Correlation in Jets

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

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

4. Factorizable terms: k q1 q2 q3 q4 Non-factorizable terms correlated Correlation of pions in jets in HIC Two-particle distribution They do not contribute to C2(1,2)

5. Pion transverse momenta p1 and p2 Hwa & Tan, PRC 72, 024908 (2005)

6. STAR, PRL 95, 152301 (2005) Trigger 4 < pT < 6 GeV/c Factor of 3 enhancement C2(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) Hard for medium modification of fragmentation function to achieve, but not so hard for recombination involving thermal partons.

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

8. jet Au+Au 0-10% preliminary J. Putschke, HP06, QM06 ridge Jet grows with trigger momentum Ridge does not. Jet+Ridge on near side 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. Jet + Ridge Jet J/R~10-15% STAR preliminary STAR preliminary Jet+ridge Jet only  trigger even lower! J. Bielcikova, HP06 --- at lower pt(assoc)

10. triggered events: Bielcikova, QM06 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) The existence of associated particles falsifies our earlier prediction. Phantom jet is the only way to understand the problem.

11. Since shower s quark is suppressed in hard scattering,  is produced by recombination of thermal partons, hence exponential in pT. 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 pT 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. meson trigger from the jet baryon trigger from the ridge M partners: 1.7<pT<2.5 GeV/c J/R < 0.1? J/R > 1? Protontriggered events A. Sickles (PHENIX) Meson yield in jet is high. Meson yield in ridge decreases exponentially with pT. Ridge is developed in very central collisions.

13. If initial transverse broadening of parton gives more hadrons at high pT, then • forward has more transverse broadening • backward has no broadening Forward-backward asymmetry in d+Au collisions Expects more forward particles at high pT than backward particles F/B > 1 B/F < 1

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

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

16. Trajectories can bend Divide into many segments: Scattering angle  at each step retains no memory of the past. 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 Markovian

17. Cone width • Step size • Energy loss simulated result Transport coefficient Comparable to Vitev’s value Our GeV2/fm Model input

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 Ei<0.3 GeV.

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

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

21. Mid- and forward/backward-rapidity correlation d-Au collision 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.

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

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

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

25. Broader in more central collisions Au+Au centrality variation |htrig|<1, 2.7<|hassoc|<3.9 3<pTtrig<10 GeV/c, 0.2<pTassoc< 2 GeV/c dN/dDf Near side consistent with zero. Away-side broad correlation in central collisions. Df Normalization fixed at |Df±1|<0.2. Systematic uncertainty plotted for 10-0% data.

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

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

28. But they are part of the background of an ocean of hadrons from other jets. GeV/c The particle detected has some associated partners. There should be no observable jet structure distinguishable from the background. 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. 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. (a very conservative view) Beyond what is known about jet quenching, not much has been learned so far about the dense medium from studies of correlation in jets. 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.