Ridges and v 2 without hydrodynamics Rudolph C. Hwa University of Oregon Int’nal Symposium on Multiparticle Dynamics Berkeley, August 2007

2 Prevailing paradigm on azimuthal asymmetry in heavy-ion collisions at low p T is hydrodynamical flow. Calling v 2 “elliptic flow” is a distinctive mark of that paradigm. Are there any alternatives? Why bother? What if hydrodynamics is found invalid at early times?

3 Results on single-particle distributions from hydro Kolb & Heinz, QGP3  0 =0.6 fm/c (RHIC 130, 200),  0 =0.8 fm/c (SPS 17) RHIC 130 GeV

4 “Elliptic flow” -- v 2 Agree with data for p T <1.5GeV/c possible only if  0 ~0.6 fm/c Huovinen, Kolb, Heinz, Ruuskanen, Voloshin Phys. Lett. B , (2001).

5 Conventional wisdom Azimuthal anisotropy can be understood in terms of hydrodynamical flow for p T <1.5 GeV/c It requires fast thermalization.  0 =0.6 fm/c high pressure gradient leads to momentum space asymmetry:  v 2 >0

6 Conventional wisdom BNL-PR strongly interacting QGP perfect liquid What is the direct experimental evidence that either verifies or falsifies the conclusion on perfect liquid? Based on a crucial assumption in theoretical calculation: fast thermalization Not expected nor understood in QCD. What if  0 =1-1.5 fm/c? If so, then the hydro results would disagree with data. How much of sQGP and perfect liquid can still be retained? Instability?

7 Alternative approach must be sensitive to the initial configuration (hard) must be able to describe the bulk behavior (soft) For p T <1.5 GeV/c (the region that hydro claims success) we consider semi-hard scattering: Semi-hard parton q T ~ 2-3 GeV/c (  0.1 fm/c) can have significant effect on thermal partons for p T <1.5 GeV/c. Ridges

8 Ridgeology

9 Jet structure Putschke, QM06     J+RJ+R R J ridge R Jet J

10 In a high p T jet, a hard- scattered parton near the surface loses energy to the medium. Recombination of enhanced thermal partons gives rise to the ridge, elongated along  The peak is due to thermal-shower recombination in both  and  Chiu & Hwa, PRC 72, (2005) ridge bg R J pTpT Power-law behavior is a sign of Jet production peak It generates shower partons outside.

11  puzzle  distribution of associated particles shows what seems like jet structure. p T distribution is exponential; thus no contribution from jets Bielcikova (STAR) Blyth (STAR) SQM 06

12 STAR data nucl-ex/ <p T trig < <p T assoc <p T trig Chiu & Hwa, All ridge ! The  puzzle is solved by recognizing that the  trigger and its associated particles are all produced by the thermal partons in the ridge.

13 Jet Ridge Putschke, QM06  

14 The ridge would not be there without a semi-hard scattering, but it does not appear as a usual jet. Ridges of low p T hadrons are there, with or without triggers, so long as there are semi-hard partons near the surface to generate enhanced thermal partons. Phantom jet It is a Jet-less jet. Summary of ridgeology Ridges are the recombination products of enhanced thermal partons stimulated by semi-hard scattering near the surface. At low p T there can be ridges without Jets (peaks). A ridge without any significant peak on top.

15 Azimuthal Asymmetry Now to

16 Relevant physics must be sensitive to the initial configuration. Phantom jets are produced at early times, if hard enough, but should be soft enough so that there are many of them produced in each collision. At low x (~0.03) there are many ‘soft’ partons to create phantom jets at  ~0. Semi-hard partons: q T ~2-3GeV/c, (<0.1 fm/c), (That is not true at large forward .)

17 |  | <  = cos -1 (b/2R)   At any given  Each scattering sends semi-hard partons in random directions. on average, the jet direction is normal to the surface. If the phantom jets are soft enough, there are many of them, all restricted to |  | < . Recoil partons thermalize the bulk medium. Initial configuration Thermalization of partons takes time, but the average direction of each ridge is determined at initial time.

18 Bulk partons pions Bulk+Ridge partons

19 v2v2

20 B+RB Thermal pions only p T <1.5 GeV/c Small p T region

21 ridge spectrum harder than inclusive h +,- (~ MeV in slope parameter) “Jet”/ridge yield vs. p t,assoc. in central Au+Au preliminary Au+Au 0-10% preliminarySTAR preliminary Ridge Jet Ridge/Jet yield STAR preliminary “jet” slope ridge slope inclusive slope Putschke HP06 TT

22 Use  T=45 MeV T=0.29 GeV Get T”=2.12 GeV PHENIX 40-50% Max of sin2  (b) at  =  /4 b=√2 R=10 fm centrality 50% At small p T The first time that a connection is made between ridge and v 2.

% 30-40% 20-30% 10-20% 5-10%

% 30-40% 20-30% 10-20% 5-10%

25 Centrality dependence v2v2 b sin2  (b)  (b)=cos -1 b/2R at p T =0.5 GeV/c Max[v2]=p T /  T’’=0.075

26 STAR: Au-Au at 130 GeV PRC 66, (2002) (what p T range not indicated)

27 Normalized impact parameter  =b/2R sin2  (b)  f(  ) = sin(2cos -1  ) f(  ) is universal, so it should be the same for Cu-Cu and at other √s. STAR data on v2 for Au-Au at 130GeV, normalized to 1 at max:  =1/√2

28 Nouicer (PHOBOS) QM06 f()f()  0-20%20-40% describes universal centrality behavior, independent of: Au or Cu, for √s=200 or 62.4 GeV 1/0.15

29 Proton 40-50% at small p T

30 Transverse kinetic energy E K p T for pion m T -m p for proton Initial slope A property that is independent of the hadron species h. T’’ is a property of the partons that recombine. It trivially satisfies the constituent quark scaling:

31 PHENIX preliminary KE T Scaling Mesons Baryons R.Lacey, ETD-HIC 07 Jet contribution Property of partons in the ridge before hadronization

32 Forward rapidity  =0  >0 Mid-rapidity region Semi-hard scattering involve small x partons more phantom jets many ridges larger x partons, thus lower multiplicity fewer phantom jets ridge effect reduced v 2 decreases with increasing 

33 Au+Au Au+Au: PHOBOS Collaboration PRL. 94, (2005) Cu+Cu: PHOBOS Collaboration PRL: nucl-ex/ Cu+Cu Preliminary v 2 measured: - broad  range - several energies Observations on v 2 of Cu+Cu : - large - similar in shape to Au+Au Nouicer QM06 (PHOBOS)

34 Conclusion Azimuthal anisotropy is mainly a ridge effect. No fast thermalization or hydrodynamical flow are needed. Hydrodynamics may still be applicable after some time, but it is not needed for v 2, for which the relevant physics at  <1 fm/c is crucial --- semi-hard scattering at q T <3. For p T <1.5 GeV/c, the analysis is simple, and the result can be expressed in analytic form that agrees with data. For p T >1.5 GeV/c, shower partons must be considered. Jet dominance (>3GeV/c) will saturate v 2. No part of the study suggests that the medium behaves like a perfect fluid.

35 EXTRA SLIDES

36 In peripheral collisions there are some complications. It is harder to produce protons in the bulk because of lower density of soft partons. (remember pp collisions) Thermal parton distributions in F uud are not factorizable. T in B(p T ) is lower. Thus phantom jets are relatively more effective in enhancing the thermal partons for p production at large b. So B(p T )/R(p T ) for proton is smaller than for pion Hence, v 2 (p T,b) continues to increase for  (b) smaller than  /4. not negligible

37 How universal is? Ridge phenomenology is rudimentary, and theoretical calculation at low p T unreliable. Enhanced thermal partons in the ridge: T’/T=1+? Since the bulk T encapsules the dependences on: energy, system size, thermalization, then T’-T=aT 2 +…, compared to  T=TT’/T’’, a=1/T’’ to first order. Thus T’’=2.12 GeV is universal to first order. T’/T=1+aT+…expand

38 PHOBOS PRL 94, (2005) v 2 at all  and various s v 2 =  ’  ’ ~ ln x for some

39 BRAHMS has p T dependence at  =3.2 nucl-ex/ Theoretical treatment of forward production is not simple. Hwa & Yang, PRC (2007). Recombination of thermal partons in comoving frame at . Exponential Ridge due to semi-hard parton at  ’>  of bulk. R/B decreases with increasing x as a function of F(x). v 2  R/B decreases with increasing  ’ as a function of F(x), thus exhibiting a scaling behavior.