1. Correlation in Jets Rudolph C. Hwa University of Oregon Workshop on Correlation and Fluctuation in Multiparticle Production Hangzhou, China November 21-24, 2006

2. 2 Two parts to this title: Jetsand Correlation Hard scattering is involved. Jets p T > 2 GeV/c, The conventional wisdom is that when then jets are produced. But that does not mean that the hard parton fragments. Recombination has been found to be important at intermediate p T, where most correlation data exist.

3. 3 shower partonsproduced hadrons correlations between colliding system e+e-e+e- Au-Au jets in

4. 4 Correlation of pions in jets in HIC Two-particle distribution k q3q3 q1q1 q4q4 q2q2 Non-factorizable terms correlated Factorizable terms: They do not contribute to C 2 (1,2)

5. 5 Hwa & Tan, PRC 72, 024908 (2005) Pion transverse momenta p 1 and p 2

6. 6 C 2 (1,2) treats 1 and 2 on equal footing. Experimental data choose particle 1 as trigger, and studies particle 2 as an associated particle. (background subtraction) STAR, PRL 95, 152301 (2005) Trigger 4 < p T < 6 GeV/c Hard for medium modification of fragmentation function to achieve, but not so hard for recombination involving thermal partons. Factor of 3 enhancement

7. 7 Hwa & Tan, PRC 72, 057902 (2005) Associated particle distributions in the recombination model Bielcikova, at Hard Probes (06) STAR preliminary Au+Au @ 200 GeV 3GeV/c<p T trigger <6GeV/c

8. 8 J. Putschke, HP06, QM06 Jet+Ridge on near side Au+Au 0-10% preliminary jet ridge Jet grows with trigger momentum Ridge does not. Ridge is understood as enhanced thermal background due to energy loss by hard parton to the medium, and manifests through TT recombination. Chiu & Hwa, PRC 72 (05).

9. 9 STAR preliminary Jet + Ridge STAR preliminary Jet J. Bielcikova, HP06 --- at lower pt(assoc) Jet+ridge Jet only J/R~10-15%  trigger even lower!

10. 10 J/R ~ 10% for 1<pt(assoc)<2 GeV/c suggests dominance of soft partons that are not part of the ‘jet’ in the numerator. Yet the ridge wouldn’t be there without hard parton, so it is a part of the jet in the broader sense. Phantom jet: ridge only -- at low pt(assoc) Bielcikova, QM06  triggered events: Phantom jet is the only way to understand the problem. The existence of associated particles falsifies our earlier prediction.

11. 11 Since shower s quark is suppressed in hard scattering,  is produced by recombination of thermal partons, hence exponential in p T. Normally, thermal partons have no associated particles distinguishable from the background. But if the s quarks that form the  are from the ridge, then  can have associated particles above the background, while having exponential p T distribution. The phantom jet is like a blind boy feeling the leg of an elephant and doesn’t know that it belongs to an elephant. Low pt(trig) and low pt(assoc) suppress the peak above the ridge, and do not show the usual properties of a jet, yet the jet is there, just as the phantom elephant is to a short blind person.

12. 12 A. Sickles (PHENIX) Proton triggered events M partners: 1.7<pT<2.5 GeV/c baryon trigger meson trigger from the jet from the ridge J/R < 0.1? J/R > 1? Meson yield in jet is high. Meson yield in ridge decreases exponentially with pT. Ridge is developed in very central collisions.

13. 13 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 more hadrons at high p T, then backward has no broadening forward has more transverse broadening F/B > 1 B/F < 1

14. 14 Backward-forward ratio at intermediate p T in d+Au collisions (STAR) B/F

15. 15 B/F asymmetry taking into account TS recombination (Hwa, Yang, & Fries, PRC 05) STAR preprint nucl-ex/0609021 There are more thermal partons in B than in F.

16. 16 2.5<pT(trig)<4 GeV/c Associated particles on the away side Collective response of the medium: Mach cone, etc. Markovian parton scattering (MPS) Chiu & Hwa (06) Non-perturbative process Trajectories can bend Markovian Divide into many segments: Scattering angle  at each step retains no memory of the past.

17. 17 Cone width Step size Energy loss simulated result Model input Transport coefficient OurGeV 2 /fm Comparable to Vitev’s value

18. 18 Individual tracks may not be realistic, but (like Feynman’s path integral) the average over all tracks may represent physical deflected jets. (a) Exit tracks: short, bend side-ways, large  (b) Absorbed tracks: longer, straighter, stay in the medium until E i <0.3 GeV.

19. 19  Energy lost during last step is thermalized and converted to pedestal distribution Exit tracks hadronized by recombination, added above pedestal Data from PHENIX (Jia) 1<pT(assoc)<2.5 GeV/c One deflected jet per trigger at most, unlike two jets simultaneously, as in Mach cone, etc. Chiu & Hwa, nucl-th/0609038 PRC (to be published)

20. 20 Extension to higher trigger momentum p T (trig)>8 GeV/c, keeping model parameters fixed. (a) 4<p T (assoc)<6 GeV/c (b) p T (assoc)>6 GeV/c Physics not changed from low to high trigger momentum.

21. 21 Mid- and forward/backward-rapidity correlation Trigger: 3<pT(trig)<10 GeV/c, |  (trig)|<1 (mid-rapidity) Associated: 0.2<pT(assoc)<2 GeV/c, (B) -3.9<  (assoc)<-2.7 (backward) (F) 2.7<  (assoc)<3.9 (forward)  distributions of both (B) and (F) peak at , but the normalizations are very different. d-Au collision

22. 22 is larger than Au d associated yield in this case x=0.7 x=0.05 Correlation shapes are the same, yields differ by x2. Au d x=0.05x=0.7 associated yield in that case Degrading of the d valence q? STAR (F.Wang, Hard Probes 06) Don’t forget the soft partons.

23. 23 Recombination of thermal and shower partons higher yield lower yield B/F ~ 2

24. 24 Backward-forward ratio at intermediate p T in d+Au collisions (STAR) B/F Inclusive single-particle distributions

25. 25 Au+Au centrality variation |  trig |<1, 2.7<|  assoc |<3.9 3<p T trig <10 GeV/c, 0.2<p T assoc < 2 GeV/c Normalization fixed at |  ±1|<0.2. Systematic uncertainty plotted for 10-0% data. dN/d   Near side consistent with zero. Away-side broad correlation in central collisions. Broader in more central collisions

26. 26 Au-Au collisions No difference in F or B recoil More path length, more deflection Less path length, less deflection Width of  distribution broadens with centrality At 2.7<|  |<3.9, the recoil parton is moving almost as fast as the cylinder front. What is the Mach cone effect?

27. 27 Two-jet recombination at LHC New feature at LHC: density of hard partons is high. High p T jets may be so dense that neighboring jet cones may overlap. If so, then the shower partons in two nearby jets may recombine. 2 hard partons 1 shower parton from each  p Hwa & Yang, PRL 97, 042301 (2006)

28. 28 The particle detected has some associated partners. There should be no observable jet structure distinguishable from the background. GeV/c But they are part of the background of an ocean of hadrons from other jets. If this prediction is verified, one has to go to pT(assoc)>>20 GeV/c to do jet tomography. What happens to Mach cone, etc?

29. 29 Conclusion Many correlation phenomena related to associated particles observed at moderate pT can be understood in terms of recombination. However, there remains a lot to be explained. More dramatic phenomena may show up at LHC, but then the medium produced may be sufficiently different to require sharper probes. We have learned a lot from experiments at SPS, RHIC, and soon from LHC. At each stage the definition of a jet has changed from >2 to >8 to >20 GeV/c. What kind of correlation is interesting will also change accordingly. Beyond what is known about jet quenching, not much has been learned so far about the dense medium from studies of correlation in jets. (a very conservative view)