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

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 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 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 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 p t (GeV/c)‏  √  ref Transverse momentum correlations in p-p 200 GeV p-p minbias transverse rapidity STAR Preliminary

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

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 (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)‏

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

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 default parameters, 200 GeV, quench off

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

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  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 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 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 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.