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Correlation of Hadrons in Jets Produced at RHIC

This workshop presentation focuses on the correlation of hadrons in jets produced at RHIC, with discussions on the classification of jets in terms of hadronization and the effects of thermal and shower recombination. It also explores the correlation functions of partons in jets and the correlation of pions in jets. The study includes comparisons with experimental data from the STAR collaboration and addresses new issues to consider in future research.

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Correlation of Hadrons in Jets Produced at RHIC

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  1. 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. pT 0 2 4 6 8 10 soft hard A different classification in terms of hadronization pT 0 2 4 6 8 10 (low) (intermediate) (high) shower-shower thermal-thermal thermal-shower Terminology used in recombination Regions of transverse momentum Traditional classification in terms of scattering pQCD + FF

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

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

  6. Thermal partons are determined from the final state, not from the initial state. k (log scale) Transverse plane 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.

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

  8. fragmentation thermal  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, 024905 (2004)

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

  10. in pA or dA collisions Cronin et al, Phys.Rev.D (1975) h kT broadening by multiple scattering in the initial state. p >  Cronin et al, Phys.Rev.D (1975) STAR, PHENIX (2003) Cronin Effect q p A Unchallenged for 30 years. If the medium effect is before fragmentation, then  should be independent of h=  or p

  11. soft-soft No pT broadening by multiple scattering in the initial state. Medium effect is due to thermal (soft)-shower recombination in the final state. d+Au collisions pion Hwa & CB Yang, PRL 93, 082302 (2004)

  12. Forward production in d+Au collisions BRAHMS Hwa, Yang, Fries, PRC 71, 024902 (2005) Underlying physics for hadron production is not changed from backward to forward rapidity.

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

  14. Normalized correlation function In-between correlation function Correlation function

  15. Correlation of partons in jets A. Two shower partons in a jet in vacuum k Fixed hard parton momentum k (as in e+e- annihilation) x1 x2 The two shower partons are correlated.

  16. no correlation  0 Hwa & Tan, nucl-th/0503052

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

  18. k q1 q2 q3 q4 Correlation of pions in jets Two-particle distribution

  19. Factorizable terms: Do not contribute to C2(1,2) Non-factorizable terms correlated Correlation function of produced pions in HIC

  20. Hwa & Tan, nucl-th/0503052

  21. along the diagonal

  22. Hwa and Tan, nucl-th/0503052

  23. Physical reasons for the big dip: • competition for momenta by the shower partons in a jet • if p1 and p2 are low, hard parton k can be low, and the competition is severe. Recall that r2(1,2) < 1 for shower partons. • if p1 and p2 are high, hard parton k can be high, but fi(k) is suppressed, so 1(1)1(2) is small, and C2(1,2) becomes positive.

  24. Correlation with trigger particle Study the associated particle distributions

  25. STAR has measured: nucl-ex/0501016 Trigger 4 < pT < 6 GeV/c Associated charged hadron distribution in pT Background subtracted  and  distributions

  26. Associated particle pT distribution p1 -- trigger p2 -- associated After background subtraction, consider only:

  27. Reasonable agreement with data Hwa & Tan, nucl-th/0503052

  28. Hwa & Tan, nucl-th/0503060

  29. Very little dependence on centrality in dAu

  30. P1 pedestal P2 subtraction point no pedestal short-range correlation? long-range correlation?  and  distributions (STAR nucl-ex/0501016)

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

  32. Longitudinal Transverse t=0 later

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

  34. enhanced thermal trigger associated particle peak in  &  Pedestal ForSTSTrecombination Sample with trigger particles and with background subtracted

  35. shower parton Shower parton angular distribution in jet cone k q2 hard parton  z Cone width

  36. P1 parton distribution 0.15 < p2 < 4 GeV/c, P1 = 0.4 2 < p2 < 4 GeV/c, P2 = 0.04 less reliable P2 T ’ adjusted to fit pedestal find T ’= 0.332 GeV/c cf. T = 0.317 GeV/c T = 15 MeV/c Pedestal in  more reliable

  37. Associated particle distribution in  Chiu & Hwa, nucl-th/0505014

  38. Associated particle distribution in  Chiu & Hwa, nucl-th/0505014

  39. The peaks in  &  arise from the recombination of thermal partons with shower partons in jets with angular spread. 1. 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). 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.

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

  41. x k 1 2 q1  q2 y z parton momentum space P() Gaussian in jet cone x  p1 p2 - 1 2 y z pion momentum space

  42. Autocorrelation Chiu & Hwa (2005b)

  43. Other recent work done on recombination Fries, Muller, Bass, PRL94, 122301(2005) Correlation Muller, Fries, Bass, nucl-th/0503003 Beyond the valence quark approximation Majumder, E. Wang, X.N. Wang, LBNL-57478 Modified fragmentation function Greco and C.M. Ko, nucl-th/0505061 Scaling of hadron elliptic flow

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

  45. G2 Porter & Trainor, ISMD2004, APPB36, 353 (2005) ( pp collisions ) STAR Transverse rapidity yt

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