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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 Jetsin 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 at 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. Links Slides will be posted at http://www.uni-muenster.de/Physik.KP/Lehre/HS-2007 Lectures on Heavy-Ion Physics (from experimentalist‘s viewpoint): http://www.uni-muenster.de/Physik.KP/Lehre/QGP-SS06 User: qgp, password: ss06 Many useful talks/lectures on Hard Scattering and Jets: http://cteq.org (→ summer schools) 3 Hard Scattering and Jets in Heavy-Ion Collisions

  4. Paper on Hard Scattering and Jets M. Tannenbaum,Review of hard scattering and jet analysisnucl-ex/0611008 A. Accardi et al.,Hard Probes in Heavy Ion Collisions at the LHC: Jet Physicshep-ph/0310274 4 Hard Scattering and Jets in Heavy-Ion Collisions

  5. 1.1 Quark-Gluon Plasma 5 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  6. Strong Interaction Nobel prize 2004 in physics David J. Gross H. David Politzer Frank Wilczek • Confinement:Isolated quarks and gluons cannot be observed, only color-neutral hadrons Meson • Asymptotic freedom:Coupling as between color charges gets weaker for high momentum transfers, i.e., for small distances (r < 1/10 fm) • Limit of low particle densities and weak coupling experimentally well tested ( QCD perturbation theory) • Nucleus-Nucleus collisions: QCD at high temperatures and density („QCD thermodynamics“) 6 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  7. Confinement Dominant at small distances (1-gluon exchange) Dominant at large distances (Confinement) 7 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  8. Asymptotic Freedom QCD perturbation theory (pQCD): pQCD works for as << 1.This is the case for Q2 >> L2 0,06 (GeV/c)2 Asymptotic freedom: In the limit Q2   quarks behave as free particles 8 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  9. Predictions from First principles: Lattice QCD only 20% deviation:qgp is an ideal gas not Tc = (160 - 190) MeVec 0.7 – 1.0 GeV/fm3 F. Karsch, E. Laermann, hep-lat/0305025 2 quark flavors: 9 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  10. QCD Phase Diagram Early universe (t  10-6 s) RHIC, LHC (?) Measure of net baryon density ρ 10 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  11. Brief History of QCD and Jets 11 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  12. A Jet in a p+p Collision 12 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  13. Jet-Quenching in Nucleus-Nucleus Collisions 13 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  14. Brief History of Heavy Ion Physics 14 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  15. CERN SPS (1985 - 2004) NA35/44NA38/50/50NA49NA45(CERES)NA57 North area (NA) Circumference: 6,9 km SPS West area (WA) WA80/98, WA97→NA57 15 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  16. Circumference 3,83 km 2 independent rings 120 „bunches“ ~109 Au-Ions per bunch „Bunch Crossings“ every 106 ns Collisions of different particle species possible Maximum energy: 200 GeV for Au+Au 500 GeV for p+p Design luminosity Au-Au: 2 x 1026 cm-2 s-1 p-p: 1,4 x 1031 cm-2 s-1 RHIC: Relativistic Heavy Ion Collider 16 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  17. RHIC beamtimes: • Run 1 (2000):Au+Au, sNN= 130 GeV • Run 2 (2001-2002):Au+Au, p+p, sNN= 200 GeV • Run 3 (2003):d+Au, p+p, sNN= 200 GeV • Run 4 (2003-2004):Au+Au, (p+p) sNN= 62, 200 GeV • Run 5 (2005):Cu+Cu, p+p sNN= 22, 62, 200 GeV • Run 6 (2006): p+p sNN= 22, 62, 200 GeV • Run 7 (2007): Au+Au sNN= 200 GeV 17 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  18. CERN: Large Hadron Collider (LHC) p+p collisions:s = 14 TeVcollision rate: 800 MHzPb+Pb collisions:s = 5,5 TeVcollision rate: 10 kHz circumference: 27 kmB-Field: 8 T100 m beneath the surfacefirst collisions: 2008 18 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  19. FAIR at GSI SIS 100/300 SIS UNILAC FRS ESR HESR Super FRS CR NESR FLAIR RESR 2007 begin of construction2012 first experiments2014 completion Planned facility: 100 – 1000 times higher beam intensities, Z = -1 – 92 (protons up to uranium, antiprotons),up to 35 GeV/nucleon Currently availablebeam particles: Z = 1 – 92 (protons up to uranium)up to 2 GeV/nucleon 19 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma

  20. 1.2 Kinematic Variables 20 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  21. Energy and Momentum „Length“ of a 4-vector is invariant under Lorentz transformation: Relativistic momentum and relativistic energy: Energy-Momentum four vector: Relativistic energy momentum relation: 21 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  22. Energy and Momentum Conservation Der energy-momentum four-vector is conserved in all components. For a reaction A+B  C+D one has: 1. energy conservation: 2. 3-momentum conservation energy-momentum four-vectors Mandelstam variables: 22 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  23. Interpretation of s und t is the total energy in the center-of-mass system Center-of-mass system (CMS) defined by: Interpretation of s: Interpretation of t: is the momentum transfer (square of four-momentum transfer) 23 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  24. s for Fixed-Target and Collider Experiments Fixed-Target-Experiment: Target Collider: Example: Anti-proton production in a fixed-target experiment: Minimum energy required for the production of an anti-proton: All produced particles at rest in CMS-frame, i.e s = 4 mp, therefore 24 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  25. Rapidity beam axis rapidity y is additive under Lorentz transformation: rapidity in system S rapidity of S‘ measured in S rapidity in S‘ Pseudorapidity h: In particular: 25 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  26. Summary: Kinematic Variables Transverse momentum Rapidity Pseudorapidity p pT  (~15) (~40) 26 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  27. Example of a Pseudorapidity Distribution Beam rapidity: dNch /dh Average number of charged particles: 27 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  28. Lorentz Invariant Phase Space Element Lorentz transformation of phase space element not Lorentz Invariant! Invariant phase space element: Invariant cross section: 28 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  29. Invariant Cross Section Example: p0 production Integral of the inv. cross section: Total inel.cross section Average particlemultiplicity per event 29 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

  30. Invariant Mass counts M (GeV/c2) Consider decay of a particle with mass M into two daughter particles Invariant Mass: Example: p0 - Decay Signal: Number of entries over combinatorial background(Peak width determined by energy resolution of the detector) Momentum of the p0 Background of g-pairs, whichdon‘t originate from the same p0 decay 30 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables

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