1. Correlations at Intermediate p T Rudolph C. Hwa University of Oregon Correlations and Fluctuations in Relativistic Nuclear Collisions MIT, April 2005

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

3. 3 Physics at Intermediate p T pTpT 0246810 hardsoftsemi-hard thermal- thermal thermal- shower shower- shower low intermediatehigh

4. 4 Basic equations for pion production by recombination Shower parton distributions are determined from Fragmentation function

5. 5 Thermal partons are determined from the final state, not from the initial state. Transverse plane (log scale) 2 No small parameter (r h /R A ) in the problem.

6. 6 thermal fragmentation softhard TS Pion distribution (log scale) Transverse momentum TT SS Phenomenological successes of this picture

7. 7  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, 024905 (2004) fragmentation thermal

8. 8 All in recombination/ coalescence model Compilation of R p/  by R. Seto (UCR)

9. 9 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 >  

10. 10 d+Au collisions Hwa & CB Yang, PRL 93, 082302 (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

11. 11 Hwa, Yang, Fries, PRC 71, 024902 (2005) Forward production in d+Au collisions Underlying physics for hadron production is not changed from backward to forward rapidity. BRAHMS

12. 12 Correlations 2. Correlation in jets: trigger, associated particle, background subtraction, etc. (e.g., Fuqiang Wang’s talk) 1. Two-particle correlation with the two particles treated on equal footing. (data to be presented tomorrow)

13. 13 Correlation function Normalized correlation function In-between correlation function

14. 14 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.

15. 15 no correlation

16. 16 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%

17. 17

18. 18 Correlation of pions in jets Two-particle distribution k q3q3 q1q1 q4q4 q2q2

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

20. 20

21. 21 along the diagonal

22. 22

23. 23 Hwa and Tan, nucl-th/0503052

24. 24 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

25. 25 Porter & Trainor, ISMD2004, APPB36, 353 (2005) Transverse rapidity y t ( pp collisions ) G2G2 STAR

26. 26

27. 27 Hwa & Tan, nucl-th/0503052

28. 28 Correlation with trigger particle Study the associated particle distributions

29. 29 STAR has measured: nucl-ex/0501016 Associated charged hadron distribution in p T Background subtracted  and  distributions Trigger 4 < p T < 6 GeV/c

30. 30 Associated particle p T distribution After background subtraction, consider only: p 1 -- trigger p 2 -- associated

31. 31 Reasonable agreement with data Hwa & Tan, nucl-th/0503052

32. 32 Hwa & Tan, nucl-th/0503060

33. 33 Very little dependence on centrality in dAu

34. 34  and  distributions (from Fuqiang Wang’s talk) P1P1 P2P2 pedestal subtraction point no pedestal short-range correlation? long-range correlation?

35. 35 New issues to consider: Angular distribution (1D -> 3D) shower partons in jet cone Thermal distribution enhanced due to energy loss of hard parton work done with C. Chiu

36. 36 Longitudinal Transverse t=0 later

37. 37 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

38. 38 For STST recombination enhanced thermal trigger associated particle Sample with trigger particles and with background subtracted Pedestalpeak in  & 

39. 39

40. 40 Pedestal in  more reliable 0.15 < p 2 < 4 GeV/c, P 1 = 0.4 2 < p 2 < 4 GeV/c, P 2 = 0.04 P1P1 P2P2 less reliable parton distribution T ’ adjusted to fit pedestal find T ’= 0.332 GeV/c cf. T = 0.317 GeV/c  T = 15 MeV/c

41. 41  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

42. 42 k q2q2  z hard parton shower parton Shower parton angular distribution in jet cone Cone width another parameter ~ 0.22

43. 43 Associated particle distribution in  Chiu & Hwa (2005)

44. 44 Associated particle distribution in  Chiu & Hwa (2005)

45. 45 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.

46. 46 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. For unbiased study without deciding on bkgd, we suggest the measure, G 2 (1,2). Is there a hole in ?

47. 47 recombination Comments to stimulate discussion 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.