1 Parton Recombination at all p T Rudolph C. Hwa University of Oregon Hard Probes 2004 Ericeira, Portugal, November 2004

2 Outline How parton recombination resolves a number of puzzles. Shower partons Inclusive distributions at all p T in Au+Au and d+Au collisions (Cronin effect) Dihadron correlations Forward production in d+Au collisions Why fragmentation is inadequate at intermediate p T in heavy-ion collisions.

3 Conventional approach to hadron production at high p T D(z) h q AA There are numerous evidences against this framework: hard scattering  fragmentation in heavy-ion collisions.

4 Exhibit #1 R p/π  1 Not possible in fragmentation model: R p/π u

5 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 Exhibit #2 in pA or dA collisions Cronin Effect Cronin et al, Phys.Rev.D (1975) p q h A  p >  

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7 Exhibit #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.

8 Exhibit #3 Jet structure for Au+Au collisions is different from that for p+p collisions pp Fuqiang Wang (STAR) Quark Matter 2004

9 Azimuthal anisotropy Exhibit #4 v 2 (p) > v 2 (  ) at p T > 2.5 GeV/c v 2 : coeff. of 2nd harmonic in  distribution

10 Exhibit #5 Backward-forward asymmetry at intermed. p T in d+Au collisions

11 The problem: Fragmentation of hard partons that works so well in leptonic and hadronic processes is only one of many components when the hard parton is in the environment of many soft partons, as in heavy-ion collisions.

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

13 D(z) h q AA Conventional approach h Thermal-shower recombination thermal shower

14 Shower partons in fragmentation process known from data (e+e-,  p, … ) known from recombination model can be determined hard parton meson fragmentation shower partons recombination

15 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.

16 Hwa & CB Yang, PRC (2004). Shower Parton Distributions u -> u valence g -> u u -> d u -> s g -> s

17 BKK fragmentation functions

18 hard parton (u quark) An example

19 Inclusive distribution of pions in any direction thermal shower Pion formation: Proton formation: uud distribution Determine T by fitting dN  /dp T at low p T (<2GeV/c) soft pions at low p T fragmentation

20 Thermal partons Determine C and T by fitting low-p T data on  production Shower partons 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  = 0.07

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

22  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, (2004) fragmentation thermal

23 Proton production in AuAu collisions TTS+TSS TSS TTT SS S

24 Puzzle #1 Proton/pion ratio resolved Hwa & CB Yang, PRC70, (2004)

25 All in recombination/ coalescence model Compilation of R p/  by R. Seto (UCR) Duke: Fries, Mueller, Nonaka, Bass, PRL90,202303(2003);PRC68,044902(2003). TAM: Greco, Ko, Levai, PRL,90,202302(2003); PRC68,034904(2003).

26 d+Au collisions Pions Hwa & CB Yang, PRL 93, (2004) No p T broadening by multiple scattering in the initial state. Medium effect is due to thermal (soft)-shower recombination in the final state.  = 1 soft-soft

27  0,  production in p+A collisions  0 : α = 1.1  : α = 1.0

28 Proton Thermal-shower recombination is negligible. Thermal-shower recombination is NOT negligible.

29 Nuclear Modification Factor because 3q  p, 2q   Puzzle #2 resolved

30 Jet Structure A simple consequence of TS recombination being more important in Au+Au collisions than in p+p collisions. Consider dihadron correlation in the same jet on the near side. Exhibit #3 Jet structure in Au+Au different from that in p+p collisions

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

32 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]

33 (TS)[TS] (TS)[SS]+(SS)[TS] (SS)[SS] for p+p collisions much lower Associated particle distribution ++

34 Associated particle distribution in central Au+Au collisions Hwa & Yang, PRC (2004) p ++ --

35 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.Exhibit #3 p+p

36 Dihadron correlation with soft parton correlation Fries, Bass, Mueller, nucl-th/ No shower partons (1) soft-soft recombination X soft-soft recom (2) fragmentation X fragmentation (3) soft-hard recom X fragmentation Meson triggerBaryon trigger (1) + (2) with 8% scaled soft parton correlation Comparable associated particle yields for meson and baryon triggers

37 Azimuthal anisotropy Exhibit #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)

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

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

40 Rapidity dependence of R CP in d+Au collisions BRAHMS nucl-ex/ R CP < 1 at  =3.2 Central more suppressed than peripheral collisions This can be understood in terms of parton recombination.

41 Forward production in d+Au collisions Notation: Centrality 0-20%  = % 0.7 for all  and  Soft component: Pion distribution C( ,  ) Same hadronization process as at  =0.

42 Centrality (Impact Parameter) Dependence d  for d + Au Collisions at 200 GeV Preliminary  can be calculated.

43 Hwa, Yang, and Fries, nucl-th/ Our prediction on the  + spectra for 0  3.2, 0.1  0.7

44 T=constant, no free parameter No new physics, e.g. gluon saturation, explicitly.

45 Include  and  dependences of T (one free parameter) and momentum degradation Hwa, Yang, Fries, nucl-th/

46 Without any more free parameters

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

48 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. Hence, parton recombination at all p T.

49 Conclusion in one sentence Due to the soft parton environment in heavy-ion collisions at RHIC, hadronization by thermal-shower recombination dominates all phenomena on particle production at intermediate p T for all centralities and all rapidities.

50 All of the work presented was done in collaboration with Chunbin Yang Hua-zhong Normal University Wuhan, China