1. INT Ridge Workshop - 5/10/20121 Correlation systematics versus RHIC/LHC theories Lanny Ray, The University of Texas at Austin The Ridge Workshop Institute of Nuclear Theory May 7-11, 2012

2. INT Ridge Workshop - 5/10/20122 Introduction and Outline A-A collision theories must include (among other things):  pQCD processes including minimum p t biased jets, and their evolution in the dense, energetic collision system  event-wise fluctuations in initial conditions, e.g. N part and N binary In this talk I will review and discuss:  Experimental challenges for theory  Theoretical expectations for data  Initial state fluctuation model predictions  Jet + medium interaction model predictions  Ideas from pQCD  Conclusions

3. INT Ridge Workshop - 5/10/20123 Correlation data challenges for Theory  Smooth evolution to the p-p collision limit  Coexistence of Glauber superposition of jet structure with large v 2  Sharp transition in same-side peak and away-side ridge 1) increased yield beyond binary scaling 2) elongation on   – “soft ridge” 3) reduced azimuth width Two-particle angular and transverse momentum correlations Au-Au 62,200 GeV STAR data arXiv:1109.4380 same-side 2D peak dipole quadrupole

4. INT Ridge Workshop - 5/10/20124 Correlation data challenges for Theory  Transverse momentum structure peak at 1 – 1.5 GeV/c 1) persistence from p-p to central Au-Au 2) increased away-side width on y t  = y t1 -y t2, “K T broadening” 3) evolution of same-side unlike-sign peak; from single to double peaks away-side unlike-sign same-side unlike-sign STAR preliminary From E. Oldag

5. INT Ridge Workshop - 5/10/20125 Correlation data challenges for Theory  Transverse momentum content of “soft ridge” 1 – 1.5 GeV/c with no softening at larger   (within 2 units) or with increasing centrality  Correspondence between p t correlations and spectra (Tom Trainor’s analysis)  Charge-ordering (US > LS) along    , and y t  volume of SS 2D peak on (y t,y t ) STAR preliminary From E. Oldag

6. INT Ridge Workshop - 5/10/20126 General expectations: jet + medium interaction pQCD minijets are expected to dissipate with increasing A-A centrality. Surprisingly, jet-like correlations follow Glauber linear superposition (GLS) to mid centrality. In transport/hydro models (strong parton interactions) jet-related correlation widths should increase, amplitudes decrease, parton p t. Hadronic corona + opaque core: away-side dijet correlations persist but fall off relative to SS jet-related correlations. Sarcevic, Ellis, Carruthers, PRD 40, 1446 (1989) Kajantie, Landshoff, Lindfors, PRL 59, 2527 (1987) Pang, Wang, X.-N. Wang, Xu, PRC 81, 031903 (2010) Nayak, Dumitru, McLerran, Greiner, NP A 687, 457 (2001) Shin, Meuller, J. Phys. G 29, 2485 (2003) STAR preliminary

7. INT Ridge Workshop - 5/10/20127 Theoretical ideas for the same-side   elongation Initial stage fluctuations plus hydro pressure driven radial flow:  Beam jets – Voloshin, Shuryak  Color-glass condensate flux tubes; glasma – many authors  Initial Energy/momentum density fluctuations in hydro – Gavin, Alver & Roland, Sorensen Spherio (3+1 event-wise hydro; no jets) Jet + medium interactions:  Jet parton + thermal parton recombination – Chiu and Hwa  Momentum kick – C-Y Wong  AMPT – 2-to-2 parton cascade  HYDJET (CMS) – collisional and gluon radiation jet quenching  NexSpherio (3+1 hydro with NEXUS initial cond. & hard scattering) pQCD preliminaries:  Color coherence – 2-to-3 soft gluon radiation  BFKL emission interference

8. INT Ridge Workshop - 5/10/20128 Initial fluctuations plus radial flow  Voloshin, Nucl. Phys. A749, 287c (2005); Shuryak, Phys. Rev. C76, 047901 (2007) – beam jet fragments pushed out by strong radial flow; ridge shaped by flow and path length attenuation. Reduced L absorption ridge projection onto azimuth  S. Gavin, Phys. Rev. Lett. 97, 162302 (2006) – initial state fluctuations with shear viscosity; driven by hydrodynamic radial expansion STAR p t angular correlation peak widths  Alver & Roland, Phys. Rev. C 81, 054905 (2010) – initial state fluctuations produce triangular flow and ridge

9. INT Ridge Workshop - 5/10/20129 CGC glasma predictions for the “ridge” Dumitru et al., Nucl. Phys. A 810, 91 (2008) Dumitru et al., Phys. Lett. B 697, 21 (2011) Gavin et al., Phys. Rev. C 79, 051902(R) (2009) Gavin, Moschelli, Nucl. Phys. A 854, 106 (2011); ibid. 836, 43 (2010) T. Lappi, Prog. Theor. Phys. Suppl. 187, 134 (2011); arXiv:1011.0821 Lappi, Srednyak, Venugopalan, JHEP 01, 66(2010); arXiv:0911.2068 Gelis et al., Ann. Rev. Nucl. Part Sci. 60, 463 (2010) radial flow From Gavin & Moschelli: Same-side amplitude;  s -1 (Q s ) adjusted to fit most-central data  width determined by radial flow blast-wave parameters STAR data: arXiv: 1109.4380 [nucl-ex]

10. INT Ridge Workshop - 5/10/201210 CGC glasma predictions for the “ridge” The correlation amplitude is predicted to increase with centrality, however the overall magnitude is adjusted to the data. Predicted azimuth width is generally too broad, requiring extreme radial boost  B =2 (0.96c) to agree with data* (0.7-1 rad). Pseudorapidity widths are not predicted. Dumitru et al., Nucl. Phys. A 810, 91 (2008); What about the p t structure of the ridge? *See: STAR, arXiv:1109.4380 Daugherity (STAR-QM08), J.Phys.G 35,104090 azimuth projection vs radial boost

11. INT Ridge Workshop - 5/10/201211 Same-side Away-side Glasma two-gluon (p t,p t ) correlations T. Lappi, Prog. Theor. Phys. Suppl. 187, 134 (2011); arXiv:1011.0821 Lappi, Srednyak, Venugopalan, JHEP 01,66(2010); arXiv:0911.2068 extraneous self-pairs per-gluon pair correlation No radial boost

12. INT Ridge Workshop - 5/10/201212 Comparing glasma (p t,p t ) predictions to data Glasma predictions, gluon-gluon correlations Charged hadron correlations in p-p collisions* This model has no radial flow. Radial boost cannot reproduce the correlations at larger p t. T. Lappi, Prog. Theor. Phys. Suppl. 187, 134 (2011) Glasma model misses this peak associated with the ridge. *See: Phys. Rev. C 84, 034906 (2011) Assume LPHD

13. INT Ridge Workshop - 5/10/201213 AMPT Essential aspects of the model [Lin, Ko, Zhang, Pal, Phys. Rev. C 72, 064901 (2005)]: HIJING production of F.S. hadrons (MC Glauber w. LUND & Pythia) In “string melting” mode all F.S. hadrons represented as q, anti-q at space-time positions corresponding to MCG and assumed formation time. Parton cascade via pQCD 2-to-2 elastic scattering; adjustable cross section. Hadronization via coalescence – 3-momentum conservation, no E cons. Hadron cascade & chemistry using ART

14. INT Ridge Workshop - 5/10/201214 LUND string fragmentation parameters (a = 0.5, b = 0.9 GeV -2 ); “string melting,” w/out parton cascade and/or jets (> 2 GeV; no quenching) 200 GeV Au-Au 46-55% - jets, parton cascade on/off No Jets,  parton = 0 No Jets,  parton = 12 mb With Jets,  parton = 0 (same as Hijing) With Jets,  parton = 12 mb with hadron scattering AMPT: Jets and parton cascade From E. Oldag

15. INT Ridge Workshop - 5/10/201215 AMPT: Jets with varying parton cross section LUND string fragmentation parameters (a = 0.5, b = 0.9 GeV -2 ); “string melting,” with parton cascade and jets (> 2 GeV; no quenching) 200 GeV Au-Au 46-55% - vary  parton (using screening mass  ) 0 mb 3 mb 6 mb 12 mb  (mb) 0 3 6 12 Data quad 0 0.064 0.115 0.153 0.136(2) A 2DG 0.116 0.247 0.309 0.373 0.207(7)   1.01 1.98 2.27 2.30 0.83(5)   0.99 0.76 0.66 0.59 0.66(2) Model fit parameters Why doesn’t the (y t,y t ) peak move down? Why does the azimuth width decrease? Increasing  enough to reproduce v 2 grossly overestimates the SS 2D peak amplitude and   width STAR data arXiv:1109.4380 From E. Oldag

16. INT Ridge Workshop - 5/10/201216 200 GeV Au-Au – centrality dependence @ fixed  =12 mb 84-93% 46-55% 18-28% The data approximately follow GLS up to ~3; AMPT with  ~ 0 follows GLS but produces no quadrupole (v 2 ). AMPT: centrality dependence LUND string fragmentation parameters (a = 0.5, b = 0.9 GeV -2 ); “string melting,” with parton cascade (12 mb) and jets (> 2 GeV; no quenching) From E. Oldag STAR arXiv:1109.4380

17. INT Ridge Workshop - 5/10/201217 AMPT: parton correlations The preceding results are counter-intuitive. We therefore studied the predicted parton correlations as a function of parton cross section (0,1.5,3,6,9,12 mb) with no coalescence 200 GeV Au-Au 46-55% - parton correlations 0 mb 1.5 mb3 mb0 mb1.5 mb3 mb 6 mb9 mb12 mb 6 mb9 mb12 mb angular (      correlations (y t,y t ) correlations SS peak: amplitude and widths  increase Quadrupole: increases to exp. value at ~6mb Jet peak: strong dissipation as expected. What is coalescence doing? From E. Oldag

18. INT Ridge Workshop - 5/10/201218 AMPT: parton correlations  (mb) 0 1.5 3 6 12 Data quad 0 0.024 0.064 0.115 0.153 0.136(2) A 2DG 0.116 0.234 0.247 0.309 0.373 0.207(7)   1.01 1.85 1.98 2.27 2.30 0.83(5)   0.99 0.86 0.76 0.66 0.59 0.66(2) Model fit parameters  (mb) 0 1.5 3 6 12 quad 0.003 0.055 0.116 0.197 0.259 A 2DG 0.063 0.146 0.234 0.343 0.541   0.44 1.01 1.28 1.65 2.48   0.44 0.69 0.66 0.59 0.57 Model fit parameters LUND string fragmentation parameters (a = 0.5, b = 0.9 GeV -2 ); “string melting,” with parton cascade and jets (> 2 GeV; no quenching) 200 GeV Au-Au 46-55% - vary  parton Quadrupole increases smoothly with  parton in both cases. The SS 2D peak evolves very rapidly in both cases. The parton SS peak azimuth width increases when parton’s scatter. Final-state hadrons: coalescencePartons at end of cascade Initial width increase, then a decrease. Is the latter due to radial flow in the parton cascade? From E. Oldag STAR arXiv:1109.4380

19. INT Ridge Workshop - 5/10/201219 Monte Carlo Models: NexSPHERIO Sharma et al., PRC 84, 054915 (2011) Au-Au 200 GeV Number correlations p t correlations   width for same-side p t correlations STAR data nexspherio Jet-like peak predicted;   width increase not predicted No away-side double ridge

20. INT Ridge Workshop - 5/10/201220 Color coherence – pQCD soft gluons p-p at 7 TeV, N > 110 1 < p t < 3 GeV/c CMS Collaboration, JHEP 1009,091(2010). Rick Field – ISMD, ECT* 2010  extended jet correlations Higher order 2→3 or 2→4 matrix elements. Color coherent soft gluon radiation: Ellis, Nucl.Phys. B286, 643 (1987) p1p1 p2p2 k Soft gluon – jet angular correlations (LR) Phys. Rev. D 84, 034020 (2011) With varied IR, collinear cut-offs

21. INT Ridge Workshop - 5/10/201221 BFKL emission and interference E. Levin and A. H. Rezaeian, Phys. Rev. D 84, 034031 (2011) Angular correlation –   independent peak at   = 0, but also away-side! azimuth quadrupole See Amir Rezaeian’s talk tomorrow morning! Two-Pomeron exchange with two-gluon emission interference See also: Kopeliovich, Rezaeian, Schmidt Phys. Rev. D 78, 114009 (2008).

22. INT Ridge Workshop - 5/10/201222 Summary and Conclusions Observed correlation structure on relative angles and (y t,y t ) pose strict challenges for theoretical models: centrality evolution of the ridge (y t,y t ) composition of the same-side ridge (y t,y t ) correlation peak – persistent position and increasing amplitude General expectations for strong jet + medium interaction, with possible thermalization, disagree with data trends. Initial state fluctuation + radial flow (e.g. Glasma) produce SS   elongation but does not produce sufficient (y t,y t ) structure at p t ~ 1 – 2 GeV/c. Jet + medium interaction models (e.g. AMPT, NexSpherio) can produce SS   elongation. But can they account for the azimuth narrowing and (y t,y t ) peak’s persistence? pQCD models for the quadrupole are appearing in the literature which do not require hydro. Perhaps the same will be developed for the ridge.