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Jets in Nuclear Collisions

Jets in Nuclear Collisions. Why jets in nuclear collisions? How do we find jets in nuclear collisions? Is hard scattering different in nuclear collisions than in e+e- or pp collisions? What happens in the nuclear medium? Is jet transport & fragmentation changed?

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Jets in Nuclear Collisions

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  1. Jets in Nuclear Collisions • Why jets in nuclear collisions? • How do we find jets in nuclear collisions? • Is hard scattering different in nuclear collisions than in e+e- or pp collisions? • What happens in the nuclear medium? • Is jet transport & fragmentation changed? • What do we still want to know? Barbara Jacak Stony Brook University June 29, 2004

  2. At high temperature and density: T~170 MeV and/or r~5r0 Debye screening by produced color-charges expect transition to “free” gas of quarks and gluons Why collide nuclei at s=200 GeV/A? high energy nuclear collisions should create quark gluon plasma Attractive potential Confinement at large distance

  3. Hard scattered or heavy q,g probes of plasma formed p, K, p, n, f, L, D, X, W, d, Hadrons reflect (thermal) properties when inelastic collisions stop (chemical freeze-out). g, g* e+e-, m+m- Real and virtual photons emitted as thermal radiation. how to probe the plasma? System expands & cools e, pressure builds up

  4. Hard quarks & gluons  jets Hard scattering happens early affected by initial state nucleus Hard partons propagate • fast quarks, gluons traverse the interesting stuff • radiate gluons • interact with QGP partons Fragmentation is last step • - outside the medium

  5. Plasma physics of the quark gluon plasma? • Want to know • pressure, viscosity, energy gradients, equation of state, • thermalization time & extent • determine from collective behavior • Other plasma parameters • radiation rate, collision frequency, conductivity, opacity, Debye screening length? • what is interaction s of q,g in the medum? • need short wavelength strongly interacting probe • high momentum q,g provide just this!

  6. schematic view of jet production hadrons leading particle q q hadrons leading particle What is the effect of the medium? before they create jets, the scattered quarks radiate energy (~ GeV/fm) in the colored medium  decreases their momentum  fewer high momentum particles  beam  “jet quenching” Approach: calculate jet rate, test in pp, compare jets in A+A to p+p

  7. gluon quark QCD Radiation interferes too BUT radiated gluons also interact with gluons in the medium!  Energy loss depends on gluon density along the path. QCD and EM Radiation EM Radiation by scattering: Interference between initial and final state radiation EM

  8. Elastic energy loss J.D.Bjorken, SLAC preprint (1982) unpublished • Inelastic (radiative) energy loss QCD is very different from QED in the ability of the gluon to reinteract Energy Loss in Dense QCD Matter Ivan Vitev,ISU

  9. Energy loss expected Since QCD is non-abelian, even 1 scattering in final state is sufficient to generate energy loss Remember that radiated gluon couples to medium! formation length of max E gluon: lF ~ 2E/m2 (m= pT kick ) • DE ~ E x L/l x L m2/2E ~ m2 L 2 /2l So:    formation time of radiated gluon ( gluon interaction probability) standard radiation with no interference In normal, cold nuclei dE/dx ~ 0.5 GeV/fm Prediction for RHIC:  10x DE of cold nuclei

  10. But medium is not static! Expands density drops A closer look at the calculation M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594, (2001); Phys.Rev.Lett.85, (2000) • Radiative energy loss • Significantly larger than the elastic • for static nuclear matter • Can be related to the density of • gluons/quarksin the system orT • Takes into accountgeometry, the • small number of scatterings, finite • kinematics

  11. Central Au+Au collision How to find the jet? s=200 GeV energy is modest; jet s not large How do we find jets in nuclear collisions? In p+p can look for hadrons in the characteristic “cone” pattern

  12. trigger 3 Ways to “Skin a Cat Jet” • Single Particle Spectra: • High pT dominantly from jets • d/dpT  RAA, RdA • nuclear modification factor “Trigger”  = 0 • 2) 2-Particle Correlations: • dN/d() Adler et al., PRL90:082302 (2003), STAR 3) Jet Reconstruction: d/dET, Fragmentation function away-side Nice work if you can get it! near-side

  13. trigger near side Df < 90° Partner from same jet away side Df > 90° opposing jet Jet physics in Au+Au • Trigger: • hadron with pT > 2.5 GeV/c • Biased, low energy, high z jets! • Df of associated partners • Count associated lower pT particles for each trigger • “conditional yield” Near side yield: number of jet associated particles from same jet in specified pT bin Away side yield: jet fragments from opposing jet

  14. Underlying event is big! Collective flow causes another correlation in them: associated particles with non-flow angular correlations -> jets! Treat as 2 Gaussians B(1+2v2(pTtrig)v2(pTassoc)cos(2)) Subtract the underlying event includes ALL triggers (even those with no associated particles in the event) combinatorial background large in Au+Au CARTOON 1 dN flow+jet Ntrig d flow jet

  15. p-p PRL 91 (2003) 241803 Good agreement with NLO pQCD Parton distribution functions Fragmentation functions To generalize for nuclei: fa/N(xa,Q2,r)  fa/N(xa,Q2) . Sa/A(xa,r) . tA(r) Nuclear modification to structure function (shadowing, saturation, etc.) Nuclear thickness function Benchmark calculation of probe rate on a simple system: p+p collisions p0 rates: dN/dpT2dy1dy2 ~  dxa dxb dzc dzd fa/N(xa,Q2) . fb/N(xb,Q2) . Dh1(zc,Q2) . Dh2(zd,Q2) . dsab /dQ2dy p0

  16. Now check that it works in Au+Au • Not so easy – cannot use anything that should be affected by the medium! • Try QCD direct photons

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

  18. Is the message in the medium? • Is there “jet quenching” as predicted from energy loss? •  count high pT particles (AA vs. pp) •  look at back-to-back jets • How much energy do fast partons lose? • What does it tell us about the medium? • Where does the “lost” energy go? • What does the presence of q and q in the QGP do to jet fragmentation?

  19. nucleons Technique to search for jet quenching • Compare to baseline: nucleon-nucleon collisions at the • same energy • To 0’th order: Au + Au collisions start with collisions of quarks & gluons in the individual N-N reactions • (+ effects of • nuclear binding and • collective excitations) • Hard scattering (p transfer > few GeV) processes scale as the number of N-N binary collisions <Nbinary> • so for pT> 2 GeV/c expect: YieldA-A = YieldN-N. <Nbinary>

  20. AA AA If no medium effect: RAA < 1 in regime of soft physics RAA = 1 at high-pT where hard scattering dominates Jet quenching: RAA < 1 at high-pT AA Nuclear Modification of Hadron Spectra? 1. Compare Au+Au to nucleon-nucleon cross sections 2. Compare Au+Au central/peripheral Nuclear Modification Factor: nucleon-nucleon cross section <Nbinary>/sinelp+p

  21. Au-Au s = 200 GeV: high pT suppressed! PRL91, 072301(2003)

  22. near side away side Medium is opaque! peripheral central look for the jet on the other side STAR PRL 90, 082302 (2003) Peripheral Au + Au Central Au + Au Trigger 4-6 GeV/c pT

  23. Measured Reflected Suppression larger out-of-plane Path Length Dependence Background Subtracted See J. Bielcikova et al., (nucl-ex/0311007) for background derivation di-hadron, 20-60% Central STAR Preliminary Out-of-plane In-plane

  24. Suppression: a final state effect? Hadron gas • Hadronic absorption of fragments: • Gallmeister, et al. PRC67,044905(2003) • Fragments formed inside hadronic medium • Hadron source is soft, after all • Recombination of flowing partons • Fries, Muller, Nonaka, Bass nucl-th/0301078 • Lin & Ko, PRL89,202302(2002), Hwa, et al. • Energy loss of partons in dense matter • Gyulassy, Wang, Vitev, Baier, Wiedemann… But absent in d+Au collisions!  d+Au is the “control” experiment

  25. probe rest frame r/ ggg • Multiple elastic scatterings (Cronin effect) • Wang, Kopeliovich, Levai, Accardi Broaden pT : Suppression: an initial state effect? • Gluon Saturation • (color glass condensate) Wavefunction of low x gluons overlap; the self-coupling gluons fuse, saturating the density of gluons in the initial state.(gets Nch right!) Levin, Ryshkin, Mueller, Qiu, Kharzeev, McLerran, Venugopalan, Balitsky, Kovchegov, Kovner, Iancu … RdAu~ 0.5 D.Kharzeev et al., hep-ph/0210033

  26. Experiments show NO suppression in d+Au! PHENIX Preliminary p0 STAR Preliminary PHOBOS Preliminary

  27. Centrality Dependence Au + Au Experiment d + Au Control PHENIX preliminary • Dramatically different and opposite centrality evolution of AuAu experiment from dAu control. • Jet Suppression is clearly a final state effect.

  28. leading particle suppressed hadrons Pedestal&flow subtracted q q ? Are back-to-back jets there in d+Au? Yes! So this is the right picture for Au+Au

  29. Property probed: density Agreement with data: Vitev, Gyulassy, Wang, others say dE/dx ~ 7.5 GeV/fm get dAu right too! initial gluon density= dNg/dy ~ 1100e ~ 15 GeV/fm3 hydro initial state same e 5-10 x ecritical dAu d-Au NB: Lowest energy radiation sensitive to infrared cutoff. Au-Au

  30. Recap • Hard partons are excellent probes of QGP • Can calculate their production rate with pQCD in Au+Au • (surprisingly) Can do jet physics in heavy ion collision • See jet quenching in single particles & back-to-back correlations • Infer: dE/dx ~ 7.5 GeV/fm • dNg/dy ~ 1100 • e ~ 15 GeV/fm3

  31. Turn to the fragmentation function Standard picture If true: fragmentation independent of medium Baryon/meson at high pT same in Au+Au and p+p

  32. Formation time of fragmentation hadrons • Uncertainty principle relates hadron formation time to hadron size, Rh and mass, mh • In laboratory frame: tf ~ Rh (Eh /mh) • consider 2.5 GeV pT hadrons • tf ~ 9-18 fm/c for pions; Rh~0.5-1 fm • tf ~ 2.7 fm/c for baryons (Rh~1 fm) • Alternatively, consider color singlet dipoles from combination of q & q from gluon splitting • Using gluon formation time, can estimate • tf ~ 2Eh (1-z)/(kT2+mh2) • for z = 0.6-0.8 and kT ~ LQCD(tf baryons) ~ 1-2 fm/c R(Au nucleus) ~ 7 fm  Baryon formation is NOT outside the medium!

  33. We observe a puzzle h/p0 ratio shows that p is enhanced only < 5 GeV/c

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

  35. Exponential: Power law: Phase space filled with partons:coalesce into hadrons Use lowest Fock state, i.e. valence quarks • ReCo of hadrons: convolution of Wigner functions • Where does ReCo win? Wab(1;2) = wa(1)wb(2) fragmenting parton: ph = z p, z<1 recombining partons: p1+p2=ph R. Fries

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

  37. But baryons show jet-like properties too… Baryons at 2-4 GeV/c pT scale with Ncoll !

  38. So baryons seem jet-like! • baryons & antibaryons not suppressed!? • parton DE depends upon what fragmentation WILL be??? • baryon excess due to fragmentation function modification? • Step 1: determine if baryons are from jets • do we see hadronic partners from the same jet? • Step 2: calculate effect of q,q in surrounding medium upon (soft part of) fragmentation function Rcp

  39. Step 1: use 2 particle correlations Select particles with pT= 2.5-4.0GeV/c Identify them as mesons or baryons via Time-of-flight Find second particle with pT = 1.7-2.5GeV/c Plot distribution of the pair opening angles

  40. Jets in PHENIX • Large multiplicity of charged particles • --solution: find jets in a statistical manner • using angular correlations of particles • mixed events give combinatorial background • 2 x 90 degree acceptance in phi and ||<0.35 --solution: correct for azimuthal acceptance, but not for  acceptance • 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

  41. Subtracting combinatorial background includes ALL triggers (even those with no associated particles in the event) CARTOON 1 dN flow+jet Ntrig d flow Associated particles from the underlying event. Collective flow causes another correlation in them: jet associated particles with non-flow angular correlations -> jets! Treat as 2 Gaussians B(1+2v2(pTtrig)v2(pTassoc)cos(2))

  42. Identify Trigger: Source of intermediate pT baryons? • jet partner equally likely for trigger baryons & mesons • Same side: only slight decrease with centrality • Away side: partner rate as in p+p confirms jet source of baryons! • See disappearance of away-side jet for both baryons and mesons

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

  44. pT spectra of same jet associated particles Spectra in lab, rather than jet, frame Allows to compare with inclusive spectra

  45. Compare slope to inclusive hadron spectra Generally higher Perhaps thermalized in most central collisions? Calculations (step 2) desperately needed!

  46. Conclusion about fragmentation function • 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 • Maybe some evidence that jet fragments are beginning to thermalize in the medium

  47. What do we still want to know? • Quantitative information on medium modification of jet fragmentation • Where does the energy radiated by fast partons go? • Many soft gluons – no (per observed multiplicity) • A few semi-hard gluons? … could be • 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?

  48. values

  49. kT, jTat RHIC from p+p Data Statistical Errors Only di-hadron J. Rak, Wed. J. Rak, DNP03 PHENIX preliminary Df near-side away-side

  50. I. Vitev, nucl-th/0308028 Induced Gluon Radiation • ~collinear gluons in cone • “Softened” fragmentation Gyulassy et al., nucl-th/0302077 Moment Analysis of QCD Matter

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