Ridges, Jets and Recombination in Heavy-ion Collisions

1. Ridges, Jets and Recombination in Heavy-ion Collisions Rudolph C. Hwa University of Oregon Shandong University, Jinan, China October, 2012

2. Outline • Introduction • Ridges • Minijets • Particle spectra and correlations • Azimuthal anisotropy • Large Hadron Collider • Conclusion

3. The conventional method to treat heavy-ion collisions is relativistic hydrodynamics ---- which can be tuned to reproduce data. There is no proof that it is the only way (necessary) ---- can only demonstrate that it is a possible way (sufficient). We propose another possible way Yang Chunbin (Wuhan) Zhu Lilin (Sichuan) Charles Chiu (U. Texas) ---- minijets and recombination. An area of focus is about Ridges which is an interesting phenomenon in its own right.

4. Ridge

5. Collision geometry pseudorapidity azimuthal angle transverse momentum 5

6. p2 p1  

7. ridge RJet J trigger J+R  R   J  STAR Putschke, QM06 Properties of Ridge Yield Dependences on Npart, pT,trig, pT,assoc, trigger  Correlation on the near side Ridgeology

8. on pT,trig 2. participants STAR preliminary Putschke, QM06 pt,assoc. > 2 GeV Jet+Ridge () Jet () Jet) Ridges observed at any pT,trig Ridge yield 0 R as Npart 0 Ridge is correlated to jet production. Surface bias of jet  ridge is due to medium effect near the surface  depends on medium Medium effect near surface 1. Dependence on Npart

9. Ridge Ridge is from thermal source enhanced by energy loss by semi-hard partons traversing the medium. 3.Dependence on pT,assoc Ridge is exponential in pT,assoc slope independent of pT,trig Putschke, QM06 STAR Exponential behavior implies thermal source. Yet Ridge is correlated to jet production; thermal does not mean no correlation.

10. 6 5 4 3 2 1 Out-of-plane Different s dependencies for different centralities --- important clues on the properties of correlation and geometry In-plane Feng, QM08 4. Dependence of jet and      ridge yields on trigger s STAR jet part, near-side ridge part, near-side jet part, near-side ridge part, near-side 20-60% top 5% s 3<pTtrig<4, 1.5<pTassoc<2.0 GeV/c

11. Auto-correlationbetween p1 and p2 0.15<pt<2.0 GeV/c, ||<1.3, at 130 GeV STAR, PRC 73, 064907 (2006) Effect of Ridge on two-particle correlation without trigger Ridges are present with or without triggers.

12. From the data on ridge, we learn that Ridge is correlated to jets (detected or undetected). Ridge is due to medium effect near the surface. Ridge is from the thermal source enhanced by energy loss by semihard partons traversing the medium. Geometry affects the ridge yield. On the basis of these phenomenological properties we build a theoretical treatment of the ridge. But first we outline the theoretical framework that describes the formation of hadrons from quarks.

13. intermediate ReCo TT TS SS Hadronization Cooper-Frye k1+k2=pT lower ki higher density Theoretical treatment Usual domains in pT at RHIC low high pT 2 6 Hydro pQCD GeV/c Fragmentation kT > pT

14. Proton formation: uud distribution usual fragmentation soft component soft semi-hard components (by means of recombination) Pion formation: distribution thermal shower

15. h fragmentation S D(z) q A A In high pT jets it is necessary to determine the shower parton distributions. Once the shower parton distributions are known, they can be applied to heavy-ion collisions. The recombination of thermal partons with shower partons becomes conceptually unavoidable.

16. h Now, a new component In high pT jets it is necessary to determine the shower parton distributions. Once the shower parton distributions are known, they can be applied to heavy-ion collisions. The recombination of thermal partons with shower partons becomes conceptually unavoidable.

17. soft TT TS hard SS thermal Pion distribution (log scale) fragmentation Transverse momentum

18. fragmentation thermal  production by TT, TS and SS recombination Hwa & CB Yang, PRC70, 024905 (2004)

19. Recall what we have learned from the ridge data: Ridge is correlated to jets (detected or undetected). Ridge is due to medium effect near the surface. Ridge is from the thermal source enhanced by energy loss by semihard partons traversing the medium. Geometry affects the ridge yield. Now, back to Ridge. How do we relate ridge to TT, TS, SS recombination?

20. Recombination of partons in the ridge associated particles SS trigger ST peak (J) TT ridge (R) These wings are useful to identify the Ridge Ridge is from enhanced thermal source caused by semi-hard scattering. Medium effect near surface   At 0 it is mainly the  distribution that is of interest.

21. Hard parton directed ats , loses energy along the way, and enhances thermal partons in the vicinity of the path. The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow. Flow direction  normal to the surface Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction . s  But parton directionsandflow direction are not necessarily the same. s  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

22. CEM  s Correlated emission model (CEM) Chiu-Hwa, PRC 79, 034901 (09) STAR Feng QM08 3<pTtrig <4 1.5 <pTassoc <2 GeV/c

23. Region where hydro claims relevance --- requires rapid thermalization 0 = 0.6 fm/c Semi-hard scattering 1<kT<3 GeV/c Copiously produced, but not reliably calculated in pQCD t < 0.1 fm/c That was Ridge associated with a trigger Single-particle distribution at low pT(<2 GeV/c) Something else happens even more rapidly 1. If they occur deep in the interior, they get absorbed and become a part of the bulk. 2. If they occur near the surface, they can get out. --- and they are pervasive.

24. Base is the background, independent of  Ridge, dependent on , hadrons formed by TT reco Correlated part of two-particle distribution on the near side ? trigger assoc part JET RIDGE Ridge can be associated with a semihard parton without a trigger. How is this untriggered ridge related to the triggered ridge on the near side of correlation measurement?

25. Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2 1 2 2 1 If events are selected by trigger(e.g. Putschke QM06, Feng QM08), the ridge yield is integrated over all associated particles 2. untriggered ridge triggered ridge yield Ridge is present whether or not 1 leads to a trigger. Semihard partons drive the azimuthal asymmetry with a  dependence that can be calculated from geometry. (next slide)

26. For every hadron normalto the surface there is a limited line segment on the surface around 2through which the semihard parton 1can be emitted. 2   elliptical integral of the second kind Ridge due to enhanced thermal partons near the surface Top view: segment narrower at higher b Side view: ellipse (larger b) flatter than circle (b=0) around =0. R(pT,,b)  S(,b) b normalized to RA nuclear density D(b) Hwa-Zhu, PRC 81, 034904 (2010) Geometrical consideration for untriggered Ridge

27.  Asymmetry of S(,b) =0 =/2 =0 =/2 S(,b) converts the spatial elliptical anisotropy to momentum anisotropy --- key step in calculating v2without free parameters.

28. y py px x Elliptic flow Momentum asymmetry Conventional hydro approach higher pressure gradient Good support for hydro at pT<2 GeV/c Assumption: rapid thermalization Inputs: initial conditions, EOS, viscosity, freeze-out T, etc.

29. More in the x direction than in the y direction  asymmetry can be expanded in harmonics: Minijet approach If minijets are created within 1 fm from the surface, they get out before the medium is equilibrated. Their effects on hadronization have azimuthal anisotropy We can show agreement with v2 data in this approach also --- with no more parameters used than in hydro and without assumption about rapid thermalization

30. base T0 to be determined ridge pT Enhancement factor factorizable b T0 is the only parameter to adjust to fit the v2 data Hwa-Zhu (12) Azimuthal anisotropy

31. STAR Npart dependence is independent of pT Agrees with <cos2>S for Npart>100 No free parameters used for Npart dependence

32. T0 = 0.245 GeV hydrodynamical elliptic flow ridge generated by minijets without hydro T’ determines pT dependence of v2 as well as the ridge magnitude (T=T-T0) One-parameter fit of pT dependence (Npart dependence already reproduced).

33. When TS recombination is also taken into account, we get better agreement with data R.Hwa - L. Zhu, Phys. Rev. C 86, 024901 (2012)

34. pT dependence of Ridge Inclusive T=0.283 GeV Base Ridge enhancement of thermal partons by minijets (inclusive) Base T0=0.245 GeV Ridge TR=0.32 GeV Inclusive ridge v2 and ridgeare intimately related  dependence due to initial parton momenta

35. Bridge B ridge Minijet TS recombination RHIC At pT>2GeV/c, we must further include SS recombination.

36. ALICE Using the same recombination model applied to Pb-Pb collisions at 2.76 TeV, we get T=0.38 GeV and good fits of all identified particle spectra. Large Hadron Collider (LHC)

38. R.H.-L.Zhu, PRC84,064914(2011)

39. We learn about the dependence of T and S on collision energy. pions quarks The pT range is too low for reliable pQCD, too high for hydrodynamics. Shower partons due to minijets are crucial in understanding the nature of hadronic spectra. TS and TTS recombination provides a smooth transition from low to high pT --- from exponential to power-law behavior.

40. As is increased from RHIC to LHC, S is significantly higher. Conclusion Study of Ridge and Minijets gives us insight into the dynamical process of hadronization: Ridge in TT reco with enhanced T due to minijets Azimuthal anisotropy (v2) can be well reproduced without hydrodynamics. Spectra of all species of hadrons are well explained by TT, TTT, TS, TTS, TSS, SS, SSS recombination. Minijets at LHC cannot be ignored --- even at low pT.

41. At LHC the Higgs boson may have been found. But in Pb-Pb collisions, nothing so spectacular has been discovered. Most observables seem to be smooth extrapolations from RHIC in ways that have been foreseen. Can we think of anything that is really extraordinary? --- unachievable at lower energies e.g., a strange nugget? solid evidence against something?

42. The End Thank you

43. Backup slides

44. Pion Recombination function q and qbar momenta, k1, k2, add to give pion pT TT Proton same T for partons, , p TTT phase space factor in RF for proton formation Hadron production by parton recombination At low pT thermal partons are most important empirical evidence

45. p Same T for , K, p --- in support of recombination. T=0.283 GeV Proton production from recombination Hwa-Zhu, PRC 86, 024901 (2012) PHENIX, PRC 69, 034909 (04) Slight dependence on centrality

46. hadronization geometrical factors due to medium q  probability of hard parton creation with momentum k k degradation b only adjustable parameter  is calculable from geometry Path length TS+SS recombination

47. Nuclear medium that hard parton traverses  Geometrical path length k D(x(t),y(t)) x0,y0 density (Glauber) Dynamical path length Average dynamical path length  to be determined Probability of hard parton creation at x0,y0 Geometrical considerations

48. R J S T Hwa-Yang PRC(04),(10) pT dependence of TS component is known  = Higher harmonics Conventional approach: fluctuations of initial configuration Minijet approach: hadronization of minijets themselves outside the medium --- plays the same role as fluctuations of initial state J stays close to the semihard parton, whose  angle is erratic; thus additional contribution to azimuthal anisotropy.

49. v2 arises mainly from v3, v4 come only from Hwa-Zhu a2=0.6, a3=1.6, a4=1.4