2. 1 Jet Structure of Baryons and Mesons in Nuclear Collisions l Why jets in nuclear collisions? l Initial state l What happens in the nuclear medium? l Medium modification of jet fragmentation PHENIX Collaboration Barbara Jacak Stony Brook University Aug. 16, 2004

3. 2  pressure builds up why jets in nuclear collisions?  K  p  n  d, Reflect (thermal) properties when collisions cease Quark gluon plasma? use short wavelength probes. Fast q, g nearly ideal Hard scattering, heavy quark production. Rate calculable from QCD + nuclear geometry. System expands & cools

4. 3 Expected interaction with the medium Hard scattering happens early affected by initial state nucleus Hard partons traverse the interesting stuff Energy loss by induced gluon radiation Modification of fragmentation outside the medium??  recombination with medium partons  radiated gluons nearby!

5. 4 Initial state: p+p collisions p-p PRL 91 (2003) 241803 Good agreement with NLO pQCD Parton distribution functions Fragmentation functions 00  0 well described by pQCD and usual fragmentation functions To generalize for nuclei: f a/N (x a,Q 2,r)  f a/N (x a,Q 2 ). S a/A (x a,r). t A (r) Nuclear modification to structure function (shadowing, saturation, etc.) Nuclear thickness function

6. 5 pQCD in Au+Au? direct photons [ w/ the real  suppression] (  pQCD x N coll ) /  background Vogelsang/CTEQ6 [if there were no  suppression] (  pQCD x N coll ) / (  background x N coll ) Au+Au 200 GeV/A: 10% most central collisions [   ] measured / [   ] background =  measured /  background Preliminary Probe calculation works! p T (GeV/c)

7. 6 Nuclear medium modifies initial state I’ll come back to this question l Probe response of cold nuclear matter with increased number of collisions. l Cronin effect for baryons > mesons l Initial state multiple scattering k T broadening or Semi-hard scattering l But shouldn’t initial state scattering and fragmentation factorize?

8. 7 Turn to nuclear collisions: single particles h/  0 ratio shows baryons enhanced for pT < 5 GeV/c

9. 8 The baryons scale with N coll ! Greco, Ko, Levai: PRC 68 (2003)034904 But observed enhancement can be explained by recombination of thermal quarks from an expanding quark gluon plasma. NOT Jet-like! Jet-like Not suppressed

10. 9 So, do jet analysis in Au+Au Trigger: hadron with p T > 2.5 GeV/c Identify as baryon or meson Biased, low energy, high z jets! Plot  of associated partners Count associated lower p T particles for each trigger  “conditional yield” Near side yield: number of jet associated particles from same jet in specified p T bin Away side yield: jet fragments from opposing jet trigger 2 particle correlations near side  < 90° Partner from same jet away side  > 90° opposing jet

11. 10 Subtract the underlying event CARTOON flow flow+jet dN N trig d  includes ALL triggers (even those with no associated particles in the event) jet Underlying event is big! Collective flow causes another correlation in them: B(1+2v 2 (p T trig )v 2 (p T assoc )cos(2  )) associated particles with non-flow angular correlations -> jets! Treat as 2 Gaussians 1 combinatorial background large in Au+Au!

12. 11 2 particle correlations Select particles with p T = 2.5-4.0GeV/c Identify them as mesons or baryons via Time-of-flight Find second particle with p T = 1.7-2.5GeV/c Plot distribution of the pair opening angles

13. 12 jet partner equally likely for trigger baryons & mesons Same side: slight decrease with centrality. Larger partner probability than pp, dAu Away side: partner rate as in p+p confirms jet source of baryons! “disappearance” of away- side jet for both baryons and mesons intermediate p T baryons ARE from jets

14. 13 pions only soft protons partners expected from recombination Yield of partners per trigger expected from recombination of purely thermal (soft) constituent quarks (dilutes jets) Many baryons ARE from jets, but medium modifies those jets Allow fast quark to combine with quarks from medium

15. 14 Jet partner distribution on trigger side Partner vs. inclusive slopes: Generally higher soften in most central collisions

16. 15 Formation time of fragmentation hadrons l Uncertainty principle relates hadron formation time to hadron size, R h and mass, m h In laboratory frame:  f ~ R h (E h /m h ) consider 2.5 GeV pT hadrons  f ~ 9-18 fm/c for pions; R h ~0.5-1 fm  f ~ 2.7 fm/c for baryons (R h ~1 fm) l Alternatively, consider color singlet dipoles from combination of q & q from gluon splitting Using gluon formation time, can estimate  f ~ 2E h (1-z)/(k T 2 +m h 2 ) for z = 0.6-0.8 and k T ~  QCD (  f baryons) ~ 1-2 fm/c R(Au nucleus) ~ 7 fm  Baryon formation is NOT outside the medium!

17. 16 Conclusion about fragmentation function l It’s modified in the medium! Au+Au jets richer in soft hadrons than p+p or d+Au Au+Au jets baryon yield increases with medium volume l Maybe some evidence that jet fragments are beginning to thermalize in the medium

18. 17 Jets in PHENIX l Large multiplicity of charged particles --solution: find jets in a statistical manner using angular correlations of particles mixed events give combinatorial background l 2 x 90 degree acceptance in phi and |  |<0.35 --solution: correct for azimuthal acceptance, but not for  acceptance l Elliptic flow correlations --solutions: use published strength values and subtract (could integrate over 90° to integrate all even harmonics to zero) PHENIX PRL 91 (2003) 182301

19. 18 Physics of the quark gluon plasma? l Want to know pressure, viscosity, energy gradients, equation of state, thermalization time & extent determine from collective behavior radiation rate, collision frequency, conductivity, opacity, Debye screening length? use interaction of fast q, g probes with medium l Expected interactions with QGP Energy loss by induced gluon bremsstrahlung Modified fragmentation functions

20. 19 Hydro. expansion at low p T + jet quenching at high p T. Coalesce (recombine) boosted quarks  hadrons enhances mid p T hadrons baryons especially pQCD spectrum shifted by 2.2 GeV T eff = 350 MeV R. Fries, et al Are extras from the (soft) underlying event?

21. 20 Phase space filled with partons:coalesce into hadrons l ReCo of hadrons: convolution of Wigner functions l Where does ReCo win? W ab (1;2) = w a (1)w b (2) fragmenting parton: p h = z p, z<1 recombining partons: p 1 +p 2 =p h Power law: Exponential: Use lowest Fock state, i.e. valence quarks R. Fries

22. 21 Coalescence Model results Fries et al: Phys.Rev. C68 (2003) 044902 Greco, Ko, Levai: PRC 68 (2003)034904 particle ratios and spectra OK intermediate p T hadrons from coalescence of flowing partons NOT from jets, so no jet-like associated particles

23. 22 What do we still want to know? l Quantitative information on medium modification of jet fragmentation l Where does the energy radiated by fast partons go? Many soft gluons – no (per observed multiplicity) A few semi-hard gluons? … could be l How is the lost energy propagated in the medium? Infer energy, color transport properties of QGP basic plasma physics! Is the lost energy thermalized in the medium?

24. 23 values B (fm) NpartR/R+F  R/R+F p Partner yield  Partner yield p 12240.450.95 0.027  0.0047 0.0014  0.0007 7.51560.650.97 0.0172  0.0030 0.0008  0.0004 03900.80.98 0.0098  0.04017 0.0005  0.0003

25. 24 k T, j T at RHIC from p+p Data J. Rak, Wed. J. Rak, DNP03 di-hadron Statistical Errors Only near-sideaway-side 

26. 25 Pions in 3 detectors in PHENIX l Charged pions from TOF l Neutral pions from EMCAL l Charged pions from RICH+EMCAL Cronin effect gone at p T ~ 8 GeV/c

27. 26 Does Cronin enhancement saturate? l A different approach: l Intrinsic momentum broadening in the excited projectile proton: l h pA : average number of collisions: X.N.Wang, Phys.Rev.C 61 (2000) : no upper limit. Zhang, Fai, Papp, Barnafoldi & Levai, Phys.Rev.C 65 (2002) : n=4 due to proton d dissociation.