1. Dependence of Ridge Formation on Trigger Azimuth Rudolph C. Hwa University of Oregon Ridge Workshop Brookhaven National Lab September 22, 2008

2. 2 The study of high p T physics in heavy-ion collisions --- the effect of medium on the properties of jets. Here, the reverse --- the effect of semihard jets on the medium. Intermediate p T physics: 1.5 < p T < 6 GeV/c The focus of this talk is on the ridge structure in azimuthal angle at mid-rapidity; in particular, on the dependence on trigger direction.

3. 3 We do not consider the problem of long-range rapidity correlation found by PHOBOS. It is a different problem. In pp collisions the correlation between transverse-momenta (p T1 -p T2 ) is due to a mechanism different from that between longitudinal-momenta (y 1 -y 2 ), so they are essentially unrelated. Soft ridge in auto-correlation without triggers integrates over  1 +  2, so it is insensitive to the jet direction.

4. 4 Putschke, Quark Matter 2006 Correlation on the near side STAR Ridge R J     J+RJ+R ridge R Jet J

5. 5 STAR data on Correlations vs. Reaction Plane Away-side: Evolves from single- to double- peak. Near-side: Amplitude drops. 3<p T trig <4GeV/c, 20-60% STAR Preliminary in-plane  S =0 o out-of-plane  S =90 o φ S : the angle between trigger particle and reaction plane. 0.15 0.5 1.0 1.5 2.0 3.0 GeV Feng QM08 In- plane Out-of- plane 1 4 3 2 5 6

6. 6 R yield increases with N part  medium effect 1. Centrality dependence Jet+Ridge (  ) Jet (  ) Jet  ) Putschke, QM06 p t,assoc. > 2 GeV STAR preliminary 2. p T,trig dependence Strongly correlated to jet production, even for trigger momentum < 4 GeV/c. Four features about Ridges

7. 7 3. Dependence on p T,assoc Putschke, QM06 Ridge is exponential in p T,assoc slope independent of p T,trig 4. Baryon/meson ratio Suarez QM08 B/M in ridge even higher than in inclusive distr. All four features suggest that the ridges are formed by recombination of thermal partons associated with jets

8. 8 P. Fachini, arXiv:0808.3110 B/M~1.7 up to p T ~11 GeV/c! How is it to be explained by fragmentation?

9. 9 p T distributions of  and p Hadronization by recombination Parton distributions fragmentation medium effect

10. 10  /K STAR 4 3 2 1 0 in recombination/coalescence model (Reco) 4. Baryon/Meson ratio in the Ridge is higher than in the Inclusive distribution 4. Large B/M ratio in the ridge suggests that ridge formation is also by recombination of partons.

11. 11 What partons? Putschke, QM06 Ridge is exponential in p T,assoc 3. Dependence on p T,assoc Thermal partons correlated to jets Inverse slope: T’ (for R) > T (for inc.)  T~40-50 MeV/c quark ~ exp(-q T /T’) hadron ~ exp(-p T /T’) RF ~  (p T -  i q iT )  T’ same for quarks and hadrons 2.-3. Ridge is formed by enhanced thermal partons p t,assoc. > 2 GeV STAR preliminary 2. p T,trig dependence

12. 12 1. Centrality dependence STAR preliminary Jet SSTS STAR preliminary Jet + Ridge TT For p T,trig as low as 3 GeV/c, the semihard parton is created not far from the surface because of medium opacity. Enhanced thermal partons are strongly dependent on medium Ridge is formed by recombination of enhanced thermal partons due to energy loss of a semihard parton created near the surface as it traverses the medium.

13. 13  associated particles  These wings are useful to identify the Ridge SS trigger TT ridge (R) STST peak (J) Partonic basis for ridge formation Our present concern: dependence on trigger direction. Mesons: Baryons: TTT in the ridgeB/M > 1 ~

14. 14 Trigger: 3 < p T < 4 GeV/c Associated: 1.5 < p T < 2 GeV/c Not hard enough for pQCD to be reliable, too hard for hydrodynamics. We have no reliable theoretical framework in which to calculate all those subprocesses. Physical processes involve: semihard parton propagating through dense medium energy loss due to soft emission induced by medium enhancement of thermal partons hydro flow and hadronization ridge formation above background

15. 15 Work done in collaboration with Charles Chiu (University of Texas, Austin) arXiv: 0809.3018

16. 16 The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow. If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened. Correlation between  s and  Semihard parton directed at  s, loses energy along the way, and enhances thermal partons in the vicinity of the path. ss But parton direction  s and flow direction  are not necessarily the same. ss  That leads to a cone of enhancement that forms the ridge around the flow direction . 

17. 17 Geometry x y h w Ellipse: grad u(x,y) => normal to the ellipse  x 0, y 0 x 1, y 1 t ss t = distance from creation point to surface along  s Survivability function: Density: D(x, y) depends on T A,B (s) -- a la Glauber t’  Fluctuation: Fluctuation of ridge hadron at  from local flow direction 

18. 18  01 Ridge particle distribution Observable ridge distribution per trigger III IIIIV III IIIIV

19. 19 top 5% 3<p T trig <4GeV/c & 1.0<p T asso <1.5GeV/c 20-60% in-plane  S =0out-of-plane  S =90 o In 20-60%, away-side evolves from single-peak (φ S =0) to double-peak (φ S =90 o ). In top 5%, double peak show up at a smaller φ S. At large φ S, little difference between two centrality bins. STAR Preliminary Quark Matter 2008 -- A. Feng (STAR) Dependence on trigger azimuthal angle 1 4 3 2 5 6 in- plane out-of-plane

20. 20 STAR Preliminary in-plane  S =0out-of-plane  S =90 o Ridge Jet 3<p T trig <4, 1.5<p T trig <2.0 GeV/c Ridge and Jet components are separated. In-plane Out-of- plane 1 4 3 2 5 6 20-60% Ridge shapes in  are similar. Study the area, which is the yield.

21. 21 Jet and Ridge Yield 20-60%top 5% jet part, near-side ridge part, near-side jet part, near-side ridge part, near-side Ridge: seem to decrease with φ s. More significant in 20-60% than top 5%. Jet: seem to slightly increase with φ s. Strong near-side jet-medium interaction in reaction plane, generating sizable ridge? Minimal near-side jet-medium interaction perpendicular to reaction plane? STAR Preliminary 3<p T trig <4, 1.5<p T trig <2.0 GeV/c

22. 22 Yield per trigger a constant t0t0 t 1 ~ 0.1 t 0 Adjust N to fit overall normalization for top 5%; relative normalization for 20-60% not adjustable. N encapsules all uncalculable effects of the soft processes involved in the ridge formation, and is not essential to the study of the  s dependence.

23. 23 3<p T trig <4, 1.5<p T trig <2.0 GeV/c Data: Feng QM08 Chiu-Hwa (0809.3018) Vary t 0 and : t 0 =0.25 R A =0.09 ~20 o

24. 24 CEM ss 

25. 25 left half ellipse

26. 26  distribution Yield involves integration over  : For  dependence, study  =  -  s ss t    --- degree of fluctuation of  around  t’ t’ is distance along  (x,y)

27. 27 Mid-Central v.s. Central Collisions Comparison top 5% 3<p T trig <4GeV/c & 1.0<p T asso <1.5GeV/c 20-60% in-plane  S =0out-of-plane  S =90 o In 20-60%, away-side evolves from single-peak (φ S =0) to double-peak (φ S =90 o ). In top 5%, double peak show up at a smaller φ S. At large φ S, little difference between two centrality bins. STAR Preliminary 15-30

28. 28  =1

29. 29 Dependence on 

30. 30 0 <  s <  /2 left shift -  /2 <  s < 0 right shift  <  s  >  s    -  s

31. 31 0 <  s <  /2 20-60% No shift for  s = 0  s =  /2

32. 32 Ridge yield integrates over , so it is not sensitive to the shifts in  for specific  s. The shifts are properties of the  s -  correlation, which can be tested directly by experiment by use of a new measure. We propose the inside-outside asymmetry function

33. 33 Asymmetry function Define + _ + _ x y A(  s )=0 along x & y axes RP inside outside

34. 34 Inside-outside Asymmetry At 0%, A=0 by symmetry At >60% A(  s ) is mostly large

35. 35 III IIIIV II

36. 36 20-60% jet part, near-side ridge part, near-side top 5% jet part, near-side ridge part, near-side STAR data on  s dependence 3<p T trig <4, 1.5<p T trig <2.0 GeV/c Why is the yield at top 5% lower than the yield at 20-60%, ----- when  s is small ?

37. 37 Why does the yield decrease as b decreases? Fix  S =5 deg, study yield/trigger vs impact parameter b. b=0 b=0.8R A At b=0, more N trig, but ridge yield does not increase due to the mismatch between  S and . So yield/trigger should decrease with decreasing b, when  S =5 deg. But not for all  S b/R A yield/trigger  S =5 deg

38. 38 triggers without ridge

39. 39

40. 40 N part Yield averaged over all  S has a dip at high N part

41. 41 PHENIX data before Ridge is separated Has always been a puzzle until now.

42. 42 Centrality dependence Jet+Ridge (  ) Jet (  ) Jet  ) Putschke, QM06 N part Need further study

43. 43 b=0 b=0.8R A Tangential jets should not lead to ridge formation for any centrality Should look for lack of ridge structure in events triggered by dijets.

44. 44 Barannikova: ISMD 07; QM 08 associates primary trigger (T1) “jet-axis” trigger (T2) Signal sit atop of a largely uncorrelated background STAR - Study of dijet events Courtesy of R.Hollis

45. 45 Shape Modifications Centrality dependence –  projection: no significant shape/yield modifications –  projection: no apparent ridge T1: p T >5GeV/c T2: p T >4GeV/c A: p T >1.5GeV/c J. Putschke, QM2006 12% Central 40-60% MB 60-80% MB  -2 01 2 345 1 _dN_ N trig d  ) 2 STAR Preliminary 0 Au+Au 12% central |  |<0.7 T2A1_T1 T1A1_T2  -1.5 0 1 -0.5 0.5 1.5 1 _dN_ N trig d  ) STAR Preliminary 0 ZYAM normalization Barannikova ISMD-2007 QM2008

46. 46 STAR Preliminary ** Surface Effects T1: p T >5GeV/c T2: p T >4GeV/c A: p T >1.5GeV/c If the triggers have tangential bias: expect a term related to the surface –Surface ~ R 2 ~ N part 2/3 ** Shown are statistical errors only Number of triggers per event (per number of binary collisions) –Single triggers and (all qualified) pairs behave similar to inclusives STAR Preliminary ** T1= 5 GeV/c 100 0 200 300 N part 0 N trig __ N evt N part 2/3 0.4 d+Au x 10 -3 STAR Preliminary ** #T1T2 pairs / #Single triggers #Di-Jets / #Single triggers 100 0 200 300 0.015 0.05 0.01 N part Surface ~ R 2 ~ N part 2/3 Barannikova ISMD-2007 From the N part 2/3 dependence, it can be inferred that these dijets are mainly tangential jets.

47. 47 As p T1 and p T2 become more unbalanced, the dijets become less tangential. We predict that as p T1 -p T2 increases, a ridge will begin to develop. It means that the flow direction becomes closer to the jet direction, and the mismatch becomes less severe.

48. 48 We have not used recombination explicitly, but hadronization of thermal partons is based on it. TT (meson) TTT (baryon) along  TS recombination is also suppressed if their directions are not parallel --- for a different reason: Reco Function SS recombination (i.e., fragmentation) would be independent of , so there would be no  s dependence.

49. 49 Summary The Correlated Emission Model (CEM) reproduces the data on the  s dependence of the ridge yield. The main input is the correlation between the directions of semihard parton and soft-parton flow. Predictions: inside-outside asymmetry a dip in centrality dependence at large N part development of ridge structure in dijet events Verification of these predictions can confirm our interpretation of the effects of jets on the medium.