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PD Dr. Klaus Reygers Institut für Kernphysik Universität Münster

Hard Scattering and Jets in Heavy-Ion Collisions Naturwissenschaftlich-Mathematisches Kolleg der Studienstiftung des deutschen Volkes Kaiserslautern 30.9. – 5.10.2007. PD Dr. Klaus Reygers Institut für Kernphysik Universität Münster. Content. 1 Introduction 1.1 Quark-Gluon Plasma

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PD Dr. Klaus Reygers Institut für Kernphysik Universität Münster

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  1. Hard Scattering and Jets in Heavy-Ion CollisionsNaturwissenschaftlich-Mathematisches Kollegder Studienstiftung des deutschen VolkesKaiserslautern 30.9. – 5.10.2007 PD Dr. Klaus ReygersInstitut für Kernphysik Universität Münster

  2. Content 1 Introduction 1.1 Quark-Gluon Plasma 1.2 Kinematic Variables 2 Lepton-Nucleon, e+e-, and Nucleon-Nucleon Collisions 2.1 Deep-Inelastic Scattering and the Quark-Parton Model 2.2 Jets in e+e--Collisions 2.3 Jets and High-pT Particle Production in Nucleon-Nucleon Collisions 2.4 Direct Photons 3 Nucleus-Nucleus Collisions 3.1 Parton Energy Loss 3.2 Point-like Scaling 3.3 Particle Yields and Direct Photons at High-pT 3.4 Further Tests of Parton Energy Loss 3.5 Two-Particle Correlations 3.6 Jets in Pb+Pb Collisions at the LHC 2 Hard Scattering and Jets in Heavy-Ion Collisions

  3. 3.1 Parton Energy Loss 3 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  4. Jet Tomography in A+A Collisions • Hard parton-parton scatterings take place in initial phase, prior to the formation of a QGP • Scattered quarks und gluons sensitive to medium properties: „jet tomography“ 4 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  5. Parton Energy Loss • Detailed numerical calculation shows: • Energy loss for gluon jets larger than for quark jets: • Energy loss due to gluon radiation dominant: • Parton energy loss in a finite, static medium consisting of colorcharge carriers • Total energy loss in the medium: (effect of quantummech. interference) Path length of the parton in the medium Typical momentum transfer frommedium to parton Mean free path of the radiated gluons in the medium 5 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  6. Parton Energy Loss: Why DE L2 ? Probability for radiating a gluon: Number of scatterings with momentum transfer kT until it decoheres: Total energy loss: 6 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  7. increases smoothly with energy density Nuclear matter Relation between Transport Coefficient andEnergy Density of the Medium ideal qgp hot, massless pion gas • QGP (and hot hadron gas): cold pion gas Medium characterized by (Momentum transfer per mean free path) 7 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  8. Parton Energy Loss in Expanding Medium Taking into account the expansion of the fire ball (Bjorken Model): Initial gluon density Transverse area(A ~ R1/3 für b = 0) Energy loss linear in L Energy loss becomes linear in L for 1D Bjorken expansion 8 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  9. Medium-Modified Fragmentation Functions (I) hadron h, energy energyloss parton Prob. Distr. for parton energy loss e (“Quenching weight”) Consider fixed parton energy loss e: Average over energy loss probability: Hadrons resultingfrom gluon bremsstrahlungneglected 9 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  10. Medium-Modified Fragmentation Functions (II) Fragmentation functionu →p for a medium with L = 7 fm and various gluon densities 10 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  11. Quenching Weights (I) quenching weight continuous quenching weight Note that P(DE) is a generalized probability which can take negative values as long as this equation holds probability to have no induced gluon radiation taken from PhD thesis of C. Loizides 11 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  12. Quenching Weights (II): Continuous Weight taken from PhD thesis of C. Loizides These quenching weights hold for parton energies E→  12 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  13. Parton Energy Loss in the Limit E→  More realistic models need to take finite parton energies into account 13 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  14. Energy loss in the GLV Formalism for Cu+Cu, Au+Au, and Pb+Pb I. Vitev, Phys.Lett.B639:38-45,2006 energy loss # radiated gluons Calculated fractional energy loss and number of radiated gluons shown for three centralities in each figure: Au+Au at sNN = 200 GeV: Cu+Cu at sNN = 200 GeV: Pb+Pb at sNN = 5500 GeV: dNg/dy = 2000, 3000, 4000 14 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  15. Simple Estimate of the Relative Energy Loss pT independence of RAA implies constant fractional energy loss p0 spectrum without energy loss: Sloss from p0RAA Constant fractional energy loss: This leads to: PHENIX, nucl-ex/0611007 p0 spectra at RHIC energy (sNN = 200 GeV) described with n 8 15 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

  16. 3.2 Point-like Scaling 16 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  17. Expectation for Particle Yields from Hard Scattering Processes in A+A collisions Only changecompared to p+p • Calculate increase of the effective luminosity of nucleons (and partons, respectively) based on known nuclear geometry • Result:Particle yields scale with the average number Ncoll of inelastic nucleon-nucleon collisions in the absence of nuclear effects 17 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  18. Digression: Luminosity of a Collider Rate of event for a given physics process: Cross section [cm2] Event rate [s-1] Luminosity [(scm2)-1] If two bunches of particles collide with frequency f then : ni: number of particles in bunch i Transverse area of the beam Example:Au+Au at RHIC: L = 2 x 1026 cm-2 s-1 18 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  19. Effective Nucleon Luminosity: The Nuclear overlap function Nuclear thickness: Normalization: “nucleon luminosity” in area at : “Total nucleon luminosity” for collisions at impact parameter b(nuclear overlap function): unit: 1/area Thus, number of interactions for process with cross section In particular: 19 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  20. Impact Parameter Distribution of a A+A collisions Glauber MC: Analytic approximation: Au+Au at sNN = 200 GeV 500 000 Glauber MC collisions probability for an inelastic A+B collision at impact parameter b slope: 2p Total cross section: 20 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  21. Averaging TAB(b) over an Impact Parameter Distribution Observable: Hard process per inelastic A+A collisions, i.e. Typical example: pT dependent pion yield per inelastic event: Averaging over an impact parameter range f (say b1 b b2): weighting factor: Note that 21 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  22. Nuclear Modification Factor (I) Consider special case b1 = 0, b2 = : (holds for hard scattering in the absence of nuclear effects) Definition of nuclear modification factor: (in the absence of nuclear effects) In practice: where is determined with a GlauberMonte Carlo code 22 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  23. Ncoll from Glauber Monte-Carlo calculation In the absence of nuclear effects:RAB = 1 at high pT (pT > 2 GeV/c) Nuclear Modification Factor (II) RAB “no medium effects” RAB = 1 RAB < 1 pT (GeV) 23 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  24. Nucleons of both nuclei randomly distributed in space according to Woods-Saxon distribution Impact parameter b drawn from distribution ds/db = 2pb Collision between two nucleons take place if their distance d in the transverse plane satisfies Glauber Monte-Carlo Approach Au+Au bei sNN = 200 GeV • Npart and Ncoll through simulation of many A+B collisions (typically ~ 106) 24 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  25. Examples of Glauber-MC Events (I) Au+Au bei sNN = 200 GeV Side view: Transverse plane: 25 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  26. Examples of Glauber-MC Events (II) Au+Au at sNN = 200 GeV Side view: Transverse plane: 26 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  27. Npart und Ncoll vs. Impact Parameter Ncoll(b) Npart(b) Approximate relation between Npart and Ncoll: 27 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

  28. 3.3 Particle Yields at Direct Photons at High-pT 28 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  29. Cronin-Effect in p+A Collisions Proton-Nucleus Collisions: p+A Collisions: Nuclear modification factorRpA > 1, at intermediate pT, before RpA = 1 is reached in the limit of very high pT Common explanation of the Cronin effect: Multiple soft scattering in p+A leads to additional transverse momentum kT 29 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  30. p0 spectra in p+p- and Au+Au Collisionen peripheral: Ncoll = 12.3  4.0 central Ncoll = 955  94 Strong suppression of the p0 spectrum in central Au+Au collisions relative to Ncoll-scaled p+p spectrum 30 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  31. p0 production in Au+Au at sNN = 200 GeV Ncoll = 5 ± 1 factor 4-5 suppression Ncoll = 12 ± 4 Ncoll = 955 ± 94 Ncoll = 603 ± 59 Ncoll = 61 ± 10 Ncoll = 29 ± 8 Ncoll = 220 ± 23 Ncoll = 374 ± 40 Ncoll = 120 ± 14 • No suppression in peripheral Au+Au collisions • Factor 4-5 suppression in central Au+Au collisions 31 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  32. Particle Composition in A+A • For a parton that hadronizes in the vacuum after traversing the medium (A+A collision), particle ratios should be similar to those in d+Au or e++e- • This is indeed approximately true for pT > 6 GeV/c • 2 < pT < 6 GeV/c: quark coalescence ? 32 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  33. What’s going on at Intermediate pT (~2 < pT < ~6 GeV/c) ? Coalescence of quarks from the QGP is a conceivablemodel for hadronization at intermediate pT 33 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  34. Alternative Explanation: Effects of Cold Nuclear Matter ? • Hadron suppression e.g. due to strong modification of parton distributions in heavy nuclei (initial state effects)? • Example: Color Glass Condensate Model • Fewer gluons in wavefunction of incoming Au nuclei • Result: Fewer hard parton-parton scatteringsand therefore fewer particles at high pT • Hadron suppression in Au+Au can be described! • Control Measurements • Hadron production in d+Au • High-pT direct photons in Au+Au Kharzeev, Levin, McLerran, Phys.Lett. B 561, 93 (2003) 34 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  35. Cold Nuclear Matter Effects studied at RHIC with d+Au RdA 1: Cold nuclear matter effectsare small at sNN = 200 GeV p0 d+Au nucl-ex/0610036 35 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  36. Centrality Dependence of RAA in d+Au and Au+Au Au + Au Experiment d + Au Control Experiment Final Data Preliminary Data 36 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  37. Production of direct photons and hadrons at high pT sensitive to the same parton luminosity Direct Photons at high pT as a as as Example: • Direct photons escape the medium unscathed 37 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  38. Direct photons from hard scattering dominate at high pT Experimental challenge: Background from hadron decays, e.g.p0 g+g,h  g+g Method:gdirekt = gGesamt – gZerfall Photon Sources in A+A Collisions hard: thermal: Decay photons 38 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  39. QCD + Ncoll scaling describes direct photon spectra in Au+Au Direct Photons in Au+Au Au+Au bei sNN = 200 GeV Phys.Rev.Lett.94:232301,2005 39 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  40. Nuclear Modification factor for direct Photons No energyloss for g‘s Factor 5 suppression energy lossfor q and g Hadrons are suppressed whereas direct photons are not:Evidence for parton energy loss (as expected in the QGP) 40 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  41. Centrality Dependence of p0 and Direct Photon Production in Au+Au at sNN = 200 GeV 41 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  42. More Recent Data with Higher Statistics Possible Explanations for direct photon suppression at pT  18 GeV/c: • Proton/neutron difference • Modification of parton distribution (EMC effect?) • Quenching of fragmentation photons 42 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  43. Reminder: Direct and Fragmentation Component NLO pQCD calculation by W. Vogelsang (p+p at s=200 GeV) direct fragm. 43 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  44. Data imply high initial gluon density high energy density Energy loss for a 10 GeV quark: Jet Quenching: Data vs. Theory Au+Au at sNN = 200 GeV without parton energy loss Levai Wang Wang with parton energy loss Vitev Levai 44 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  45. 3.4 Further Tests of Parton Energy Loss 45 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  46. How to Learn More about Jet Quenching ? • Suppression of high pT hadron yields • Dependence on colliding system • Dependence on center-of-mass energy • Dependence on path length L in the medium • Difference between energy loss for light (up, down) and heavy quarks (charm) • Study modification of di-hadron correlations in Au+Au with respect to p+p 46 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  47. p0RAA in Au+Au and Cu+Cu at sNN = 200 GeV Approximately same RAA in Au+Au and Cu+Cu for similar Npart values in accordance with jet quenching models 47 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  48. sNN Dependence of RAA (I):Au+Au at 62 GeV and 200 GeV Similar RAA for pT > 6 GeV in Au+Au at 62 and 200 GeV 48 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  49. sNN Dependence of RAA (II):RAA in Cu+Cu at 22.4, 62.4 and 200 GeV Cronin enhancement appears to win over parton energy loss in central Cu+Cu collisions at 22 GeV 49 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

  50. sNN Dependence of RAA (III): RAA in Pb+Pb Collisions at the CERN SPS Suppression in very central Pb+Pb collisions (Npart > 300) 50 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

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