1. Resolution of Several Puzzles at Intermediate p T and Recent Developments in Correlation Rudolph C. Hwa University of Oregon Quark Matter 05 Budapest, Hungary, August 2005

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

3. 3 Puzzles at intermediate p T 1.Proton/pion ratio 2.Azimuthal anisotropy 3.Cronin effect in pion and proton production 4.Forward-backward asymmetry in dAu collisions 5.Same-side associated particle distribution QM04

4. 4 Puzzle #1 R p/π  1 Not possible in fragmentation model: R p/π u

5. 5 inclusive distribution of pions in any direction soft component thermal-shower recombination usual fragmentation (by means of recombination) Proton formation: uud distribution In the recombination model

6. 6  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, 024905 (2004) fragmentation thermal

7. 7 All in recombination/ coalescence model compilation by R.Seto (UCR)

8. 8 Molnar and Voloshin, PRL 91, 092301 (2003). Parton coalescence implies that v 2 (p T ) scales with the number of constituents STAR data Puzzle #2 Azimuthal anisotropy

9. 9 Puzzle #3 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 >  

10. 10 R CP for d-Au collisions because 3q  p, 2q   more partons at 1/3 than at 1/2 Argument does not extend to, nor to higher p T because of ST and SS recombination. Hwa & CB Yang, PRL 93, 082302 (04). PRC 70, 037901 (04).

11. 11 Puzzle #4 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 B/F < 1

12. 12 Backward-forward ratio at intermed. p T in d+Au collisions (STAR) B/F

13. 13 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 data

14. 14 STAR : nucl-ex/0501016 Trigger 4 < p T < 6 GeV/c Puzzle #5: Associated particle pT distribution (near side) factor of 3 difficult for medium modification of fragmentation function to achieve Hwa & Tan, nucl-th/0503060 Recombination model because of T-S recombination

15. 15 PHENIX (preliminary) STAR (preliminary) N. Grau J. Bielcikova RIKEN/BNL Workshop 3/05

16. 16 Correlations 1.Correlation in jets: distributions in  and  2. Two-particle correlation without triggers 3. Autocorrelations 4. Away-side distribution (jet quenching)

17. 17  and  distributions P1P1 P2P2 Pedestal Why? Are these peaks related? How?

18. 18 For STST recombination enhanced thermal trigger associated particle with background subtracted Pedestal peak in  & 

19. 19 Chiu & Hwa, nucl-th/0505014 pedestal  T=15 MeV

20. 20 Chiu & Hwa, nucl-th/0505014

21. 21 Correlation without triggers Correlation function Normalized correlation function

22. 22 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 kinematically constrained dynamically uncorrelated

23. 23 no correlation Hwa & Tan, nucl-th/0503052  0

24. 24 Correlation of pions in jets Two-particle distribution k q3q3 q1q1 q4q4 q2q2 The shower partons are anti-correlated

25. 25 Hwa and Tan, nucl-th/0503052

26. 26

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

28. 28 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

29. 29 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

30. 30 Chiu and Hwa (05)

31. 31 Away-side  distribution

32. 32 Random walker on a circular mount Most walks are absorbed inside the medium Step size depends on local density Direction of walk is random within a Gaussian peak

33. 33 Sample tracks those that emergethose that are absorbed away-side distribution Chiu & Hwa work in progress

34. 34 Conclusion  Hadronization by recombination resolves several puzzles at intermediate pT.  The pedestal and peak structure in the near-side jets is due to enhanced thermal partons and to jet cone structure of shower partons.  A dip is predicted in the correlation function due to anti-correlation among the shower partons.  Promising start made in the  distribution on the away-side by simulating parton rescattering and absorption.