High p T Physics in Heavy Ion Collisions Rudolph C. Hwa University of Oregon CIAE, Beijing June 13, 2005

2 Well studied for 20 years ---- pQCD What was a discovery yesterday is now used for calibration today. Instead of being concerned with 5% discrepancy in pp collisions, there are problems involving factors of 10 differences to understand in nuclear collisions. High p T Physics of Nuclear Collisions at High Energy particle

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4 Chunbin Yang (HZNU, Wuhan; UO) Rainer Fries (Univ. of Minnesota) Zhiquang Tan (HZNU, Wuhan; UO) Charles Chiu (Univ. of Texas, Austin) Work done in separate collaborations with

5 Outline Anomalies at high p T according to the “standard model of hadronization” -- - parton fragmentation The resolution: parton recombination Recombination in fragmentation Shower partons Inclusive distributions at all p T Cronin effect Hadron correlations in jets

6 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.

7 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)

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

9 cm energy

10 Anomaly #2 in pA or dA collisions 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 Cronin Effect Cronin et al, Phys.Rev.D (1975) p q h A STAR, PHENIX (2003) Cronin et al, Phys.Rev.D (1975)  p >  

11 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.

12 Anomaly # 2 STAR

13 Anomaly #3 Azimuthal anisotropy v 2 (p) > v 2 (  ) at p T > 2.5 GeV/c v 2 : coeff. of 2nd harmonic of  distribution PHENIX, PRL 91 (2003)

14 Anomaly #4 Forward-backward asymmetry at intermed. p T in d+Au collisions (STAR) B/F

15 Forward-backward asymmetry in d+Au collisions Expects more forward particles at high p T than backward particles If initial transverse broadening of parton gives hadrons at high p T, then backward has no broadening forward has more transverse broadening

16 Rapidity dependence of R CP in d+Au collisions BRAHMS PRL 93, (2004) R CP < 1 at  =3.2 Central more suppressed than peripheral collisions Interpreted as possible signature of Color Glass Condensate.

17 Anomaly #5 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.

18 Anomaly #5 Jet structure for Au+Au collisions is different from that for p+p collisions pp Fuqiang Wang (STAR) nucl-ex/

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

20 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

21 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.

22 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

23 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.

24 Shower Parton Distributions Hwa & CB Yang, PRC 70, (04)

25 BKK fragmentation functions

26 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

27 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

28 hard parton (u quark)

29 Inclusive distribution of pions in any direction PionDistribution

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

31 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.

32 thermal fragmentation softhard TS Pion distribution (log scale) Transverse momentum TT SS Now, we go to REAL DATA, and real theoretical results.

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

34 Proton production in AuAu collisions TTS+TSS TSS

35 Anomaly #1 Proton/pion ratio resolved

36 All in recombination/ coalescence model Compilation of R p/  by R. Seto (UCR)

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

38 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. soft-soft

39 Proton Thermal-shower recombination is negligible. Hwa & Yang, PRC 70, (2004)

40 Nuclear Modification Factor Anomaly #2 because 3q  p, 2q   This is the most important result that validates parton recombination.

41 Molnar and Voloshin, PRL 91, (2003). Parton coalescence implies that v 2 (p T ) scales with the number of constituents STAR data Anomaly #3 Azimuthal anisotropy

42 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 backward (Au) direction. Less TS recombination in forward than in backward direction. Anomaly #4 Forward-backward asymmetry

43 Hwa, Yang, Fries, PRC 71, (2005) Forward production in d+Au collisions Underlying physics for hadron production is not changed from backward to forward rapidity. BRAHMS data

44 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 #5 Jet structure in Au+Au different from that in p+p collisions

45 Correlations 1. Correlation in jets: trigger, associated particle, background subtraction, etc. 2. Two-particle correlation with the two particles treated on equal footing.

46 Correlation function Normalized correlation function In-between correlation function

47 Correlation of partons in jets A. Two shower partons in a jet in vacuum Fixed hard parton momentum k (as in e+e- annihilation) k x1x1 x2x2 The two shower partons are correlated.

48 no correlation Hwa & Tan, nucl-th/

49 B. Two shower partons in a jet in HIC Hard parton momentum k is not fixed.  f i (k)  f i (k) is small for 0-10%, smaller for 80-92%

50 Hwa & Tan, nucl-th/

51 Correlation of pions in jets Two-particle distribution k q3q3 q1q1 q4q4 q2q2

52 Correlation function of produced pions in HIC Factorizable terms: Do not contribute to C 2 (1,2) Non-factorizable terms correlated

53 Hwa & Tan, nucl-th/

54 along the diagonal

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56 Hwa and Tan, nucl-th/

57 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 Correlation studied with triggers

58 Correlation of pions in jets Two-particle distribution background associated particle 2<p 2 <4 GeV/c must also involve S trigger 4<p 1 <6 GeV/c must involve S q4q4 q2q2 k q3q3 q1q1

59 STAR has measured: nucl-ex/ Associated charged hadron distribution in p T Background subtracted  and  distributions Trigger 4 < p T < 6 GeV/c

60  and  distributions P1P1 P2P2 pedestal subtraction point no pedestal short-range correlation? long-range correlation?

61 New issues to consider: Angular distribution (1D -> 3D) shower partons in jet cone Thermal distribution enhanced due to energy loss of hard parton

62 Longitudinal Transverse t=0 later

63  z 11  p 1 trigger Assoc p2p2 k q2q2  z hard parton shower parton Expt’l cut on  trigger : -0.7 <  1 < +0.7 k jet cone

64 Events without jets Thermal medium enhanced due to energy loss of hard parton Events with jets in the vicinity of the jet T’- T =  T > 0 new parameter Thermal partons

65 For STST recombination enhanced thermal trigger associated particle Sample with trigger particles and with background subtracted Pedestal peak in  & 

66 Pedestal in  0.15 < p 2 < 4 GeV/c, P 1 = < p 2 < 4 GeV/c, P 2 = 0.04 more reliable P1P1 P2P2 less reliable parton dist found T ’= GeV/c cf. T = GeV/c T ’ adjusted to fit pedestal  T = 15 MeV/c

67 Chiu & Hwa, nucl-th/

68 Chiu & Hwa, nucl-th/

69 We have not put in any (short- or long-range) correlation by hand. The pedestal arises from the enhanced thermal medium. The peaks in  &  arise from the recombination of enhanced thermal partons with the shower partons in jets with angular spread. Correlation exists among the shower partons, since they belong to the same jet.

70 Summary Traditional classification by scattering pTpT hardsoft pQCD + FF More meaningful classification by hadronization pTpT hardsoftsemi-hard (low)(intermediate) thermal-thermalthermal-shower (high) shower-shower

71 All anomalies at intermediate p T can be understood in terms of recombination of thermal and shower partons Recombination is the hadronization process ---- at all p T. Parton recombination provides a framework to interpret the data on jet correlations. There seems to be no evidence for any exotic correlation outside of shower-shower correlation in a jet. Conclusion

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73 k q2q2  z hard parton shower parton Shower parton angular distribution in jet cone Cone width another parameter ~ 0.22

74 Correlation without triggers Correlation function Normalized correlation function

75 Physical reasons for the big dip: (a) central: (ST)(ST) dominates S-S correlation weakened by separate recombination with uncorrelated (T)(T) (b) peripheral: (SS)(SS) dominates SS correlation strengthened by double fragmentation The dip occurs at low p T because at higher p T power-law suppression of  1 (1)  1 (2) results in C 2 (1,2) ~  2 (1,2) > 0

76 Porter & Trainor, ISMD2004, APPB36, 353 (2005) Transverse rapidity y t ( pp collisions ) G2G2 STAR

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