1 High-p T Physics at RHIC and Evidences of Recombination Rudolph C. Hwa University of Oregon International Symposium on Multiparticle Dynamics Sonoma, CA, July 2004

2 In collaboration with Chunbin Yang Hua-zhong Normal University Wuhan, China

3 Outline Anomalies at high p T according to the “standard model” Alternative to the “standard model” at high p T Recombination in fragmentation Shower partons Inclusive distributions at all p T Dihadron correlations All anomalies can be understood in terms of parton recombination

4 Conventional approach to hadron production at high p T D(z) h q AA Hard scattering near the surface because of energy loss in medium --- jet quenching.

5 If hard parton fragments in vacuum, then the fragmentation products should be independent of the medium. h q Particle ratio should depend on the FF D(z) only. The observed data reveal several anomalies according to that picture. D(z)

6 Anomaly #1 R p/π  1 Not possible in fragmentation model: R p/π u

7 k T broadening by multiple scattering in the initial state. Unchallenged for ~30 years. If the medium effect is before fragmentation, then  should be independent of h=  or p Anomaly #2 in pA or dA collisions Cronin Effect Cronin et al, Phys.Rev.D (1975) p q h A  p >   RHIC expt (2003)

8 RHIC data from dAu collisions at 200 GeV per NN pair Ratio of central to peripheral collisions: R CP PHENIX and STAR experiments found (2002) Can’t be explained by fragmentation.

9 Anomaly # 2

10 Anomaly #3 Jet structure Hard parton  jet {  (p 1 ) +  (p 2 ) +  (p 3 ) + ···· } trigger particleassociated particles The distribution of the associated particles should be independent of the medium if fragmentation takes place in vacuum.

11 Anomaly #3 Jet structure for Au+Au collisions is different from that for p+p collisions pp Fuqiang Wang (STAR) nucl-ex/

12 Azimuthal anisotropyAnomaly #4 Anomaly #5 Forward-backward asymmetry at intermediate p T Come back later when there is time. Resolution of the anomalies

13 How can recombination solve the puzzles? Parton distribution (log scale) p p 1 +p 2 pq (recombine)(fragment) hadron momentum higher yieldheavy penalty

14 The black box of fragmentation  q A QCD process from quark to pion, not calculable in pQCD z 1 Momentum fraction z < 1 Phenomenological fragmentation function D  /q z 1

15 Let’s look inside the black box of fragmentation.  q fragmentation z 1 gluon radiation quark pair creation Although not calculable in pQCD (especially when Q 2 gets low), gluon radiation and quark-pair creation and subsequent hadronization nevertheless take place to form pions and other hadrons.

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

17 Shower parton distributions u g s s d duvalence sea L L  D  Sea K NS L  D  V G G  D  G L L s  D K Sea G G s  D K G RR RKRK 5 SPDs are determined from 5 FFs.

18 Hwa & CB Yang, hep-ph/ Shower Parton Distributions u -> u valence g -> u u -> d u -> s g -> s

19 BKK fragmentation functions

20 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. D(z) h q AA Conventional approach

21 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. h Now, a new component

22 hard parton (u quark)

23 Inclusive distribution of pions in any direction PionDistribution

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

25 Thermal distribution Fit low-p T data to determine C & T. Shower distribution in AuAu collisions hard parton momentum distribution of hard parton i in AuAu collisions SPD of parton j in shower of hard parton i fraction of hard partons that get out of medium to produce shower calculable Contains hydrodynamical properties, not included in our model.

26 density of hard partons with p T = k Input: parton distributions CTEQ5L nuclear shadowing EKS98 hard scattering pQCD Srivastava, Gale, Fries, PRC 67, (2003) C, B,  are tabulated for i=u, d, s, u, d, gK=2.5

27 2-shower partons in 1 jet: Negligible at RHIC, but can be important at LHC. 2-shower partons in 2 jets:

28  production in AuAu central collision at 200 GeV Hwa & CB Yang, nucl-th/ , PRC(2004)

29 Proton production in AuAu collisions TTS+TSS TSS

30 Anomaly #1 Proton/pion ratio resolved

31 Greco, Ko & Levai, PRL (2003) Monte Carlo Calculation in Coalescence model

32 Production of  and  in central Au+Au Hwa & Yang, nucl-th/

33 d d central peripheral more  T  more TS less  T  less TS Anomaly #2 d+Au collisions (to study the Cronin Effect)

34 d+Au collisions Hwa & CB Yang, nucl-th/ , PRL(2004) Pions No p T broadening by multiple scattering in the initial state. Medium effect due to thermal-shower recombination.

35 Proton Thermal-shower recombination is negligible. nucl-th/

36 Nuclear Modification Factor because 3q  p, 2q   Anomaly #2 resolved

37 Jet Structure Since TS recombination is more important in Au+Au than in p+p collisions, we expect jets in Au+Au to be different from those in p+p. Consider dihadron correlation in the same jet on the near side. Anomaly #3 Jet structure in Au+Au different from that in p+p collisions

38 Trigger at 4 < p T < 6 GeV/c p+p:mainly SS fragmentation Au+Au: mainly TS Associated particle p 1 (trigger) p 2 (associated) k q1q1 q2q2 q3q3 q4q4 trigger associated

39 There are other contributions as well. (TS) + [SS] (SS) + [TS] (SS) + [SS] too small for Au+Au but the only term for p+p trigger associated ( TS) + [TS]

40 Associated particle distribution in p 2 with trigger at p 1 trigger at p 1 integrated over 4 < p 1 < 6 GeV/c

41 (TS)[TS] (TS)[SS]+(SS)[TS] (SS)[SS] for p+p collisions much lower Central Au+Au collisions ++

42 Central Au+Au collisions Hwa & Yang, nucl-th/

43 Centrality dependence of associated-particle dist. Distributions Ratios Au+Au central d+Au peripheral d+Au central d+Au peripheral Jets in Au+Au and in p+p are very different.Anomaly #3 p+p resolved

44 Azimuthal anisotropy Anomaly #4 v 2 (p) > v 2 (  ) at p T > 2.5 GeV/c v 2 : coeff. of 2nd harmonic of  distribution PHENIX, PRL 91 (2003)

45 Molnar and Voloshin, PRL 91, (2003). Parton coalescence implies that v 2 (p T ) scales with the number of constituents STAR data

46 Anomaly #5 Forward-backward asymmetry at intermed. p T in d+Au collisions STAR preliminary data

47 More interesting behavior found in large p T and large p L region. It is natural for parton recombination to result in forward-backward asymmetry Less soft partons in forward (d) direction than in backward (Au) direction. Less TS recombination in forward than in backward direction.

48 Summary Traditional picture pTpT hardsoft pQCD + FF More realistic picture pTpT hardsoftsemi-hard (low)(intermediate) thermal-thermalthermal-shower (high) shower-shower

49 All anomalies at intermediate p T can be understood in terms of recombination of thermal and shower partons Recombination is the hadronization process. At p T > 9 GeV/c fragmentation dominates, but it can still be expressed as shower-shower recombination. Thus we need not consider fragmentation separately any more.

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51 Backup slides

52 Rapidity dependence of R CP in d+Au collisions BRAHMS nucl-ex/ R CP < 1 at  =3.2 Central more suppressed than peripheral collisions Interpreted as possible signature of Color Glass Condensate.

53  =0 R CP > 1  =3.2 R CP < 1 At forward rapidity, parton x is degraded (stopping) more for central than for peripheral x distributions at various b accounted for by recombination central < peripheral  R CP < 1 at large  BRAHMS data

54 Forward R CP in d+Au collisions

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57 Forward p T spectra in d+Au collisions

58 At very high p T and very high energy like at LHC, then the density of hard partons produced will be so high as to make jet-jet recombination very important. The effect should be dramatic.

59 near side away side

60 PHENIX

61 Thermal partons No prediction from our model (without hydro input) Fit data on  spectrum for p T < 2GeV/c C = 23.2 GeV -1,T = GeV Shower partons  = 0.07 fraction of hard partons that can get out of the dense medium to produce shower Au+Au: adjusted to fit the data at intermediate p T. d+Au: = 1