Recombination in Nuclear Collisions

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

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

3. Usual domains in pT low intermediate high pT 2 6 GeV/c TT TS SS Hadronization Cooper-Frye k1+k2=pT lower ki higher density 1. Introduction Hydro ReCo pQCD Fragmentation kT > pT

4.  (fm/c) 1 8 0.6 hadronization rapid thermalization hydro What about semihard scattering (kT<3GeV/c) at <0.6 fm/c? Regions in time Cronin effect: --- initial-state transverse broadening What about Cronin effect for proton, larger than for ? In ReCo: Final-state effect,not hard-scattering+Frag, not hydro. Early-time physics: CGC, P violation, … Pay nearly no attention to hadronization at late times.

5. Pion at y=0 Recombination function q and qbar momenta, k1, k2, add to give pion pT TT Protonat y=0 TTT same T for partons, , p phase space factor in RF for proton formation 2. Earlier evidences for Recombination A. pT distribution at mid-rapidity It doesn’t work with transverse rapidity yt At low pT empirical evidence

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

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

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

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

10. 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 • Basic assumptions • valon distribution is independent of probe • parton distribution in a valon is independent of the hadron U p U D

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

12. At higher pT Hard scattering calculable in pQCD Hadronization by fragmentation Fragmentation: D(z) => SS recombination, but there can also be TS recombination at lower pT pion ∫dk k fi(k) G(k,q) T(q1)S(q2/q)R(q1,q2,pT) proton q k D. Shower partons in AA collisions In between hard scattering and fragmentation is jet quenching. Fine, at very high pT (> 6GeV/c), but not reliable at intermediate pT We need shower parton distribution.

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

14. assume factorizable, but constrained kinematically. 5 SPDs are determined from5 FFs. u d s L L DSeaKNS L  DV GG  DGL Ls  DKSeaG Gs  DKG u d s g Hwa & CB Yang, PRC 70, 024904 (04) BKK FF(mesons) Hwa-Yang, PRC 73, 064904 (06) Shower parton distributions Using SSS we can calculate baryon FF

15. Other topics: Constituent quarks, valons, chiral-symmetry breaking, f Collinear recombination Entropy Hadronization of gluons Dominance of TS over TT at pT>3 GeV/c Single-particle distributions RCPp(pT)> RCP(pT) Forward-backward asymmetry in dAu collisions Large p/ ratio at large  v2 (pT) Quark-number scaling Ridges Correlations earlier later recent

16. A. pT < 2 GeV/c B. pT > 2 GeV/c 3. Recent development Azimuthal dependence PHENIX 0903.4886 0<<15 30<<45 pT 85<<90  Npart

17. 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 A. 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. [Tom Trainor’s minijets (?)]

18. Recombination of enhanced thermal partons ridge particles Base, independent of , not hydro bulk Ridge, dependent on , hadrons formed by TT reco • 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 How are these two ridges related? trigger assoc part JET RIDGE Putschke On the way out of the medium, energy loss enhances the thermal partons --- but only locally. • Ridge can be associated with a hard parton, which can give a high pT trigger.

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

20. 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. |2-1|<~0.33 Correlated emission model (CEM)Chiu-Hwa, PRC 79 (09) ~ 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) Enhanced thermal partons on average move mainly in the direction normal to the surface

21.   2 S(,b) Ridge due to enhanced thermal partons near the surface R(pT,,b)  S(,b) nuclear density Base Ridge b normalized to RA Geometrical consideration in Ridgeology For every hadron normalto the surface there is a limited line segment on the surface around 2through which the semihard parton 1can be emitted.

22. T0 forbase T1(b) for ridge a can be determined from v2, since S(,b) is the only place that has  dependence. inclusive ridge ridge inclusive base base RH-L.Zhu (preliminary) Single-particle distribution at low pT without elliptic flow, but with Ridge

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

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

25. art Summary Ridge R(pT,,b) v2(pT,b)=<cos 2 > yield YR() RAA(pT,,b)  dependencies in are all inter-related --- for pT<2 GeV/c Nuclear modification factor Hwa-Zhu, 0909.1542 PRC (2010)

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

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

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

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

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

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

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

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

34. Back-to-back dijets Forward production of p and  Large  correlation 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

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

36. SNN(yt) is independent of  Strong enhancement of hard component at small yt minijets Similar to our Base, B ~ exp(-pT/T0), T0 independent of b Similar to our Ridge, R ~ exp(-pT/T1), T1 depends on b Ridgedue to semihard partons --- minijets?

37. no dependence on  depend on b and  Comparison Recombination2-component semihard partonsminijets recombination of enhancedfragmentationthermal partons Ridges --- TT reco effect of jet on mediumlow-yt enhancement Jets --- TS+SS effect of medium on jethigh-yt suppression 1 = B + R + J1 = S + H B+R accounts for v2 at pT<2GeV/csome quadrupole componentwithout hydrowithout hydro

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

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

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

41. BACKUP

42. Proton inclusive distribution 1D longitudinal 1D transverse pT distribution at midrapidity Pion distribution has

43. ridge RJet J J+R     Ridge Jet: effect of medium on hard parton Ridge: effect of hard parton on medium Structure of particles associated with a trigger Putschke, Quark Matter 2006 STAR R J

44. 6 5 4 3 2 1 Out-of-plane In-plane Feng, QM08 Jet and Ridge Yield STAR Preliminary 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 Different s dependencies for different centralities --- important clues on the properties of correlation and geometry

45. associated particles Suarez QM08 SS trigger ST peak (J) TT ridge (R)  Mesons:  Baryons: TTT in the ridge B/M in ridge even higher than in inclusive distr. Partonic basis for ridge formation

46. v2

47. Is fragmentation assumed? Can and recombine, or with ? Hadronization occurs at late times, when B is low --- no observable chiral magnetic effect.

48. p/ ratio can be large at large  Dusling, Gelis, Lappi, Venugopalan arXiv: 0911.2720 PHOBOS data are for all charged particles, integrated over pT