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Ridges and v 2 without hydrodynamics

Ridges and v 2 without hydrodynamics. Rudolph C. Hwa University of Oregon. Int’nal Symposium on Multiparticle Dynamics Berkeley, August 2007. Prevailing paradigm on azimuthal asymmetry in heavy-ion collisions at low p T is hydrodynamical flow.

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Ridges and v 2 without hydrodynamics

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  1. Ridges and v2without hydrodynamics Rudolph C. Hwa University of Oregon Int’nal Symposium on Multiparticle Dynamics Berkeley, August2007

  2. Prevailing paradigm on azimuthal asymmetry in heavy-ion collisions at low pT is hydrodynamical flow. Calling v2 “elliptic flow” is a distinctive mark of that paradigm. What if hydrodynamics is found invalid at early times? Are there any alternatives? Why bother?

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

  4. Huovinen, Kolb, Heinz, Ruuskanen, Voloshin Phys. Lett. B 503 58, (2001). “Elliptic flow” -- v2 Agree with data for pT<1.5GeV/c possible only if 0~0.6 fm/c

  5. high pressure gradient leads to momentum space asymmetry: v2>0 Conventional wisdom Azimuthal anisotropy can be understood in terms of hydrodynamical flow for pT<1.5 GeV/c It requires fast thermalization. 0=0.6 fm/c

  6. Based on a crucial assumption in theoretical calculation:fast thermalization Conventional wisdom BNL-PR strongly interacting QGP perfect liquid What is the direct experimental evidence that either verifies or falsifies the conclusion onperfect liquid? Not expected nor understood in QCD. Instability? 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?

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

  8. Ridgeology

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

  10. peak ridge It generatesshower partons outside. The peak is due to thermal-shower recombination in both  and  Recombination of enhanced thermal partons gives rise to the ridge, elongated along  J bg R pT Chiu & Hwa, PRC 72, 034903 (2005) In a high pT jet,a hard- scattered parton near the surface loses energy to the medium. Power-law behavior is a sign of Jet production

  11. Bielcikova (STAR) 0701047 pT distribution is exponential; thus no contribution from jets  puzzle Blyth (STAR) SQM 06  distribution of associated particles shows what seems like jet structure.

  12. All ridge ! STAR data nucl-ex/0701047 2.5<pTtrig<4.5 1.5<pTassoc<pTtrig Chiu & Hwa, 0704.2616 The  puzzle is solved by recognizing that the  trigger and its associated particles are all produced by the thermal partons in the ridge.

  13. Ridge 3 - 4   Putschke, QM06 Jet

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

  15. Azimuthal Asymmetry Now to

  16. Semi-hard partons: qT~2-3GeV/c, (<0.1 fm/c), At low x (~0.03) there are many ‘soft’ partons to create phantom jets at ~0. 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. (That is not true at large forward .)

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

  18. pions Bulk+Ridge partons pions Bulk partons

  19. v2

  20. B+R B Thermal pions only pT<1.5 GeV/c Small pT region

  21. “jet” slope ridge slope inclusive slope STAR preliminary Ridge Jet T “Jet”/ridge yield vs. pt,assoc. in central Au+Au STAR preliminary preliminary Au+Au 0-10% preliminary Ridge/Jet yield Putschke HP06 ridge spectrum harder than inclusive h+,- (~ 40-50 MeV in slope parameter)

  22. PHENIX 40-50% At small pT Max of sin2(b) at =/4 b=√2 R=10 fm centrality 50% The first time that a connection is made between ridge and v2. Use T=45 MeV T=0.29 GeV Get T”=2.12 GeV

  23. 40-50% 30-40% 20-30% 10-20% 5-10%

  24. 40-50% 30-40% 20-30% 10-20% 5-10%

  25. v2 sin2(b) b Centrality dependence (b)=cos-1 b/2R atpT=0.5 GeV/cMax[v2]=pT/T’’=0.075

  26. STAR: Au-Au at 130 GeV PRC 66, 034904 (2002) (what pT range not indicated)

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

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

  29. 40-50% at small pT Proton

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

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

  32. v2 decreases with increasing  Mid-rapidity region Forward rapidity • Semi-hard scattering involve small x partons • more phantom jets • many ridges >0 • larger x partons, thus lower multiplicity • fewer phantom jets • ridge effect reduced =0

  33. Nouicer QM06 (PHOBOS) Au+Au:PHOBOS CollaborationPRL. 94, 122303 (2005) Au+Au v2measured:-broad h range- several energies Observations on v2 of Cu+Cu : - large - similar in shape to Au+Au Cu+Cu Preliminary Cu+Cu:PHOBOS CollaborationPRL: nucl-ex/0610037

  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 v2, for which the relevant physics at <1 fm/c is crucial --- semi-hard scattering at qT<3. • For pT<1.5 GeV/c, the analysis is simple, and the result can be expressed in analytic form that agrees with data. • For pT>1.5 GeV/c, shower partons must be considered. Jet dominance (>3GeV/c) will saturate v2. • No part of the study suggests that the medium behaves like a perfect fluid.

  35. EXTRA SLIDES

  36. not negligible 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 Fuud are not factorizable. T in B(pT) is lower. Thus phantom jets are relatively more effective in enhancing the thermal partons for p production at large b. So B(pT)/R(pT) for proton is smaller than for pion Hence, v2(pT,b) continues to increase for (b) smaller than /4.

  37. expand T’/T=1+aT+… then T’-T=aT2+…,compared toT=TT’/T’’, a=1/T’’ to first order. Thus T’’=2.12 GeV is universal to first order. How universal is ? Ridge phenomenology is rudimentary, and theoretical calculation at low pT unreliable. Enhanced thermal partons in the ridge: T’/T=1+? Since the bulk T encapsules the dependences on: energy, system size, thermalization,

  38. v2 = 0.014 - 0.0075’ PHOBOS PRL 94, 122303 (2005) v2 at all  and various s ’ ~ ln x for some <mT>

  39. Theoretical treatment of forward production is not simple. Hwa & Yang, PRC (2007). BRAHMS has pT dependence at =3.2 nucl-ex/0602018 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 ofF(x). v2 R/B decreases with increasing ’ as a function of F(x), thus exhibiting a scaling behavior.

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