Do two-dimensional correlation data falsify RHIC paradigms?

1. Do two-dimensional correlation data falsify RHIC paradigms? Lanny Ray University of Texas at Austin and STAR Collaboration • Outline: • Introduction • p-p reference • A-A results • Minijet transition and soft ridge • Constraints on models; falsification • Conclusions RHIC Paradigms Workshop – April 14-17, 2010

2. High Energy Collision Perspective • The philosophy behind this analysis is based on an old and simple idea: • measure p-p and try to understand those data in terms of pQCD, 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. • A high energy physicist description of ultra-relativistic A+A: • PDF + Partonic s + Fragmentation Functions & Re-scattering • (initial state) (partonic/hadronic) • shadowing, novel medium equilibration, • gluon diagrams, modifications dissipation • saturation re-scattering Possible new QCD physics with A+A

3. Correlation measure ρ(p1,p2)= 2 particle density ρsibling(p1,p2) Event 1 ρreference(p1,p2) Event 2 Fill 2D histograms (a,b), e.g. (f1,f2), (h1,h2), (f1-f2,h1-h2), (pt1,pt2), etc. measures number of correlated pairs per final state particle square-root of rref(a,b); (for h,f space) normalized ratio of 2D binned histograms; acceptance cancellation; two-track ineff. corrections Motivated by p-p superposition null hypothesis

4. NSD p-p Collision Reference

5. Angular correlations for p-p cut larger yt pairs and project onto relative h,f: cut low yt pairs and project onto relative h,f: include all yt pairs φΔ ηΔ φΔ ηΔ Longitudinal fragmentation (charge ordering) plus HBT for like-sign Same-side 2D Gaussian plus away-side ridge – classic jet-like structure STAR Preliminary φΔ ηΔ transverse rapidity:

6. Relation to correlations in p-p STAR observes angular correlated charged hadron pairs with pt ~ 1 – 1.5 GeV/c corresponding to typical parton pt of order >(3/2)(2)(1 to 1.5) ~ 4 GeV/c, well within reach of the UA1 data and pQCD descriptions. X.-N.Wang and M. Gyulassy implemented the UA1 observations into HIJING (PYTHIA) (Phys. Rev. D 44, 3501 (1991)) using standard PDFs and pQCD. In Au-Au we cannot reconstruct low Q0 jets event-wise; requires correlations among all pairs [Xin-Nian Wang, Phys. Rev. D 46, R1900 (1992)]. How would these low Q0minijets appear in our 2D (h,f) angular correlations? pQCD calc. C. Albajar (UA1) Nucl. Phys. B 309, 405 (1988) “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 pt structures are “jet-like.”

7. Jet-A proton p-p 200 GeV parton-parton cm Jet-B NN cm A-A B-B h A-B B-A A-A B-B A-B B-A STAR preliminary proton Number of pairs Number of pairs h1-h2 0 Φ1 - Φ2 large azimuth peak 0 p fD=f1-f2 small angle peak η1 - η2 Example: di-minijets sum over many events

8. Minijets in HIJING from pQCD • HIJING: • standard PDFs • pQCD cross sections • standard FFs p + p at 200 GeV Jets on soft pt pairs removed STAR Preliminary agrees within ~20% fD hD Jets off fD additional sharp peak: HBT, conversion electrons hD fD hD • We conjecture that the bump at 1 GeV/c in the (yt,yt) and the above angular • correlations are generated by the fragmentation of semi-hard scattered partons. • Minijets are simply jets with no low pt cut-off. • We study the evolution of these correlations in A+A, invoking new physics only when required by the data.

9. Nucleus + Nucleus Collisions

10. (yt1,yt2) correlations for same-side pairs Au-Au 200 GeV Like Sign peripheral central pp HBT peripheral Unlike Sign central pp minijets persist; pt dissipation STAR Preliminary From M. Daugherity’s Ph.D Thesis (2008)

11. the “other” KT broadening (yt1,yt2) correlations for away-side pairs Au-Au 200 GeV Like Sign peripheral central pp minijets STAR Preliminary peripheral Unlike Sign central pp minijets persist; some pt dissipation From M. Daugherity’s Ph.D Thesis (2008)

12. (yt1,yt2) for unlike-sign, away-side pairs Au-Au 200 GeV STAR Preliminary From E. Oldag, L. Li

13. Fits to 62 & 200 GeV Au-Au data SS Peak Amplitude Peak η Width Peak φ Width STAR Preliminary STAR Preliminary statistical errors only 200 GeV 62 GeV STAR Preliminary n n peripheral central From D. Prindle (2010) Dipole Amplitude Binary scaling: Kharzeev and Nardi STAR Preliminary HIJING 1.382 default parameters, 200 GeV, quench off n Deviations from binary scaling represent new physics unique to heavy ion collisions; the departure from N-N superposition is referred to as a transition in the trends.

14. How much do different (yt,yt) regions contribute? STAR Preliminary IV I III II From E. Oldag (2010)

15. How do different (yt,yt) regions contribute to the 2D Gaussian? III IV II I STAR Preliminary (fitting errors not shown) IV. Hard Circle Region of “soft” ridge III. Hard Rest II. neck I. soft From E. Oldag (2010)

16. 200 GeV Au-Au data 64-74% 55-64% 46-55% 38-46% 28-38% φΔ ηΔ Analyzed 1.2M minbias 200 GeV Au+Au events; included all tracks with pt > 0.15 GeV/c,|η| <1, fullφ cos(2fD) and 2D exponential subtracted from data STAR Preliminary Growth of the “soft-ridges” – same and away-side From D. Prindle (2009)

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

18. SS 2D Gaussian Peak Amplitude Au-Au Cu-Cu 200 GeV 62 GeV STAR Preliminary n200 n200 ntrans 2.5 – 2.7 2.7 – 2.9 2.8 – 3.0 3.0 – 3.2 %stot 60 – 64 43 – 55 22 – 30 7 - 14 Au-Au 200 Au-Au 62 Cu-Cu 200 Cu-Cu 62 Scaling of the Transition: final-state density? Hypothesis: the transition centrality location depends on final-state transverse particle density, as might be expected if final state effects dominate. Approximate scaling with transverse particle density at each energy; but the scaling hypothesis does not work as well for different collision systems. Scaling hypothesis doubtful, pending improved multiplicity and error estimates. STAR Preliminary *(errors only account for ntrans) S = overlap area (Monte Carlo Glauber)

19. Au-Au 200 GeV 2D Gaussian amplitude Au-Au 200 GeV 2D Gaussian amplitude Scaling of the Transition: pristine vs. wounded nucleons? • Hypothesis: in A-A collisions • binary interactions between pristine nucleons produce minijets as in p-p, • pristine-“wounded” nucleon interactions also produce minijets as in p-p • (e.g. no “ridge” observed in d-Au), • but interactions between the diffractive scattering products of preceding • N-N interactions, so-called wounded-wounded nucleon interactions, might • produce very different yields and pseudorapidity distributions in proportion • to the Glauber model estimate of the relative number of each type of binary • interaction. Au-Au 200 GeV wrong shape, hypothesis FALSIFIED 1.0 approx. linear unlike the data sum w-w 0.5 from MC Glauber pr-pr + w-w 0 qualitative trends

20. b interaction area proxy 2.5 2.0 AuAu 200 AuAu 62 CuCu 200 CuCu 62 1.5 1.0 0.5 0 Scaling of the Transition: initial parton overlap? Consider the low-x gluon overlap in the boosted frame of the beam nucleus in the initial state: [Kopeliovich, Levin et al. PRC79, 064906 (2009)] Hypothesis: the transition is due to an initial-state effect depending on initial-state overlap of low-x gluons (partons). Eikonal nuclear profile density – a proxy for low-x gluons: (ignore differences between low-x structure functions in Au and Cu.) Hypothesis NOT FALSIFIED candidate scaling variable for transition

21. Cu-Cu 200 GeV 62 GeV Au-Au 200 GeV 62 GeV 2D Gaussian amp STAR Preliminary STAR Preliminary incoherent coherent incoherent coherent Initial state low-x parton overlap – coherent scattering? incoherent vs. coherent Incoherent (binary) and coherent scaling for semi-hard partonic scattering (fixed phase) If the transition is from incoherent to coherent partonic scattering, then: gluon saturation?

22. Q ~ 2 GeV minijets, nucleon KT , acoplanarity Low-x parton KT ~ 1 GeV/c KT broadening pz Low-x parton events 1,2,3… p 0 sum events φΔ p 0 away-side φΔ -3p -pp 3p 0 Away-side ridge – local pt conservation 200 GeV 62 GeV QM08 The dipole matches the centrality dependence of the same-side Gaussian and shows the same transition point. It’s origin is pt conservation: global + jets (global – overall CM constraint; local, e.g. jets - processes). STAR Preliminary estimated global pt conservation Hijing – jets on (no soft pt)

23. Dipole Amplitude STAR Preliminary n Away-side ridge (dipole): centrality dependence • Hypotheses: • The away-side ridge (other than the quadrupole) is caused by global momentum conservation, where the correlation amplitude ~ • (2) The away-side ridge is caused by back-to-back minijets, but only those emitted tangentially from the surface due to strong QGP attenuation; away-side pt escapes, but is • dispersed among many more pairs. opaque core + corona with minijets wrong shapes, hypotheses FALSIFIED Tangential jets: initially follow binary, reduces to surface area scaling when opaque core develops (qualitative trend suggested) For Dr/sqrt{rref} global pt conservation is approximately constant with centrality Au-Au 200 GeV

24. Minijets & Quadrupole STAR Preliminary STAR Preliminary Quadrupole amplitude 2D Gaussian amp expected v2? Below the transition the Au-Au system appears transparent (e.g. no width increases in minijet peak), casting doubt on scenarios which assume pressure driven collective flow (see slide 30, Pang et al.). If a few secondary collisions (LDL) produce v2 in peripheral collisions, why aren’t the minijets also affected? STAR Preliminary What produces a smooth centrality dependence and a uniformly boosted v2? From D. Kettler

25. Evidence for semi-hard jets in A-A - summary • UA1 calorimeter energy clusters • HIJING pQCD agreement with correlations from p-p • Smooth evolution of p-p correlations to mid-central A-A • Binary scaling of jet-like correlations up to the transition • Constancy of the (yt,yt) peak structure from p-p to central AuAu • Monotonic, binary scaling increase in pt (h,f) correlation amplitude • Away-side ridge mirrors the same-side correlation amplitude • Charge ordering on (h,f) and ytD=yt1-yt2 in yt range of minijet peak • KT broadening in azimuth and on yt1-yt2 • PID composition? – not yet measured.

26. Constraints on Theoretical Models • Features of correlations in (yt,yt) and (hD,fD) which theory • must comprehensively address, i.e. not piecemeal: • Smooth evolution down to the p-p limit • Transverse rapidity structure (peak at 1 – 1.5 GeV/c) • Increased yield beyond binary scaling • Elongation on hD – “soft ridge” • Azimuth narrowing of small angle structure • Away-side ridge amplitude growth • Charge-ordering along hD, fD, and ytD • Away-side KT broadening on both fD and ytD

27. 1 2 3 pT minijet peak 0-30% central Parton/hadron strong re-scattering models; thermalization Expected behavior of minijets: • widths increase • pt correlation amplitudes reduced • dissipation to lower pt Comparison with data: 2D Gaussian f width hwidths increase butfwidths decrease STAR Preliminary pt correlation amplitude follows binary scaling beyond transition AuAu 200 pp Minijet peak remains at original yt yt peripheral central yt Expected trends not observed

28. pT minijet peak 0-30% centrality Theoretical predictions: minijets with partonic collisions; hydrodynamics L. Pang, Q. Wang, Xin-Nian Wang, R. Xu, Phys. Rev. C 81, 031903(R) (2010) arXiv:0910:3838 – HIJING minijets with early parton re-scattering; minijets in viscous hydrodynamic medium; Kajantie et al. PRL 59,2527 predicted pt correlations: amplitude reduction and width broadening jet quenching increased viscosity Same-side pt correlation amplitude and widths Predicted amplitude reduction: disagrees with n<4 data Predicted azimuth width increase: disagrees with data STAR: J Phys G 32 L37

29. Jets + re-scattering, radial flow: • Chiu and Hwa, Phys. Rev. C72, 034903 (2005) – Jet driven, recombination, re-scattering; hot spots pushed out by radial flow. These will have a problem with the narrowing on azimuth plus other constraints • C.-Y. Wong, Phys. Rev. C76, 054908 (2007) – Jet driven “momentum kick” (re-scattering) model. • Majumder et al., Phys. Rev. Lett. 99, 042301 (2007); Dumitru et al., arXiv:0710.1223 [hep-ph] - Jet driven with plasma instability redirection of jet fragments. Theoretical models – same-side ridge Initial Fluctuations + Radial Flow: • Voloshin, Nucl. Phys. A749, 287c (2005); • Shuryak, Phys. Rev. C76, 047901 (2007) – • beam-jet fragments pushed out by radial flow. These fail to predict the growth of the away-side ridge • Dumitru, Gelis, McLerran, Venugopalan, arXiv:0804.3858[hep-ph] - • glasma flux tubes pushed out by radial flow. • S. Gavin, Phys. Rev. Lett. 97, 162302 (2006) – initial state energy fluctuations spread along h by shear viscosity; pushed out by radial flow.

30. Summary and Conclusions • Correlation structures in minbias p-p collisions can be understood with pQCD, PDFs, and standard FFs as implemented in HIJING. • The A-A correlation data are described with five functional components including a same-side 2D Gaussian + dipole attributed to minijets. • Minijets are an essential component of RHIC collisions and display a transitional centrality trend in Au & Cu which may scale with initial state low-x parton overlap. • Up to the transition minijets escape from the entire collision volume (binary scaling) with little broadening as if from a transparent medium, yet elliptic flow is large for these same collisions – why? • Above the transition same- and away-side number correlations increase • and away-side (yt,yt) correlations persist in the minijet region, none of • which are expected for strongly interacting or opaque systems. • None of the proposed theoretical explanations for the same-side ridge successfully address all the relevant features of the correlation data. At the present time I conclude that these models have been falsified. • The 2D correlation data provide an opportunity to learn something new about QCD in dense environments. e.g. secondary interactions, gluon saturation, coherent parton-parton scattering, strong radiation.