1. Correlation in Jets at RHIC Rudolph C. Hwa University of Oregon Institute of Nuclear Theory University of Washington December 5, 2006

2. 2 Outline General comments on hadron production at high pT d-Au collisions Au-Au collisions centrality dependence of correlation ridge under the jet peak Omega puzzle and its resolution proton trigger and meson partners Transfragmentation region Mid-F/B rapidity correlation Away-side correlation 2-jet recombination -- LHC

3. 3 Regions of transverse momentum Traditional classification in terms of scattering pTpT 0246810 hardsoft pQCD + FF

4. 4 Regions of transverse momentum Traditional classification in terms of scattering pTpT 0246810 hardsoft pQCD + FF A different classification in terms of hadronization pTpT 0246810 (low)(intermediate)(high) thermal-thermalthermal-shower shower-shower Terminology used in recombination

5. 5 thermal fragmentation softhard TS Pion distribution (log scale) Transverse momentum TT SS Phenomenological successes of this picture

6. 6  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, 024905 (2004) fragmentation thermal TT SS TS

7. 7 Basic equation for meson production by recombination Shower parton distributions are determined from Fragmentation function Basic assumption: Dynamically independent, kinematically constrained.

8. 8 Proton production by recombination TTS+TSS Proton recombination function determined in the valon model e e p p U U D

9. 9 for p T ~ 3 GeV/c in Au-Au collision at 200 GeV. There is no “baryon anomaly”, if fragmentation is not regarded as the standard hadronization process. recombination/ coalescence Commonly regarded as “baryon anomaly”.

10. 10 Conventional thinking: Jets  fragmentation of hard partons That’s true in e+e- annihilation, and pp collision, but false in heavy-ion collisions at moderate pT (even with modified fragmentation function). Since, the p/  ratio is characteristic of fragmentation. May still be valid for p T >8 GeV/c

11. 11 shower partonsproduced hadrons correlations between colliding system e+e-e+e- Au-Au jets in x

12. 12 no correlation  0 Hwa & Tan, PRC 72, 024908 (2005) x1x1 x2x2

13. 13  f i (k) is small for 0-10%,  f i (k) but smaller for 80-92%

14. 14 Correlation of pions in jets in HIC Two-particle distribution k q3q3 q1q1 q4q4 q2q2 Non-factorizable terms correlated Factorizable terms: They do not contribute to C 2 (1,2)

15. 15 Hwa & Tan, PRC 72, 024908 (2005) Pion transverse momenta p 1 and p 2 negative correlation

16. 16 C 2 (1,2) treats 1 and 2 on equal footing. Experimental data choose particle 1 as trigger, and studies particle 2 as an associated particle. (background subtraction) STAR, PRL 95, 152301 (2005) Trigger 4 < p T < 6 GeV/c Hard for medium modification of fragmentation function to achieve, but not so hard for recombination involving thermal partons. Factor of 3 enhancement

17. 17 Hwa & Tan, PRC 72, 057902 (2005) Associated particle distributions in the recombination model Bielcikova, at Hard Probes (06) STAR preliminary Au+Au @ 200 GeV 3GeV/c<p T trigger <6GeV/c

18. 18 Forward-backward asymmetry in d+Au collisions Expects more forward particles at high p T than backward particles If initial transverse broadening of parton gives more hadrons at high p T, then backward has no broadening forward has more transverse broadening F/B > 1 B/F < 1

19. 19 Backward-forward ratio at intermediate p T in d+Au collisions (STAR) B/F

20. 20 B/F asymmetry calculated in the Recombination Model (Hwa, Yang, & Fries, PRC 05) STAR preprint nucl-ex/0609021

21. 21 Large  BRAHMS data show that in d+Au collisions there is suppression at larger . BRAHMS, PRL 93, 242303 (2004) Hwa, Yang, Fries, PRC 71, 024902 (2005). No change in physics from  =0 to 3.2 Soft parton density decreases, as  is increased (faster for more central collisions). TS recombination diminishes at higher . More suppressed in central than in peripheral collisions.

22. 22 Correlation with triggers  and  distributions P1P1 P2P2 Pedestal Why? STAR, PRL 95, 152301 (2005)

23. 23 Longitudinal Transverse t=0 later

24. 24 Events without jets Thermal medium enhanced due to energy loss of hard parton Events with jets in the vicinity of the jet T’- T =  T > 0 new parameter Thermal partons

25. 25 For STST recombination enhanced thermal trigger associated particle Sample with trigger particles and with background subtracted Pedestal peak in  & 

26. 26

27. 27 Pedestal in  more reliable 0.15 < p 2 < 4 GeV/c, P 1 = 0.4 2 < p 2 < 4 GeV/c, P 2 = 0.04 P1P1 P2P2 less reliable parton distribution T ’ adjusted to fit pedestal find T ’= 0.332 GeV/c cf. T = 0.317 GeV/c  T = 15 MeV/c

28. 28 Chiu & Hwa, PRC 72, 034903 (2005) pedestal  T=15 MeV

29. 29 Associated particle distribution in  Chiu & Hwa, PRC 72, 034903 (2005)

30. 30  and  production at intermediate p T For  Strange quark shower is very suppressed. p T distribution of  by recombination

31. 31 ss recombination sss s hard parton scattering fragmentation If it is hard scattering followed by fragmentation, one expects jets of particles. There are other particles associated with and Thermal-parton recombination Hwa & CB Yang, nucl-th/0602024

32. 32 A prediction that can be checked now! Since shower partons make insignificant contribution to  production for p T <8 GeV/c, no jets are involved. Select events with  or  in the 3<p T <6 region, and treat them as trigger particles. Thermal partons are uncorrelated, so all associated particles are in the background. Predict: no associated particles giving rise to peaks in , near-side or away-side. STAR did the analysis to check our prediction, and reported their result at QM06.

33. 33 STAR Ruan (Tuesday, plenary) Barranikova (Wed, plena.) Bielcikova (Sunday, 3.1) At face value the data falsify the prediction and discredits RM. Phantom jet I now explain why the prediction was wrong and how the data above can be understood. Recombination still works, but we need a deeper understanding of what is going on.

34. 34 The core issue is the (seemingly) contradictory phenomena: (1) means that there is no contribution from hard scattering, which is power-law behaved; hence, there is no jet. The resolution is to recognize that it is a phantom jet. (2) means that there is jet structure. (1)  spectrum is exponential up to 6 GeV/c. (2)  triggered events have associated particles.

35. 35     3<p t,trigger <4 GeV p t,assoc. >2 GeV Au+Au 0-10% preliminary Calderon showed on Tuesday preliminary Jet+Ridge (  ) Jet (  ) Jet  ) yield ,  ) N part But p/  ratio depends on centrality. A lot of action is going on in the ridge! Jet yield is independent of centrality.

36. 36 J. Putschke, QM-1.3 Jet+Ridge on near side Unidentified charged hadron Jet+ridge Jet only J/R~10-15%  trigger even lower! J. Bielcikova (HP06, QM06) at lower pt(assoc)

37. 37 Thus we have a ridge without any significant peak on top. The ridge would not be there without a hard scattering, but it is not a usual jet, because it contain no shower partons, only thermal partons. Phantom Jet One can see the usual peak when pT(assoc) is increased, and the ridge height will decrease. When pT(trig) is low, and the trigger is , it is not in the jet, since s quark is suppressed in the shower partons. The s quarks in the ridge form the .

38. 38 Radial expansion does not broaden the ridge under the peak in  The ridge has been interpreted as the recombination of enhanced thermal partons due to the energy loss to the medium by the passage of hard parton. Longitudinal expansion results in broad  ridge Chiu & Hwa, PRC 72, 034903 (2005)

39. 39 Resolution of the  puzzle The ridge contains thermalized partons: u, d, s Hence, sss recombine to form the trigger . Other partons can form the associated particles. (1) The pT distribution of  is exponential. (2) There are associated particles. The  looks like a peak, but it is all ridge. Our earlier prediction that there is no jet is still right, if ‘jet’ is meant to be the usual jet. But we were wrong to conclude that there would be no associated particles, because a phantom jet is associated with the  and it is the ridge that sits above the background.

40. 40 Since  is among the particles in the ridge and is formed by TTT recombination, everything calculated previously remains valid. Predictions for  triggered events: The ridge should be found in . The ridge has abundant u, d, s. So the associated particles should have the characteristic feature of recombination, i.e., large p/  and  /K ratios, ~O(1). Since the ridge arises out of enhanced thermal partons, the associated particles should have exponential pT distribution.

41. 41 Baryon vs meson triggered events (PHENIX) from the jet from the ridge J/R < 0.1? J/R > 1? Meson yield in jet is high. Meson yield in ridge decreases exponentially with pT. Ridge is developed in very central collisions. baryon trigger meson trigger

42. 42 Forward production of hadrons Back et al, PRL 91, 052303 (2003) PHOBOS, nucl-ex/0509034 Without knowing p T, it is not possible to determine x F

43. 43 BRAHMS, nucl-ex/0602018

44. 44 x F = 0.9 x F = 0.8 TFR

45. 45 Theoretically, can hadrons be produced at x F > 1? It seems to violate momentum conservation, p L > √s/2. In pB collision the partons that recombine must satisfy p B But in AB collision the partons can come from different nucleons BA (TFR) In the recombination model the produced p and  can have smooth distributions across the x F = 1 boundary.

46. 46 proton-to-pion ratio is very large. proton pion Hwa & Yang, PRC 73,044913 (2006)  : momentum degradation factor Regeneration of soft parton has not been considered. Particles at x F >1 can be produced only by recombination.

47. 47 TT TS TTT x F = 0.9 x F = 0.8 TFR x F = 1.0 ?

48. 48 Hwa & Yang, nucl-th/0605037

49. 49 Hwa & Yang, nucl-th/0605037 (to be revised)

50. 50  no shower partons involved Hwa & Yang, nucl-th/0605037 High R p/  is already known from 200 GeV data, not 62.4 GeV yet. This is not a ridge effect, since jets are suppressed at large . Thermal distribution fits well  no jets involved  no jet structure  no associated particles

51. 51 Mid- and forward/backward-rapidity correlation Trigger: 3<pT(trig)<10 GeV/c, |  (trig)|<1 (mid-rapidity) Associated: 0.2<pT(assoc)<2 GeV/c, (B) -3.9<  (assoc)<-2.7 (backward) (F) 2.7<  (assoc)<3.9 (forward)  distributions of both (B) and (F) peak at , but the normalizations are very different. d-Au collision

52. 52 is larger than Au d associated yield in this case x=0.7 x=0.05 Correlation shapes are the same, yields differ by x2. Au d x=0.05x=0.7 associated yield in that case Degrading of the d valence q? STAR (F.Wang, Hard Probes 06) Don’t forget the soft partons.

53. 53 Recombination of thermal and shower partons higher yield lower yield B/F ~ 2

54. 54 Backward-forward ratio at intermediate p T in d+Au collisions (STAR) B/F Inclusive single-particle distributions

55. 55 Au+Au centrality variation |  trig |<1, 2.7<|  assoc |<3.9 3<p T trig <10 GeV/c, 0.2<p T assoc < 2 GeV/c Normalization fixed at |  ±1|<0.2. Systematic uncertainty plotted for 10-0% data. dN/d   Near side consistent with zero. Away-side broad correlation in central collisions. Broader in more central collisions

56. 56 Au-Au collisions No difference in F or B recoil More path length, more deflection Less path length, less deflection Width of  distribution broadens with centrality At 2.7<|  |<3.9, the recoil parton is moving almost as fast as the cylinder front. What is the Mach cone effect?

57. 57 Even though the Mach cone effect is weaker, its presence implies collective medium response to the passage of a parton. What is the speed of sound? It seems to be too low. F. Wang, Ponta Delgada, 2006 The dominant effect seems to be due to deflected jets -- at midrapidity and forward region. What is the nature of the “shock wave” at forward rapidity?

58. 58 2.5<pT(trig)<4 GeV/c Associated particles on the away side Collective response of the medium: Mach cone, etc. Markovian parton scattering (MPS) Chiu & Hwa (06) Non-perturbative process Trajectories can bend Markovian Divide into many segments: Scattering angle  at each step retains no memory of the past.

59. 59 Cone width Step size Energy loss simulated result Model input Transport coefficient OurGeV 2 /fm Comparable to Vitev’s value

60. 60 Individual tracks may not be realistic, but (like Feynman’s path integral) the average over all tracks may represent physical deflected jets. (a) Exit tracks: short, bend side-ways, large  (b) Absorbed tracks: longer, straighter, stay in the medium until E i <0.3 GeV.

61. 61  Energy lost during last step is thermalized and converted to pedestal distribution Exit tracks hadronized by recombination, added above pedestal Data from PHENIX (Jia) 1<pT(assoc)<2.5 GeV/c One deflected jet per trigger at most, unlike two jets simultaneously, as in Mach cone, etc. Chiu & Hwa, nucl-th/0609038 PRC (to be published)

62. 62 Extension to higher trigger momentum p T (trig)>8 GeV/c, keeping model parameters fixed. (a) 4<p T (assoc)<6 GeV/c (b) p T (assoc)>6 GeV/c Physics not changed from low to high trigger momentum.

63. 63 Two-jet recombination at LHC New feature at LHC: density of hard partons is high. High p T jets may be so dense that neighboring jet cones may overlap. If so, then the shower partons in two nearby jets may recombine. 2 hard partons 1 shower parton from each  p Hwa & Yang, PRL 97, 042301 (2006)

64. 64 overlap probability pion Given p T, k and k’ can be smaller, thus enhancing f i (k)f i’ (k’). Effect is even more pronounced for proton formation.

65. 65 Limiting distribution for 1-jet fragmentation Does not approach limiting dist. for 1-jet Fragmentation of a parton to a proton has very low probability, but recombination of shower partons from two jets increases the yield.

66. 66 Proton-to-pion ratio at LHC  -- probability of overlap of 2 jet cones Hwa & Yang, PRL (to appear), nucl- th/0603053 single jet If  (p T )~p T -7, then we get

67. 67 The particle detected has some associated partners. There should be no observable jet structure distinguishable from the background. GeV/c That is very different from a super-high p T jet. But they are part of the background of an ocean of hadrons from other jets. A jet at 30-40 GeV/c would have lots of observable associated particles.

68. 68 If this prediction is verified, one has to go to pT(assoc)>>20 GeV/c to do jet tomography. What happens to Mach cone, etc? We predict for 10<p T <20 Gev/c at LHC Large p/  ratio NO associated particles above the background

69. 69 Conclusion Many correlation phenomena related to associated particles observed at moderate pT can be understood in terms of recombination. More dramatic phenomena may show up at LHC, but then the medium produced may be sufficiently different to require sharper probes. We have learned a lot from experiments at SPS, RHIC, and soon from LHC. At each stage the definition of a jet has changed from >2 to >8 to >20 GeV/c. What kind of correlation is interesting will also change accordingly. Beyond what is known about jet quenching, not much has been learned so far about the dense medium from studies of correlation in jets. For example, nothing learned about critical behavior from recoil parton traversing the dense medium undergoing phase transition. (a very conservative view)

70. 70 Backup slides

71. 71 STAR preliminary Jet + Ridge STAR preliminary Jet J. Bielcikova, HP06 --- at lower pt(assoc) Jet+ridge Jet only J/R~10-15%  trigger even lower!