. Stephans Collaboration Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland, Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Bolek Wysłouch ARGONNE NATIONAL LABORATORYBROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOWMASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWANUNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLANDUNIVERSITY OF ROCHESTER

3. Workshop at RHIC&AGS Users’ Meeting 20091-June3George S.F. Stephans Talk Roadmap  Introduction to correlations in  In the spirit of this workshop, I will concentrate on the more technical aspects of the correlations  Correlations using a “trigger” track with p T >2.5 GeV/c  Correlations between inclusive particles (no high p T cut)  Effects of limited pseudorapidity acceptance  Summary

4. Workshop at RHIC&AGS Users’ Meeting 20091-June4George S.F. Stephans Correlation Measurements In both cases: Associated particles detected in a single layer of silicon Broad η coverage (-3< η <3) No p T information !! p T >7 ( η =3)  35 MeV/c ( η =0) Inclusive Correlations: Pairs start with an inclusive particle detected in a single layer of silicon (-3< η <3) Triggered Correlations: “Trigger” particles detected in the Spectrometer (high p T trigger 0< η <1.5) The correlation functions are the suitably normalized ratio of signal (same-event pairs) over background (mixed-event pairs). The effect of elliptic flow is removed either by subtraction (triggered correlations) or by integrating over  (inclusive correlations).

5. Workshop at RHIC&AGS Users’ Meeting 20091-June5George S.F. Stephans Correlations with p T >2.5 GeV/c Trigger p T trig >2.5 GeV/c p T assoc > 4 - 35 MeV/c p+p(PYTHIA) NB: PYTHIA closely matches STAR data at mid-rapidity for a similar set of p T cuts arXiv:0903.2811 Au+Au 0-30% 200 GeV

6. Workshop at RHIC&AGS Users’ Meeting 20091-June6George S.F. Stephans Construction of Correlated Yield Raw correlation: ratio of per-trigger same event pairs to mixed event pairs Elliptic flow: V(Δη) = V(Δη) = Scale factor: accounts for small multiplicity difference between signal and mixed events a(Δη) B(Δη) Normalization term: relates flow-subtracted correlation to correlated yield + PHOBOS Phys. Rev. C 72, 051901(R) (2005)

7. Workshop at RHIC&AGS Users’ Meeting 20091-June7George S.F. Stephans Comments on Correlation Function  The normalization ( s and b normalized by the number of triggers) is designed to measure the “correlated yield” aspects of the data, i.e. the number of associated particles per unit phase space.  By definition and construction, the correlation function must be positive everywhere.  The effect of elliptic flow must be removed using a scale factor ( a (  ), very close to unity) which results from well- understood features of the data.

8. Workshop at RHIC&AGS Users’ Meeting 20091-June8George S.F. Stephans Subtraction of elliptic flow 0100100-100-1000 1 1.005 1.015 1.01 ΔφΔφ s(Δφ,Δη) b(Δφ,Δη) PHOBOS arXiv:0903.2811 -4 < Δη < -2-1 < Δη < 1 Elliptic Flow [deg] Short RangeLong Range [deg] a (  )

9. Workshop at RHIC&AGS Users’ Meeting 20091-June9George S.F. Stephans a( Δη ) Elliptic Flow Scale Factor ( a( Δη ) =ZYAM) 45-50% 40-45% 35-40% 30-35% 25-30% 20-25% 15-20% 10-15% 6-10% 3-6% 0-3% a(Δη) Δη ZYAM factors from 2d-fit in Δη and N part PHOBOS preliminary arXiv:0812.1172 (2008) Constant term: bias of the p T -triggered signal distribution to higher multiplicity Gaussian term: Δη correlation structure underneath v 2 -subtracted Δφ correlations. Width/amplitude/N part -dependence same as inclusive correlations (to be discussed in 2nd part of this talk) Constant term: bias of the p T -triggered signal distribution to higher multiplicity Gaussian term: Δη correlation structure underneath v 2 -subtracted Δφ correlations. Width/amplitude/N part -dependence same as inclusive correlations (to be discussed in 2nd part of this talk)

10. Workshop at RHIC&AGS Users’ Meeting 20091-June10George S.F. Stephans “Ridge” at small  : Extent in Δη Au+Au @ 200 GeV 0.25 Long-range ridge yield

11. Workshop at RHIC&AGS Users’ Meeting 20091-June11George S.F. Stephans Au+Au PYTHIA PHOBOS arXiv:0903.2811 Short- range |Δ  | <1 Long- range –4<Δ  <–2 0-10% 200 GeV Integrated Ridge Yield: |  |<1 vs  4<  <  2 # of participant nucleons (N part ) long-range (PYTHIA≈0) short-range minus PYTHIA NEAR side

12. Workshop at RHIC&AGS Users’ Meeting 20091-June12George S.F. Stephans # of participant nucleons (N part ) Au+Au 200 GeV arXiv:0903.2811 Integrated Ridge Yield: |  |<1 vs  4<  <  2 short-range minus PYTHIA NEAR side short-range, long-range both minus PYTHIA AWAY side long-range (PYTHIA≈0) Au+Au PYTHIA PHOBOS arXiv:0903.2811 200 GeV Short- range |Δ  | <1 Long- range –4<Δ  <–2

13. Workshop at RHIC&AGS Users’ Meeting 20091-June13George S.F. Stephans # of participant nucleons (N part ) Au+Au 200 GeV arXiv:0903.2811 Triggered Correlation Observations short-range minus PYTHIA NEAR side short-range, long-range both minus PYTHIA AWAY side long-range (PYTHIA≈0) Near side (small  ) ridge yield extends to at least |  |~4 Short-range (|  |<1) and long- range (-4<  <-2) ridge yields are very similar in size at all centralities Ridge disappears for N part below about 80 Excess yield on the away side (  ~  is also uniform in  and decreases for more peripheral collisions

14. Workshop at RHIC&AGS Users’ Meeting 20091-June14George S.F. Stephans Inclusive 2-Particle Correlations 66 Cu+Cu@200GeV -6 6 p+p@200GeVAu+Au@200GeV Phys. Rev. C75(2007)054913arXiv: 0812.1172 Project onto  axis and fit with a simple parameterization of a cluster model average over  PHOBOS p+p @ 200 GeV Phys. Rev. C75(2007)054913 

15. Workshop at RHIC&AGS Users’ Meeting 20091-June15George S.F. Stephans Comments on Correlation Function  The (n-1) normalization is included to specifically bring out the “cluster-like” aspects of the data.  The foreground and background distributions are independently normalized to unity so the correlation function will be positive or negative in regions where the former or the latter is larger.  Small regions where the foreground and background are comparable give R equal to zero. R would be zero everywhere if there were no correlations.  Elliptic flow is removed (for now) by averaging over  and only studying the correlation function versus .

16. Workshop at RHIC&AGS Users’ Meeting 20091-June16George S.F. Stephans Cluster-like Correlation Structure 6 Phys. Rev. C75(2007)054913 PHOBOS p+p@200GeV high p T clusters lower p T clusters -6

17. Workshop at RHIC&AGS Users’ Meeting 20091-June17George S.F. Stephans Cluster-Model Fit to Correlation Function scale error Phys. Rev. C75(2007)054913 K eff : effective cluster size  : cluster decay width PHOBOS K eff  1        

18. Workshop at RHIC&AGS Users’ Meeting 20091-June18George S.F. Stephans Inclusive Correlation Results Cluster sizes are large: Up to ~5 charged particles (after correction for  acceptance, see later discussion). and scale with the fraction of inelastic cross-section, rather than N part. Model studies suggest that centrality dependence is due to the hadronic cascade phase and that cluster size is strongly dependent on string fragmentation parameters observed sizes are too large to be reproduced by simple decay kinematics). HIJING does a poor job of reproducing the cluster properties of both p+p and A+A. Cluster sizes in p+p are low in HIJING (about 30% fewer associated particles). In A+A, cluster sizes in HIJING are comparable to those for semi-central but have little or no centrality dependence. 1-   Cluster size Cluster width 6 2 1.5 0.5 AMPT Cu+Cu 200 GeV Au+Au        

19. Workshop at RHIC&AGS Users’ Meeting 20091-June19George S.F. Stephans Expanded 2-Particle Correlation Result N part ~2050100200300 Au+Au @ 200 GeV N part ~2050100200300 Cluster sizeCluster width

20. Workshop at RHIC&AGS Users’ Meeting 20091-June20George S.F. Stephans Acceptance Effect on Correlations For A+A data in the range |  |<3, the correction is roughly a factor of 2 for the cluster size and 40% for the cluster width. Ratio |  |<3 over full acceptance Limited  range causes loss of correlated particles leading to smaller measured sizes and widths for the clusters. 1 Measured cluster width 00 11 0

21. Workshop at RHIC&AGS Users’ Meeting 20091-June21George S.F. Stephans Cluster Fits to MC in |  |<3 and |  | <1 |  |<3|  |<1 Identical MC independent cluster model events thrown into different detector acceptances and then fit with the simple cluster parameterization.

22. Workshop at RHIC&AGS Users’ Meeting 20091-June22George S.F. Stephans MC Study of Acceptance Effect Events from cluster model plus flow are fit with a multi-component parameterization (similar to arxiv:0806.2121v2) |  |<3 |  |<1 |  |<3 R(  ) MC correlationFitIndividual components

23. Workshop at RHIC&AGS Users’ Meeting 20091-June23George S.F. Stephans MC Study of Acceptance Effect Events from cluster model plus flow are fit with a multi-component parameterization (similar to arxiv:0806.2121v2) |  |<3 |  |<1 Note the almost complete disappearance of the 1D  component in the reduced acceptance case |  |<3 |  |<1 R(  ) MC correlationFitIndividual components

24. Workshop at RHIC&AGS Users’ Meeting 20091-June24George S.F. Stephans MC Study of Acceptance Effect Note the almost complete disappearance of the 1D  component in the reduced acceptance case |  |<3|  |<1 Events from cluster model plus flow are fit with a multi-component parameterization (similar to arxiv:0806.2121v2) R(  )

25. Workshop at RHIC&AGS Users’ Meeting 20091-June25George S.F. Stephans Summary  Correlations in Au+Au @ 200 GeV using a trigger particle with p T >2.5 GeV/c show a “ridge” of enhanced yield at small  which extends to at least |  =4  Appears to be a constant “ridge” under Pythia-like fragmentation  Effect seems to disappear for N part below about 80  Inclusive 2-particle correlations suggest that particles are emitted in very large “clusters” whose size scales with the geometry of the collision as opposed to N part  Quantitative interpretation of any correlation result needs to take into account the effect of  acceptance  For example comparing to models or comparing &

26. Backup Slides

27. Workshop at RHIC&AGS Users’ Meeting 20091-June27George S.F. Stephans Estimating the Flow Term Parameterize published PHOBOS data as v 2 (N part,p T,η) = A(N part ) B(p T ) C(η) Correct v 2 (N part,,η trig ) for occupancy and v 2 (N part,,η assoc ) for secondaries PHOBOS: PRC 72, 051901 V = +

28. Workshop at RHIC&AGS Users’ Meeting 20091-June28George S.F. Stephans Au+Au PYTHIA PHOBOS arXiv:0903.2811 Short-range |Δ  | <1 Long-range –4< Δ  <–2 Integrated Ridge Yield: |  |<1 vs  4<  <  2 0-10% Project 2D correlation onto  axis. Subtract out the Pythia peaks and then plot versus centrality for short- and long-range 200 GeV

29. Workshop at RHIC&AGS Users’ Meeting 20091-June29George S.F. Stephans Inclusive 2-Particle Methodology ForegroundBackground uncorrected : Secondary effects:  -electron,  conversion MC correction for secondary effects Occupancy corrections in A+A (multiplicity independent!) Two-particle correlation function: Event 1 Event 2 Foreground: F n  (correlated + uncorrelated pairs): Background: B n  (uncorrelated pairs):

30. Workshop at RHIC&AGS Users’ Meeting 20091-June30George S.F. Stephans Cluster Model Fit to Inclusive Correlations -5 5 Two-particle  correlation function Cu+Cu@200GeV Au+Au@200GeV 5-5 5 5 5 40%-50%30%-40%20%-30%10%-20%0%-10% (scale errors are shown as grey bands)

31. Workshop at RHIC&AGS Users’ Meeting 20091-June31George S.F. Stephans New Inclusive Correlation Result Au+Au @ 200 GeV: Peripheral collisions 65-70% 60-65% 55-60% 50-55% R(  ) R(  ) -5  5 

32. Workshop at RHIC&AGS Users’ Meeting 20091-June32George S.F. Stephans Inclusive Correlation Results         N part Cluster size Cluster width 6 2 1.5 0.5 Cluster sizes are large: Up to ~5 charged particles (after correction for  acceptance, see later discussion). Cu+Cu 200 GeV Au+Au AMPT

33. Workshop at RHIC&AGS Users’ Meeting 20091-June33George S.F. Stephans UA5 ISR HIJING PYTHIA PHOBOS Data vs. HIJING Expected from resonances (UA5 collaboration)

34. Workshop at RHIC&AGS Users’ Meeting 20091-June34George S.F. Stephans Expanded 2-Particle Correlation Result N part :2050100200300 Au+Au @ 200 GeV Not corrected for acceptance N part :2050100200300 Cluster sizeCluster width