1. 1 The transition observed in two- dimensional correlation data from STAR Lanny Ray University of Texas at Austin STAR Collaboration Outline:  p-p phenomenology  Centrality evolution  Same-side structures  Away-side ridge  Implications Tamura Symposium – Nov. 20-22, 2008

2. 2 Begin with proton-proton spectra Two-component soft + (semi)hard model: PRD 74, 032006 (nucl-ex/0606028) 200 GeV p t spectra for increasing N ch “soft” “semi-hard” + pQCD hard… S pp replot on “transverse rapidity” Data – S pp semi-hard component: gaussian on y t

3. 3 measures number of correlated pairs per final state particle Event 1 Event 2 ρ sibling ( p 1,p 2 ) ρ reference ( p 1,p 2 ) Correlation measure normalized ratio of 2D binned histograms; acceptance cancellation; two-track ineff. corrections square-root of  ref (a,b); (for  space) Fill 2D histograms (a,b), e.g. (  1,  2 ), (  1,  2 ), (  1 -  2,  1 -  2 ), (p t1,p t2 ), etc. ρ( p 1,p 2 ) = 2 particle density Motivated by p-p superposition null hypothesis

4. 4 SOFT component – Levy Distribution HARD component – Gaussian on y t (!) Peak y t =2.66 y t =2.66 p t ~ 0.5 p t ~ 1.0 p t ~ 2.0 y t1 y t2 PRD 74, 032006 Proton-Proton: from spectra to correlations STAR Preliminary

5. 5 y t1 y t2 p-p transverse correlations ηΔηΔ φΔφΔ p-p axial correlations semi-hard component ηΔηΔ φΔφΔ soft component ηΔηΔ φΔφΔ Longitudinal Fragmentation: 1D Gaussian on η Δ HBT peak at origin, LS pairs only Minijets: 2D Gaussian at origin plus broad away-side peak: -cos( φ Δ ) We hypothesize that this structure is caused by semi-hard partonic scattering & fragmentation - minijets Proton-Proton components STAR Preliminary

6. 6 Why minijets? Jets observed by UA1 down to 5 GeV/c in p-pbar collisions at sqrt{s} = 200 – 900 GeV; accounted for with pQCD; angular correlations and p t structures are “jet-like.” C. Albajar (UA1) Nucl. Phys. B 309, 405 (1988) pQCD calc.

7. 7 Why minijets? STAR observes correlated charged hadron pairs with p t ~ 1 – 1.5 GeV/c corresponding to typical parton p t of order >(3/2)(2)(1 – 1.5) = 3-4.5 GeV/c, well within reach of the UA1 data and pQCD descriptions. In Au-Au we cannot hope to identify these low p t jets directly. There is also no identifiable trigger particle at lower p t ; thus we use both angular and (p t1,p t2 ) correlations as suggested by Xin-Nian Wang a long time ago (Phys. Rev. D 46, R1900 (1992)). How would these low p t, minimum-bias jets, or minijets, appear in our 2D (  ) angular correlations?

8. 8 proton NN cm parton-parton cm Jet-A Jet-B        0  Number of pairs A-A B-B A-B B-A Number of pairs     0 A-A B-B A-BB-A sum over many events small angle peak large azimuth peak Φ 1 - Φ 2 η 1 - η 2 p-p 200 GeV STAR preliminary Example: di-jets

9. 9 X.-N.Wang and M. Gyulassy implemented the UA1 observations into their Monte Carlo code HIJING (w. PYTHIA) (Phys. Rev. D 44, 3501 (1991)) using standard PDFs, pQCD parton-parton cross sections, and fragmentation functions. p + p at 200 GeV STAR Preliminary Minijets in HIJING & PYTHIA In this analysis “minijets” are simply jets with no low p t cut-off. Hijing Jets on Hijing Jets off additional sharp peak: HBT, conversion electrons       soft p t pairs removed

10. 10 Centrality evolution of the 2D correlations (Expectation is that minijets will be thermalized.)

11. 11 84-93% 28-38% 74-84% 18-28% 64-74%55-64%46-55% 9-18% 5-9%0-5% proton-proton note: 38-46% not shown We observe the evolution of several correlation structures including the same-side low p t ridge ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ Analyzed 1.2M minbias 200 GeV Au+Au events; included all tracks with p t > 0.15 GeV/c, |η| < 1, full φ STAR Preliminary 200 GeV Au-Au data From M. Daugherity’s Ph.D Thesis (2008)

12. 12 Proton-Proton fit function =+ STAR Preliminary longitudinal fragmentation 1D gaussian HBT, e+e- 2D exponential ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ Au-Au fit function Use proton-proton fit function plus cos(2φ Δ ) quadrupole term (~ elliptic flow). Note: from this point on we’ll include entire momentum range instead of using soft/hard cuts ηΔηΔ φΔφΔ dipole quadrupole cos(2φ Δ ) Fit function Same-side “Minijet” Peak, 2D gaussian Away-side -cos(φ) “soft”“hard”

13. 13 Centrality and energy trends Au-Au at 62 and 200 GeV 200 GeV 62 GeV 200 GeV 62 GeV STAR Preliminary From M. Daugherity’s Ph.D Thesis (2008) Transition

14. 14 Same-side correlation structure   <  /2 The “soft” ridge

15. 15 Deviations from binary scaling represent new physics unique to heavy ion collisions Binary scaling: Kharzeev and Nardi model 200 GeV 62 GeV constant widths STAR Preliminary Peak AmplitudePeak η WidthPeak φ Width Same-side 2D Gaussian & binary scaling - AuAu Statistical and fitting errors as shown Systematic error is 9% of correlation amplitude peripheralcentral HIJING 1.382 default parameters, 200 GeV, quench off

16. 16 Same-side 2D Gaussian amplitude,  -width, volume scale with particle density Peripheral bins are compressed. Peak Amplitude N part Peak η Width STAR Preliminary 200 GeV 62 GeV Depends on formation time (assumed 1 fm/c), difficult to compare energies. ε BJ Peak AmplitudePeak η Width Bjorken Energy Density STAR Preliminary 200 GeV 62 GeV Transverse Particle Density Peak amplitude  width  aspect ratio volume S = overlap area (Monte Carlo Glauber) STAR Preliminary Does the transition point scale?

17. 17 p t correlations follow binary scaling well past the transition Numberptpt J Phys G 32 L37 = inclusive mean p t 2D angular correlations for p t This leads to the hypothesis that semi-hard partons continue to underlie the same-side gaussian number correlations above the transition. 200 GeV Au+Au p T minijet peak 0-30% centrality Same-side amplitude and widths

18. 18 (y t1,y t2 ) correlations for same-side pairs Like Sign Unlike Sign STAR Preliminary Au-Au 200 GeV HBT peripheral central pp minijets persist; p t dissipation From M. Daugherity’s Ph.D Thesis (2008)

19. 19 Away-side correlation structure   >  /2 The away-side ridge

20. 20 The dipole matches the centrality dependence of the same-side gaussian and shows the same transition point. It’s origin is p t conservation: global + jets Away-side ridge (dipole) – local p t conservation calculated global p t conservation Low-x parton K T ~ 1 GeV/c pzpz Q ~ 2 GeV minijets, nucleon K T, acoplanarity Low-x parton 200 GeV 62 GeV φΔφΔ 0 0  φΔφΔ -3  -   3  K T broadening 0  events 1,2,3… sum events away-side STAR Preliminary Hijing – jets on (no soft p t )

21. 21 (y t1,y t2 ) correlations for away-side pairs Au-Au 200 GeV Like Sign Unlike Sign pp STAR Preliminary peripheral central minijets persist; p t dissipation minijets From M. Daugherity’s Ph.D Thesis (2008)

22. 22 Elliptic flow measurement using 2D (  ) correlations

23. 23 Quadrupole component (~ elliptic flow) Datacos(2φ Δ ) component 62 and 200 have the same shape Substantial amp. change with energy no transition 200 GeV 62 GeV ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ Amplitudes D. Kettler, T. Trainor arXiv:0704.1674 The η-dependence separates quadrupole (v 2 ) from non-flow STAR Preliminary quadrupole determined by initial conditions; medium (EoS, viscosity) not relevant. Initial state QCD source for v 2 : Boreskov et al., arXiv:0809.0625 [hep-ph] Kopeliovich et al., arXiv:0809.4327 [hep-ph] Au-Au

24. 24 Implications for theory and phenomenology

25. 25 Expected behavior: Comparison with data: Implications: superposition model  Minijet shape unchanged, amplitude follows binary scaling.  Minijet peak on (y t,y t ) unchanged except for amplitude. Superposition model approximates data to the transition point but radically fails at higher density, more central collisions. STAR Preliminary

26. 26 Minijets & Quadrupole Below the transition the Au-Au system appears transparent, i.e. no collisional pressure build-up, no flow, at least up to the transition point. What mechanism(s) produces a smooth v 2 ? expected v 2 ? STAR Preliminary

27. 27 Comparisons with data: Implications: opaque, thermalized medium  Semi-hard partons thermalize, sound waves(?) – but number correlations disperse  p t correlations on  disperse  Minijet peak on (y t,y t ) dissipated Peak Volume 8x increase STAR Preliminary 200 GeV 62 GeV Narrowing azimuth width 1 2 Any new mechanism above the transition must seamlessly match minijets. p T minijet peak 0-30% central Minijet correlation region in (y t,y t ) remains strong 3 Observations contradict expectations for a rapidly thermalized system. Semi-hard partons persist; number correlations do not vanish, but increase dramatically. Expected behavior of minijets:

28. 28  p t correlations remain  (y t,y t ) dissipates but amplitude remains at minijet y t  same-side 2D Gaussian remains  However, same-side yield decreases unless enough hadrons from surface are correlated with minijet.  Some jets will lose away-side partner, reducing –cos(   ) away-side p t escapes, but is dispersed among many more pairs Implications: opaque core + hadronic corona Expected behavior: Comparison with data: Ratio of away-side ridge to same-side Gaussian is ~constant from peripheral to most-central; data are inconsistent with this scenario

29. 29 beam z time novel QCD environment hadrons increasing   correlation width means earlier source if more central is hydro But the “soft-ridge” implies more: For more central collisions the 2D Gaussian correlation must have an earlier source when the system is supposedly opaque (Perfect Liquid). Rather than diminish, the same-side correlations increase! Minijets & Quadrupole

30. 30 Theoretical models – same-side ridge  Chiu and Hwa, Phys. Rev. C72, 034903 (2005) – Jet driven; recombination; hot spots pushed out by radial flow.  Voloshin, Nucl. Phys. A749, 287c (2005); Shuryak, Phys. Rev. C76, 047901 (2007) – beam-jet fragments pushed out by radial flow.  S. Gavin, Phys. Rev. Lett. 97, 162302 (2006) – initial state energy fluctuations spread along  by shear viscosity; pushed out by radial flow.  Dumitru, Gelis, McLerran, Venugopalan, arXiv:0804.3858[hep-ph] - glasma flux tubes pushed out by radial flow. None explain all the observations:  Majumder et al., Phys. Rev. Lett. 99, 042301 (2007); Dumitru et al., arXiv:0710.1223 [hep-ph] - Jet driven with plasma instability  C.-Y. Wong, Phys. Rev. C76, 054908 (2007) – Jet driven “momentum kick” model. smooth extrapolation to p-p limit away-side ridge transition point narrowing width on azimuth

31. 31 Implications for phenomenology Novel QCD field: forward scattered debris (diffractive), glasma flux tubes,… Below the transition the system is transparent to semi-hard scattered partons. Above the transition p t transport begins suddenly. Correlations on z map to width increase on  Azimuth width is constant if only p t is transported. p t correlations are preserved. pzpz Results suggest p t transport which suddenly turns on at a critical density.

32. 32 Summary and Conclusions  Same-side 2D Gaussian (minijets) follows binary scaling, then a remarkable transition occurs which scales in Au-Au with transverse particle density.  The away-side ridge is crucial to understanding the RHIC data; it shows a transition, follows the minijet amplitude, and may be explained in terms of recoiling minijets.  Momentum dissipation is evident yet minijet correlation structures persist to most-central.  Preponderance of correlation data contradict expectations based on strong, random scattering such as in rapid thermalization scenarios.  The data suggest novel QCD processes in which p t transport/emission suddenly increases and v 2 is generated in the initial stage.