Correlations and Fluctuations in Relativistic Nuclear Collisions

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

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. Physics at Intermediate pT intermediate high low pT 0 2 4 6 8 10 soft semi-hard hard thermal-thermal thermal-shower shower-shower

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

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

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

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

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

9. 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

10. 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)

11. 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.

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

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

14. 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.

15. no correlation

16. 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

21. along the diagonal

23. Hwa and Tan, nucl-th/0503052

24. (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 Physical reasons for the big dip: The dip occurs at low pT because at higher pT power-law suppression of 1(1)1(2) results in C2(1,2) ~ 2(1,2) > 0

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

27. Hwa & Tan, nucl-th/0503052

28. Correlation with trigger particle Study the associated particle distributions

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

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

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

32. Hwa & Tan, nucl-th/0503060

33. Very little dependence on centrality in dAu

34. P1 pedestal P2 subtraction point no pedestal short-range correlation? long-range correlation?  and  distributions (from Fuqiang Wang’s talk)

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. Longitudinal Transverse t=0 later

37. 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

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

40. 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

41. shower parton q2 hard parton k   z k jet cone Assoc p1 trigger p2 1  z Expt’l cut on trigger: -0.7 < 1 < +0.7

42. Cone width another parameter ~ 0.22 shower parton Shower parton angular distribution in jet cone k q2 hard parton  z

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

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

45. We have not put in any (short- or long-range) correlation by hand. Correlation exists among the shower partons, since they belong to the same jet. 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.

46. Is there a hole in ? 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, G2(1,2).

47. but not for AA collisions. recombination Comments to stimulate discussion • 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.