Correlation of Hadrons in Jets Produced at RHIC Rudolph C. Hwa University of Oregon Workshop on QCD and RHIC physics Wuhan, June 22, 2005

2 Work done in collaboration with Chunbin Yang (Hua-Zhong Normal University, Wuhan) Rainer Fries (University of Minnesota) Ziguang Tan (Hua-Zhong Normal University, Wuhan) Charles Chiu (University of Texas, Austin)

3 Regions of transverse momentum Traditional classification in terms of scattering pTpT hardsoft pQCD + FF A different classification in terms of hadronization pTpT (low)(intermediate) thermal-thermalthermal-shower (high) shower-shower Terminology used in recombination

4 recombination What about string fragmentation? Fragmentation is not important until p T > 9 GeV/c. String model may be relevant for pp collisions, String/fragmentation has no phenomenological support in heavy-ion collisions. but not for AA collisions.

5 Basic equations for pion production by recombination Shower parton distributions are determined from Fragmentation function

6 Thermal partons are determined from the final state, not from the initial state. Transverse plane (log scale) 2 An event generator takes care of the spatial problem. cf. Duke and TAMU work on recombination. We deal in momentum space only, with all partons collinear until we treat angular dependence. k

7 thermal fragmentation softhard TS Pion distribution (log scale) Transverse momentum TT SS Phenomenological successes of this picture

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

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

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

11 d+Au collisions 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 pion

12 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

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

14 Correlation function Normalized correlation function In-between correlation function

15 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.

16 no correlation  0 Hwa & Tan, nucl-th/

17 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%

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

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

21 Hwa & Tan, nucl-th/

22 along the diagonal

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24 Hwa and Tan, nucl-th/

25 Physical reasons for the big dip: competition for momenta by the shower partons in a jet if p 1 and p 2 are low, hard parton k can be low, and the competition is severe. Recall that r 2 (1,2) < 1 for shower partons. if p 1 and p 2 are high, hard parton k can be high, but f i (k) is suppressed, so  1 (1)  1 (2) is small, and C 2 (1,2) becomes positive.

26 Correlation with trigger particle Study the associated particle distributions

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

28 Associated particle p T distribution After background subtraction, consider only: p 1 -- trigger p 2 -- associated

29 Reasonable agreement with data Hwa & Tan, nucl-th/

30 Hwa & Tan, nucl-th/

31 Very little dependence on centrality in dAu

32  and  distributions (STAR nucl-ex/ ) P1P1 P2P2 pedestal subtraction point no pedestal short-range correlation? long-range correlation?

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

34 Longitudinal Transverse t=0 later

35 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

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

37 k q2q2  z hard parton shower parton Shower parton angular distribution in jet cone Cone width

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

40 Associated particle distribution in  Chiu & Hwa, nucl-th/

41 Associated particle distribution in  Chiu & Hwa, nucl-th/

42 The peaks in  &  arise from the recombination of thermal partons with shower partons in jets with angular spread. 2.The pedestal arises from the enhanced thermal medium. That is the feedback from the hard parton through lost energy to the soft partons. By longitudinal expansion it gives rise to the long-range correlation. Correlation exists among the shower partons, since they belong to the same jet. That may be regarded as the short-range correlation --- though only kinematical (sufficient so far). 1.

43 Autocorrelation Correlation function 1,2 on equal footing --- no trigger Define Autocorrelation: Fix and, and integrate over all other variables in The only non-trivial contribution to near, would come from jets

44 p2p2 p1p1 x y z  11 22 pion momentum space q2q2 q1q1 x y z  22 11 k parton momentum space -- P(  ) Gaussian in jet cone

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46 Autocorrelation Chiu & Hwa (2005b)

47 Other recent work done on recombination Fries, Muller, Bass, PRL94, (2005) Correlation Muller, Fries, Bass, nucl-th/ Beyond the valence quark approximation Majumder, E. Wang, X.N. Wang, LBNL Modified fragmentation function Greco and C.M. Ko, nucl-th/ Scaling of hadron elliptic flow

48 Conclusion 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. If future analysis finds no hole in, then some dynamical correlation among the shower partons may be needed. Autocorrelation without subtraction is a good place to compare theory and experiment.

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

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51 Hwa & Tan, nucl-th/

52  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