1. 1 The away-side ridge in two-dimensional correlation data from STAR Lanny Ray University of Texas at Austin STAR Collaboration

2. 2 Outline:  Definitions  p-p and QCD  Centrality evolution  Same-side structures  Away-side ridge  Implications The philosophy behind the analysis presented here is based on an old and simple idea: measure p-p and try to understand those data in terms of QCD, PDFs, FFs. then move to p+Au (d+Au) and understand those data (initial state, sequential scattering effects)‏ then move to Au-Au and see if the data require anything else interpret data with new physics mechanisms, beyond that in p-p, p-A only when the data demand it. This is not a new idea, e.g. in Sept. 1992 at a STAR collaboration meeting Miklos Gyulassy outlined this very program. I hope that this workshop will live up to its title of critically assessing the data and its Interpretation. Our Philosophy and Challenge

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 SS - same side AS - away side LS – like signUS – unlike sign Two-component soft + semi-hard structure away-side bump at 1 GeV/c is independent of charge pair same-side bump at 1 GeV/c for US; soft structure varies  √  ref 0.15 1.0 10.0 p t (GeV/c)‏  √  ref Transverse momentum correlations in p-p 200 GeV p-p minbias transverse rapidity 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 This looks like a jet – but is it? 2D Gaussian + away-side ridge STAR Preliminary Angular correlations for p-p

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

7. 7 Relation of UA1 jets to p-p correlations STAR observes angular 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. X.-N.Wang and M. Gyulassy implemented the UA1 observations into their Monte Carlo code HIJING (PYTHIA) (Phys. Rev. D 44, 3501 (1991)) using standard PDFs, pQCD parton-parton cross sections, and standard fragmentation functions. The low-pt parton energy follows a power-law until a cut-off at Q 0 ~ 2 GeV. The majority of produced jets have Q 0 ~ few GeV and only produce a few hadronic fragments. In Au-Au we cannot hope to identify these low Q 0 jets directly. There is also no identifiable trigger particle at lower p t. Thus we use both angular and (p t1,p t2 )‏ correlations for all pairs as suggested by Xin-Nian Wang a long time ago (Phys. Rev. D 46, R1900 (1992)). These soft, untriggered jets are known in the literature as minijets. How would 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-minijets

9. 9 p + p at 200 GeV Minijets in HIJING & PYTHIA We conjecture that the bump at 1 GeV/c in the (y t,y t ) and the above angular correlations are generated by the fragmentation of semi-hard scattered partons. These minijets are simply jets with no low p t cut-off. soft p t pairs removed STAR Preliminary Hijing Jets on Hijing Jets off additional sharp peak: HBT, conversion electrons       ~20% agreement

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

11. 11 (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)‏

12. 12 (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)‏

13. 13 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)‏

14. 14 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”

15. 15 Same-side correlation structure   <  /2 The “soft” ridge

16. 16 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 are ~5-10% Systematic error is 9% of correlation amplitude peripheralcentral HIJING 1.382 default parameters, 200 GeV, quench off

17. 17 2D Gaussian amplitude,  -width, volume scale with particle density in Au-Au 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?

18. 18 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 in same-side ridge 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 (Au-Au 200 GeV)‏

19. 19 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, implying an approximately transparent system, but radically fails at higher density, more central collisions. STAR Preliminary

20. 20 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. If a few secondary collisions (LDL) produce v 2 in peripheral collisions, why aren’t the minijets affected (same p t range)? What mechanism(s) produces a smooth v 2 ? expected v 2 ? STAR Preliminary

21. 21 Away-side correlation structure   >  /2 The away-side ridge

22. 22 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 )‏

23. 23  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

24. 24 Mach Cone ? Au+Au 200 GeV 0-5% most-central    Shown are Data – Quadrupole which isolates the away-side dipole structure STAR Preliminary No indication of a double away- side ridge – no Mach cone

25. 25 Please stop using ZYAM! ZYAM method assumes non-overlapping peaks above background – questionable Example: fake “data” generated by same-side Gaussian + dipole v 2 {2} obtained from due to SS Gauss. ZYAM procedure subtracts v 2 and adjusts offset. ZYAM deduced correlation wrong amplitude! spurious shape! nonphysical  Always plot the raw correlation data  v 2 is being over-subtracted; v 2 {2} or [v 2 {2} + v 2 {4}]/2 includes SS peak contribution, i.e. non-flow, which is larger at higher p t where this analysis is usually done. Plots from Tom Trainor ZYAM input correlation

26. 26 Summary and Conclusions  Correlation structures in minbias p-p collisions can be understood with pQCD, PDFs, and standard FFs.  Minijets (jets with no low-pt cut-off) are an essential component of RHIC collisions and are manifest in (y t,y t ) and 2D angular correlations.  Up to the transition minijets escape from the entire collision volume (binary scaling) with little broadening as if from a transparent medium.  The transition, observed in the same-side peak, is also observed in the away-side ridge.  The transition is not manifest in v 2 (quadrupole) implying that v 2 is not affected by post-impact rescattering.  The minimum-bias away-side correlations do not show evidence of a double-hump structure reported in leading particle-associated   analyses.