1. 1 Observation of dramatic transition in 2D correlation data Lanny Ray For the STAR Collaboration University of Texas at Austin April 7, 2008 24 th Winter Workshop on Nuclear Dynamics Outline:  Definitions and p-p reference  Au-Au data – surprising results  Implications & Speculations

2. 2 Introduction and Overview Our philosophy: determine a “complete” map of the 2-particle correlations in p-p and A+A collisions, then interpret. Correlations are sensitive to physical processes: e.g. parton scattering and fragmentation (jets & minijets), elliptic flow, resonances, HBT, etc. Each source generally makes a unique contribution, facilitating decomposition and interpretation. A surprising trend in same-side correlations was found and first reported at QM 2008 (M. Daugherity, University of Texas, for STAR). The implications of these new results suggest a different scenario from the ubiquitous, rapid thermalization hydrodynamic models for the bulk collision environment at RHIC.

3. 3 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 Data – S pp semi-hard component: gaussian on y t replot on “transverse rapidity”

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: spectra to correlations STAR Preliminary

5. 5 Δρ as a histogram on bin (a,b): Normalize measures number of correlated pairs per final state particle ρ( p 1,p 2 ) = 2 particle density in momentum space Event 1 Event 2 ρ sibling ( p 1,p 2 ) ρ reference ( p 1,p 2 ) ε = bin width, converts density to bin counts Start with a standard definition in statistics: Correlation Measure

6. 6 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

7. 7 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 from peripheral to central Au+Au 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

8. 8 84-95% 28-37% 75-84% 18-28% 65-75%56-65%46-56% 9-18%5-9%0-5% note: 37-46% not shown Analyzed 13M 62 GeV Au+Au minbias events; included all tracks with p T > 0.15 GeV/c, |η| < 1, full φ 62 GeV Au-Au Data A similar evolution appears but is delayed on centrality relative to the 200 GeV data. STAR Preliminary

9. 9 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 + cos(2φ Δ ) quadrupole term (“flow”). This gives the simplest possible way to describe Au+Au data. 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 (5 easy pieces) Same-side “Minijet” Peak, 2D gaussian Away-side -cos(φ) “soft”“hard”

10. 10 Deviations from binary scaling represent new physics unique to heavy ion collisions Binary scaling: Kharzeev and Nardi model 200 GeV 62 GeV small increase before transition constant widths STAR Preliminary Peak AmplitudePeak η WidthPeak φ Width Same-side 2D gaussian & binary scaling Note the absence of a transition point in the quadrupole: v 2 & elliptic flow STAR Preliminary Statistical and fitting errors as shown Systematic error is 9% of correlation amplitude peripheralcentral

11. 11 The observed minijet correlation is much larger than HIJING (factor of 4) HIJING 1.382 default parameters, 200 GeV, quench off Quench on causes slight amplitude decrease 200 GeV 62 GeV STAR Preliminary Peak AmplitudePeak η WidthPeak φ Width mid (40-50%) very little centrality dependence HIJING minijet predictions HIJING 1.382 φΔφΔ ηΔηΔ

12. 12 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 Dipole – transverse momentum conservation Global p t conservation Low-x parton K T ~ 1 GeV/c pzpz Q ~ 2 GeV/c 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

13. 13 Same-side gaussian amplitude and  -width 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 AmplitudePeak η Width S = overlap area (Monte Carlo Glauber) STAR Preliminary 200 GeV 62 GeV Does the transition point scale?

14. 14 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

15. 15 Peak Volume 8x increase STAR Preliminary 200 GeV 62 GeV See also T. Trainor, arXiv:0710.4504, accepted to J Mod Phys E Multiplicity fractions – same-side gaussian 1) Probability that minbias p-p collision produces semi-hard parton: 2) Number of semi-hard partons in Au-Au assuming binary scaling (p t correlations) 3) Total number of same-side 2D gaussian correlated pairs per event: 4) Number of final state particles associated with each semi-hard parton: 5) Fraction of total multiplicity associated with same-side gaussian correlation: For central Au+Au we estimate about 30%; a significant fraction of the bulk particles.

16. 16 Sudden onset at lower y t corresponding to transition point for same-side gaussian. proton-proton How the correlations evolve in transverse momentum Correlations remain at original y t – surface jets? increase at higher y t. (y t,y t ) correlations, 200 GeV Au+Au (peripheral) (central) STAR Preliminary (protons: see arXiv:0710.4504)

17. 17 Expected behavior: Comparison with data: Implications: Superposition model  Minijets unchanged, except amplitude increases with binary scaling; widths remain constant.  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

18. 18 Expected behavior: Comparison with data: Implications: parton/hadron scattering model  Widths of both number and p t angular correlations increase  Amplitude of p t correlation falls below binary scaling  Minijet peak on (y t,y t ) dissipates to lower momentum  widths increase but  widths decrease p t correlation amplitude follows binary scaling beyond transition; doesn’t decrease until here Minijet peak dissipates, strength remains at original y t, increases at higher y t 1 3 2 p T minijet peak 0-30% central

19. 19 Expected behavior: Comparison with data: Implications: opaque, thermalized medium  Semi-hard partons stopped; produce local hot spots; isotropic thermal motion - number angular correlations vanish, radially flowing hot spots could produce correlations [e.g. +cos(   )].  momentum conserved - p t correlations on  may persist  Minijet peak on (y t,y t ) completely dissipated; saddle shape appears at lower p t (J.Phys.G 34, 799) Semi-hard partons persist; number correlations do not vanish, but increase dramatically. Peak Volume 8x increase STAR Preliminary 200 GeV 62 GeV Narrow azimuth width from p-p to central Au-Au, no transition point. 1 2  width initially due to minijets. If more central dominated by other mechanisms, the latter must seamlessly match minijets. STAR Preliminary p T minijet peak 0-30% central

20. 20 Implications: opaque, thermalized medium The minijet correlation region in (y t,y t ) does not vanish, but increases and extends to higher y t ; a saddle shape develops (see J.Phys.G 34, 799) Comparison with data (cont.): 3 The observed correlations contradict expectations for a rapidly thermalized system. peripheral central 200 GeV Au+Au 4 Boosted hot spots produce +cos(   ) correlations; opposite sign to data  STAR Preliminary

21. 21 beam z time (lab) pre-hadrons hadrons Interpretation: below the transition point scattered parton moderate scattering and dissipation minijet fragmentation with moderate   width increase approximate binary scaling STAR Preliminary What causes the reduction in azimuth width? Perhaps there is a competition between collisional broadening and an unknown narrowing mechanism which affects low-pt and depends on the first few N-N collisions.

22. 22 scattered parton earlier, stronger momentum dissipation parton fragments plus correlated hadrons spread over much larger   range Interpretation: above the transition point (personal speculation) beam z time novel QCD environment hadrons larger   width STAR Preliminary Why does the  width remain narrow? Somehow the scattered parton’s azimuth direction of motion is transferred to the bulk hadrons which are associated/correlated with it. STAR Preliminary

23. 23 Implications for phenomenology Novel, 1D Hubble expanding gluon field (in co-moving frame of parton) transverse momentum loss; no change in direction p t transfered to gluons along z-coordinate correlation along z maps to width increase on  p t not transferred on , azimuth width stays constant increased number of correlated pairs p t correlations preserved But what causes the interaction with the gluon field to suddenly change at the transition ? (personal speculation) pzpz

24. 24 Summary and Conclusions  Angular correlations on (  ) were shown for Au+Au collisions at 62 and 200 GeV: large structures associated with semi-hard partons/fragments, dipole and quadrupole.  The same-side 2D peak follows binary scaling (minijets) until an abrupt transition: number of correlated pairs and  -width increase dramatically;  -width decreases.  The quadrupole, typically interpreted as elliptic flow, does not show the transition.  The transition point occurs at the same transverse particle density at 62 and 200 GeV.  Increased correlations appear due to more soft hadrons being correlated with scattered partons, rather than due to more correlated groups, or clusters (beyond binary scaling).  Up to ~30% of the final state hadrons in central Au+Au are associated with the same-side 2D correlation peak.  These angular correlations together with p t angular and (y t,y t ) correlations contradict expectations based on rapid thermalization; but do indicate strong modifications of parton scattering and fragmentation.  Phenomenological implications of these results are suggested.

25. 25 Extra Slides

26. 26 200 GeV Model 26 ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ STAR Preliminary Fit model 84-93% 28-38% 75-84% 19-28% 65-75%55-65%46-55% 9-19%5-9%0-5%

27. 27 200 GeV Residual 27 Fit residual = data - model We have a good fit with the simplest possible fit function. Other than adding the cos(2φ Δ ) quadrupole term, no other modification was necessary. ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ STAR Preliminary 84-93% 28-38% 75-84% 19-28% 65-75%55-65%46-55% 9-19%5-9%0-5%

28. 28 peripheral central Observations Amplitude and η widths start small and experience a sharp transition Transition occurs at ~55% centrality at 200 GeV, is more central (~40%) for 62 φ width has a very different centrality dependence STAR Preliminary X-axis shows mean participant path-length 200 GeV 62 GeV Statistical and fitting errors as shown Systematic error is 9% of correlation amplitude STAR Preliminary Peak AmplitudePeak η WidthPeak φ Width Same-side 2D gaussian

29. 29 Does interaction between same-side peak and cos(φ Δ ) terms cause the transition? fix cos(φ Δ ) and cos(2φ Δ ) on away-side then fit remaining terms The results are consistent Cancellation in fit terms does not cause the amplitude increases. Two-stage fit: Result 200 GeV: standard, two-stage fit cos(φ Δ )cos(2φ Δ ) minijet peakminijet η width ν ν ν ν Consistency Check

30. 30 Does the transition from narrow to broad η Δ occur quickly or slowly? data - fit (except same-side peak) Shape changes little from peripheral to the transition The transition occurs quickly STAR Preliminary 83-94%55-65% Large change within ~10% centrality 46-55% Smaller change from transition to most central low-pt manifestation of the “ridge” 0-5% η Δ width Transition – close-up

31. 31 Suite of correlation and differential spectra measures: Three example scenarios for RHIC collision environments: Focus attention on the 2D same-side gaussian Implications: measures and media Number of pair correlations on relative angles: (     ) p t correlations on (     ) 2D transverse momentum: (y t,y t ) Charge independent (CI) and dependent (CD) PID dependent (not yet explored, need TOF) Differential p t spectra (as in p-p analysis)  Superposition of p-p collisions  Parton/hadron scattering, moderate cross sections  Opaque medium, zero mean-free path

32. 32 Centrality and Energy Trends

33. 33 Quadrupole Component Datacos(2φ Δ ) component Instead of removing a background, we can make a measurement 62 and 200 have the same shape Substantial amp. change with energy 200 GeV 62 GeV ηΔηΔ φΔφΔ ηΔηΔ φΔφΔ 33 flow data from PRC 72 014904 D. Kettler, T. Trainor arXiv:0704.1674 accepted to J Mod Phys E The η-dependence of correlations separates quadrupole from other components STAR Preliminary v 2 {2} v 2 {2D} v 2 {4} Amplitudes

34. 34 Another scenario: opaque core plus novel QCD corona If an opaque core developed then minijet yield would decrease, but perhaps those that escape from the outer region pick up enough associated particles to make up for the deficit caused by the core to account for what we see. - pt correlations remain - ytxyt dissipates but amplitude remains at minijet yt - same-side 2D gaussian remains But… However, many jets will lose their away-side partner, only tangential jets will have the broad away- side correlations to produce the –cos(   ). In this scenario the ratio of dipole to 2D gaussian amplitude decreases. In the STAR data this ratio is flat from pp to central AuAu.

35. 35 Implications for phenomenology momentum loss increased number of correlated pairs Brownian motion induces  and  width broadening – the latter is not seen Semi-hard parton traversing thermal medium: 1D Hubble expanding gluon field (in co-moving frame of parton) transverse momentum loss; no change in direction p t transfered to gluons along z-coordinate, not  correlation along z maps to width increase on  azimuth width constant increased number of correlated pairs p t correlations preserved But what causes the gluon field to suddenly change ? (personal speculation)