1. 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. 2 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  + Fragmentation Functions & Re-scattering (initial state) (partonic/hadronic) shadowing, novel medium equilibration, gluon diagrams, modifications dissipation saturation re-scattering High Energy Collision Perspective Possible new QCD physics with A+A

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 NSD p-p Collision Reference

5. 5 Angular correlations for p-p ηΔηΔ φΔφΔ φΔφΔ φΔφΔ ηΔηΔ ηΔηΔ cut low y t pairs and project onto relative  : Longitudinal fragmentation (charge ordering) plus HBT for like-sign cut larger y t pairs and project onto relative  : Same-side 2D Gaussian plus away-side ridge – classic jet-like structure include all y t pairs STAR Preliminary transverse rapidity:

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. Relation to correlations in p-p 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 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 Q 0 jets event-wise; requires correlations among all pairs [Xin-Nian Wang, Phys. Rev. D 46, R1900 (1992)]. How would these low Q 0 minijets appear in our 2D (  ) angular correlations?

7. 7 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

8. 8 p + p at 200 GeV Minijets in HIJING from pQCD  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.  Minijets are simply jets with no low p t cut-off.  We study the evolution of these correlations in A+A, invoking new physics only when required by the data. soft p t pairs removed STAR Preliminary Jets on Jets off additional sharp peak: HBT, conversion electrons       agrees within ~20% HIJING: standard PDFs pQCD cross sections standard FFs

9. 9 Nucleus + Nucleus Collisions

10. 10 (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)

11. 11 (y t1,y t2 ) correlations for away-side pairs Au-Au 200 GeV Like Sign Unlike Sign pp STAR Preliminary peripheral central minijets persist; some p t dissipation minijets From M. Daugherity’s Ph.D Thesis (2008) the “other” K T broadening

12. 12 STAR Preliminary (y t1,y t2 ) for unlike-sign, away-side pairs Au-Au 200 GeV From E. Oldag, L. Li

13. 13 Fits to 62 & 200 GeV Au-Au data SS Peak AmplitudePeak η WidthPeak φ Width STAR Preliminary statistical errors only peripheralcentral Dipole Amplitude 200 GeV 62 GeV HIJING 1.382 default parameters, 200 GeV, quench off 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. Binary scaling: Kharzeev and Nardi STAR Preliminary From D. Prindle (2010)

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

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

16. 16 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 D. Prindle (2009) cos(2   ) and 2D exponential subtracted from data Growth of the “soft-ridges” – same and away-side 28-38% 55-64%46-55% 38-46% φΔφΔ ηΔηΔ 64-74%

17. 17 p t correlations follow binary scaling well past the transition Numberptpt STAR: 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 S = overlap area (Monte Carlo Glauber) 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. Au-Au 200 Au-Au 62 Cu-Cu 200 Cu-Cu 62 trans 2.5 – 2.7 2.7 – 2.9 2.8 – 3.0 3.0 – 3.2 %  tot 60 – 64 43 – 55 22 – 30 7 - 14 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. SS 2D Gaussian Peak Amplitude Au-Au Cu-Cu  STAR Preliminary 200 GeV 62 GeV *(errors only account for trans ) STAR Preliminary

19. 19 0 0.5 1.0 Au-Au 200 GeV approx. linear unlike the data 2D Gaussian amplitude Au-Au 200 GeV 2D Gaussian amplitude Au-Au 200 GeV wrong shape, hypothesis FALSIFIED w-w sum pr-pr + w-w 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. from MC Glauber qualitative trends

20. 20 Consider the low-x gluon overlap in the boosted frame of the beam nucleus in the initial state: [Kopeliovich, Levin et al. PRC 79, 064906 (2009)] Eikonal nuclear profile density – a proxy for low-x gluons: (ignore differences between low-x structure functions in Au and Cu.) interaction area proxy b 0 0.5 1.0 1.5 2.0 2.5 AuAu 200 AuAu 62 CuCu 200 CuCu 62 Hypothesis NOT FALSIFIED candidate scaling variable for transition Scaling of the Transition: initial parton overlap? Hypothesis: the transition is due to an initial-state effect depending on initial-state overlap of low-x gluons (partons).

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

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 (global – overall CM constraint; local, e.g. jets - processes). Away-side ridge – local p t conservation estimated 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 QM08 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 Dipole Amplitude STAR Preliminary Away-side ridge (dipole): centrality dependence Au-Au 200 GeV For  /sqrt{  ref } global p t conservation is approximately constant with centrality Tangential jets: initially follow binary, reduces to surface area scaling when opaque core develops (qualitative trend suggested) wrong shapes, hypotheses FALSIFIED Hypotheses: (1)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

24. 24 Minijets & Quadrupole 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 v 2 in peripheral collisions, why aren’t the minijets also affected? expected v 2 ? STAR Preliminary Quadrupole amplitude What produces a smooth centrality dependence and a uniformly boosted v 2 ? From D. Kettler STAR Preliminary 2D Gaussian amp

25. 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 (y t,y t ) peak structure from p-p to central AuAu  Monotonic, binary scaling increase in p t (  ) correlation amplitude  Away-side ridge mirrors the same-side correlation amplitude  Charge ordering on (  ) and y t  =y t1 -y t2 in y t range of minijet peak  K T broadening in azimuth and on y t1 -y t2  PID composition? – not yet measured.

26. 26 Constraints on Theoretical Models Features of correlations in (y t,y t ) and (     ) 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   – “soft ridge”  Azimuth narrowing of small angle structure  Away-side ridge amplitude growth  Charge-ordering along    , and y t   Away-side K T broadening on both   and y t 

27. 27 Expected behavior of minijets: Comparison with data: Parton/hadron strong re-scattering models; thermalization  widths increase  p t correlation amplitudes reduced  dissipation to lower p t p t correlation amplitude follows binary scaling beyond transition Minijet peak remains at original y t 1 3 2  widths increase but  widths decrease p T minijet peak 0-30% central pp AuAu 200 ytyt ytyt Expected trends not observed peripheral central 2D Gaussian  width STAR Preliminary

28. 28 Theoretical predictions: minijets with partonic collisions; hydrodynamics Predicted azimuth width increase: disagrees with data 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 p t correlations: amplitude reduction and width broadening p T minijet peak 0-30% centrality Same-side p t correlation amplitude and widths Predicted amplitude reduction: disagrees with <4 data jet quenching increased viscosity STAR: J Phys G 32 L37

29. 29 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.  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  by shear viscosity; pushed out by radial flow. These fail to predict the growth of the away-side ridge 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.  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. These will have a problem with the narrowing on azimuth plus other constraints

30. 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.