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

4. 3 1. Early evidences for Recombination A. Revisit very early formulation of recombination [at the suggestion of organizers: Hwa, PRD22,1593(1980)] For p+p  p+X we need Consider the time-reversed process p+p  +X Feynman x distribution at low p T

5. 4 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

6. 5 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

7. 6 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)

8. 7 B. p T distribution in nuclear collisions 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

9. 8 Hwa-Zhu (preliminary) p PHENIX, PRC 69, 034909 (04) went on to m T plot Proton production from recombination Same T for , K, p --- in support of recombination. Slight dependence on centrality --- to revisit later

10. 9 C. 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

11. 10 D. Shower partons in AA collisions At high p T hard scattering and jet quenching are calculable in pQCD, followed by fragmentation. But the reliability decreases with decreasing p T. T(q 1 )S(q 2 /q)  R(q 1,q 2,p T ) We consider shower partons such that D(z) => SS recombination at all p T, but there can also be TS recombination at lower p T pion We need shower parton distribution. ∫dk k f i (k) G(k,q) k q

12. 11 Description of fragmentation known from data (e+e-,  p, … ) known from recombination model can be determined recombinationshower partons hard parton meson fragmentation by recombination

13. 12 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)

14. 13 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.Cronin Effect and 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

15. 14 2. 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

16. 15 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 (?)]

17. 16 But a ridge can also be associated with a semihard parton without a trigger. Then, the ridge can be a major component of 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. Correlated part of two-particle distribution on the near side Putschke triggerassoc partJETRIDGE How are these two ridges related?

18. 17 BOOM Hard parton Ridge without trigger but one may have to wait a long time Semihard partons, lots of them in each event Ridges without triggers --- contribute significantly to single-particle distribution ratatatatatata We need an analogy

19. 18 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)

20. 19 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

21. 20 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. p

22. 21 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 RM anisotropic R(p T, ,b),

23. 22 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

24. 23 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)

25. 24 B. p T >2 GeV/c PHENIX 0903.4886 Need some organizational simplification.  and b are obviously related by geometry.

26. 25 Scaling behavior in  --- a dynamical path length Lines are results of calculation in RM. Hwa-Yang, PRC 81, 024908 (2010) 5 centralities and 6 azimuthal angles (  ) in one universal curve for each p T Complications to take into account: details in geometry dynamical effect of medium hadronization

27. 26 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

28. 27 Define KNO scaling For every pair of  and c: we can calculate PHENIX data gives  We can plot the exp’tal data

29. 28 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 )

30. 29 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

31. 30 3. 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  =10 -3 : 1-jet (S 1 S’ 1 )  =10 -1 : 2-jet (S 1 S 2 )

32. 31 Scaling 1 jet Scaling badly broken Hwa-Yang, PRC 81, 024908 (2010) 2 jet 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)

33. 32 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

34. 33 Two-component model T.Trainor, 0710.4504, IJMPE17,1499(08) Hwa-Yang, PRC70,024905(04)

35. 34 Similar to our Base, B ~ exp(-p T /T 0 ), T 0 independent of b minijets Enhancement of hard component at small y t Similar to our Ridge, R ~ exp(-p T /T 1 ), due to energy loss of semihard partons, enhanced thermal partons at low p T. S NN (y t ) is independent of Ridge due to semihard partons --- minijets?

36. 35 Comparison Recombination 2-component semihard partonsminijets recombination of enhanced fragmentation thermal partons Ridges --- TT reco enhanced thermal low-y t enhancement Jets --- TS+SS energy loss by jets 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

37. 36 In Recombination averaged over  B(p T )R(p T,b) In 2D autocorrelation UW-UTA alliance  dependence

38. 37 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

39. 38 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.