2. Recombination in Nuclear Collisions Rudolph C. Hwa University of Oregon Critical Examination of RHIC Paradigms University of Texas at Austin April 14-17, 2010

3. Outline 1. Introduction 2. Earlier evidences for recombination 3. Recent development A. Azimuthal dependence --- ridges B. High p T jets --- scaling behavior 4. Future possibilities and common ground

4. 1. Introduction pQCDReCoHydro Fragmentation k T > p T Hadronization Cooper- Frye k 1 +k 2 =p T lower k i higher density TTTSSS lowhighintermediate 26 Usual domains in p T pTpT GeV/c

5. Regions in time  (fm/c) 18 hadronization 0.6 rapid thermalization hydro Cronin effect: --- initial-state transverse broadening What about Cronin effect for proton, larger than for  ? Early-time physics: CGC, P violation, … Pay nearly no attention to hadronization at late times. In ReCo: Final-state effect, not hard-scattering+Frag, not hydro. What about semihard scattering (k T <3GeV/c) at  <0.6 fm/c?

6. 2. Earlier evidences for Recombination A. p T distribution at mid-rapidity Recombination function q and qbar momenta, k 1, k 2, add to give pion p T It doesn’t work with transverse rapidity y t TTTTT same T for partons, , p empirical evidence At low p T phase space factor in RF for proton formation Pion at y=0Proton at y=0

7. PHENIX, PRC 69, 034909 (04) went on to m T plot Hwa-Zhu (preliminary) Proton production from reco Same T for , K, p --- a direct consequence of ReCo. Slight dependence on centrality --- to revisit later

8. B. p/  ratio At higher p T shower partons enter the problem; TS recombination enters first for pion, and lowers the ratio. It is hard to get large p/  ratio from fragmentation of hard partons. dominated by thermal partons at low p T ReCo

9. C. Revisit very early formulation of recombination [at the suggestion of organizers: Hwa, PRD22,1593(1980)] The notion of valon needs to be introduced. For p+p  p+X we need Consider the time-reversed process p+p  +X Feynman x distribution at low p T

10. Deep inelastic scattering e e p FqFq We need a model to relate to the wave function of the proton FqFq Valon model p U U D valons A valence quark carries its own cloud of gluons and sea quarks --- valon

11. p U U D Basic assumptions valon distribution is independent of probe parton distribution in a valon is independent of the hadron valence quark distr in proton valon distr in proton, independent of Q valance quark distribution in valon, whether in proton or in pion  initiated DY process

12. p + p  h + X in multiparticle production at low p T p U U D valon distribution collision process partons chiral-symmetry breaking quarks gain masses momenta persist U D RF ++ No adjustable parameters 1979 data (Fermilab E118) Not sure whether anyone has done any better Feynman’s original parton model PRL(69)

13. D. Shower partons in AA collisions At higher p T Hard scattering calculable in pQCD Hadronization by fragmentation In between hard scattering and fragmentation is jet quenching. Fine, at very high p T (> 6GeV/c), but not reliable at intermediate p T T(q 1 )S(q 2 /q)  R(q 1,q 2,p T ) Fragmentation: D(z) => SS recombination, but there can also be TS recombination at lower p T pion proton We need shower parton distribution. ∫dk k f i (k) G(k,q) k q

14. Description of fragmentation known from data (e+e-,  p, … ) known from recombination model can be determined recombinationshower partons hard parton meson fragmentation by recombination

15. Shower parton distributions u g s s d du L L  D  Sea K NS L  D  V GG  D  G L L s  D K Sea G G s  D K G 5 SPDs are determined from 5 FFs. assume factorizable, but constrained kinematically. Hwa & CB Yang, PRC 70, 024904 (04) BKK FF(mesons) Using SSS we can calculate baryon FF Hwa-Yang, PRC 73, 064904 (06)

16. Other topics: 1.Constituent quarks, valons, chiral-symmetry breaking, f  2.Collinear recombination 3.Entropy 4.Hadronization of gluons 5.Dominance of TS over TT at p T >3 GeV/c 6.Single-particle distributions 7.R CP p (p T )> R CP  (p T ) 8.Forward-backward asymmetry in dAu collisions 9.Large p/  ratio at large  10.v 2 (p T ) Quark-number scaling 11.Ridges 12.Correlations earlier later recent

17. 3. Recent development Azimuthal dependence PHENIX 0903.4886 85<  <90 30<  <45 0<  <15  pTpT N part A. p T < 2 GeV/cB. p T > 2 GeV/c

18. A. p T <2 GeV/c Region where hydro claims relevance --- requires rapid thermalization  0 = 0.6 fm/c Something else happens even more rapidly Semi-hard scattering 1<k T <3 GeV/c Copiously produced, but not reliably calculated in pQCD  t < 0.1 fm/c 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. [Tom Trainor’s minijets (?)]

19. On the way out of the medium, energy loss enhances the thermal partons --- but only locally. Recombination of enhanced thermal partons  ridge particles Base, independent of , not hydro bulk Ridge, dependent on , hadrons formed by TT reco Ridge can be associated with a hard parton, which can give a high p T trigger. But a ridge can also be associated with a semihard parton, and a trigger is not necessary; then, the ridge can be a major component of Correlated part of two-particle distribution on the near side Putschke triggerassoc partJETRIDGE How are these two ridges related?

20. BOOM Hard parton Ridge without trigger but that is a rare occurrence Semihard partons, lots of them in each event Ridges without triggers --- contribute significantly to single-particle distribution ratatatatatata We need an analogy

21. 1 2 1 2 Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same  2 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. Hwa-Zhu, 0909.1542, PRC (2010) If events are selected by trigger (e.g. Putschke QM06, Feng QM08), the ridge yield is integrated over all associated particles  2. Enhanced thermal partons on average move mainly in the direction normal to the surface ~ |  2 -  1 |<  ~0.33 Correlated emission model (CEM) Chiu-Hwa, PRC 79 (09)

22. Geometrical consideration in Ridgeology For every hadron normal to the surface there is a limited line segment on the surface around  2 through which the semihard parton  1 can be emitted. b normalized to R A Ridge due to enhanced thermal partons near the surface R(p T, ,b)  S( ,b) nuclear density S( ,b)   2  2 BaseRidge

23. base ridge inclusive base ridge inclusive RH-L.Zhu (preliminary) Single-particle distribution at low p T without elliptic flow, but with Ridge T 0 for base T 1 (b) for ridge a can be determined from v 2, since S( ,b) is the only place that has  dependence.

24. ridge base Azimuthal dependence of  1 (p T, ,b) comes entirely from Ridge --- In hydro, anisotropic pressure gradient drives the  asymmetry x y requiring no rapid thermalization, no pressure gradients. Since there more semihard partons emerging at  ~0 than at  ~  /2, we get in ReCo anisotropic R(p T, ,b),

25. Hwa-Zhu, PRC (10) Ridge yield’s dependence on trigger  Feng QM08 Normalization adjusted to fit, since yield depends on exp’tal cuts Normalization is not readjusted.  s dependence is calculated S( ,b) correctly describes the  dependence of correlation

26. Nuclear modification factor art Summary  dependencies in Ridge R(p T, ,b) v 2 (p T,b)= yield Y R (  ) R AA (p T, ,b) are all inter-related --- for p T <2 GeV/c Hwa-Zhu, 0909.1542 PRC (2010)

27. B. p T >2 GeV/c PHENIX 0903.4886 Need some organizational simplification.  and b are obviously related by geometry.

28. Scaling behavior in  --- a dynamical path length 5 centralities and 6 azimuthal angles (  ) in one universal curve for each p T Lines are results of calculation in Reco. Hwa-Yang, PRC 81, 024908 (2010) Complications to take into account: details in geometry dynamical effect of medium hadronization

29. Nuclear medium that hard parton traverses  x 0,y 0 k Dynamical path length  to be determined Geometrical path length D(x(t),y(t)) Geometrical considerations Average dynamical path length Probability of hard parton creation at x 0,y 0

30. Define KNO scaling For every pair of  and c: we can calculate PHENIX data gives  We can plot the exp’tal data

31. There exist a scaling behavior in the data when plotted in terms of Theoretical calculation in the recombination model Hwa-Yang, PRC 81, 024908 (2010) (  = 0.11 )

32. b  q TS+SS recombination degradation hadronization k probability of hard parton creation with momentum k geometrical factors due to medium Nuclear modification factor only adjustable parameter  = 0.11

33. 4. Future Possibilities At k T not too large, adjacent jets can be so close that shower partons from two parallel jets can recombine.  - probability for overlap of two shower partons At LHC, the densities of hard partons is high. A. Two-jet recombination at LHC Two hard partons

34. Scaling 1jet Scaling badly broken Hwa-Yang, PRC 81, 024908 (2010) 2jet Pion production at LHC Observation of large R AA at p T ~10 GeV/c will be a clear signature of 2-jet recombination. >1 ! Proton production due to qqq reco is even higher. Hwa-Yang, PRL 97 (06)

35. B.Back-to-back dijets C.Forward production of p and  D.Large  correlation E.Auto-correlation F. P violation: hadronization of chirality-flipped quarks G. CGC: hadronization problem Common ground with the 2-component model of UW-UTA alliance

36. B. Two-component model T.Trainor, 0710.4504, IJMPE17,1499(08) Hwa-Yang, PRC70,024905(04)

37. Similar to our Base, B ~ exp(-p T /T 0 ), T 0 independent of b minijets Strong enhancement of hard component at small y t Similar to our Ridge, R ~ exp(-p T /T 1 ), T 1 depends on b S NN (y t ) is independent of Ridge due to semihard partons --- minijets?

38. Comparison Recombination 2-component semihard partonsminijets recombination of enhanced fragmentation thermal partons Ridges --- TT reco effect of jet on medium low-y t enhancement Jets --- TS+SS effect of medium on jet high-y t suppression  1 = B + R + J  1 = S + H no dependence on  depend on b and  B+R accounts for v 2 at p T <2GeV/c some quadrupole component without hydrowithout hydro

39. In Recombination averaged over  B(p T )R(p T,b) In 2D autocorrelation UW-UTA alliance  dependence

40. Scaling in variable that depends on initial-state collision parameters only No hydro Trainor, Kettler, Ray, Daugherity minijet contribution φΔφΔ ηΔηΔ from the hard comp 2<y t <4 I would like to know how it depends on   at each b  cf. our ridge component

41. Conclusion We should seek common grounds as well as recognize differences. Has common ground with minijets. At p T <2GeV/c, ridges due to semihard scattering and TT reco account for various aspects of the data. At p T >2GeV/c, hard scattering and TS+SS reco account for the scaling behavior observed. Recombination can accommodate fragmentation. Has thermal distribution at late times, though not thermalization and hydro expansion at early times.