1. 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

2. 2 Hard Scattering and Jets in Heavy-Ion Collisions 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-p T 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-p T 3.4 Further Tests of Parton Energy Loss 3.5 Two-Particle Correlations 3.6 Jets in Pb+Pb Collisions at the LHC

3. 3 Hard Scattering and Jets in Heavy-Ion Collisions 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)

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

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

6. 6 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma  Confinement: Isolated quarks and gluons cannot be observed, only color- neutral hadrons Meson  Asymptotic freedom: Coupling  s 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) Strong Interaction  Nucleus-Nucleus collisions: QCD at high temperatures and density („QCD thermodynamics“) Nobel prize 2004 in physics David J. GrossH. David PolitzerFrank Wilczek

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

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

9. 9 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma Predictions from First principles: Lattice QCD F. Karsch, E. Laermann, hep-lat/0305025 2 quark flavors: T c = (160 - 190) MeV  c  0.7 – 1.0 GeV/fm 3 only 20% deviation: qgp is an ideal gas not

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

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

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

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

14. 14 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma Brief History of Heavy Ion PhysicsStartAcceleratorProjectile Energy (  s) per NN pair ~1985AGS (BNL)Si~5 GeV ~1985SPS (CERN)O, S~20 GeV 1994SPS (CERN)Pb17 GeV 2000RHIC (BNL)Au200 GeV 2008LHC (CERN)Pb5500 GeV

15. 15 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma CERN SPS (1985 - 2004) SPS West area (WA) North area (NA) NA35/44 NA38/50/50 NA49 NA45(CERES) NA57 WA80/98, WA97→NA57 Circumference: 6,9 km

16. 16 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma RHIC: Relativistic Heavy Ion Collider  Circumference 3,83 km  2 independent rings  120 „bunches“  ~10 9 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 10 26 cm -2 s -1  p-p: 1,4 x 10 31 cm -2 s -1

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

18. 18 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma CERN: Large Hadron Collider (LHC) p+p collisions:  s = 14 TeV collision rate: 800 MHz Pb+Pb collisions:  s = 5,5 TeV collision rate: 10 kHz circumference: 27 km B-Field: 8 T 100 m beneath the surface first collisions: 2008

19. 19 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma FAIR at GSI UNILAC SIS FRS ESR SIS 100/300 HESR Super FRS NESR CR RESR FLAIR Currently available beam particles: Z = 1 – 92 (protons up to uranium) up to 2 GeV/nucleon Planned facility: 100 – 1000 times higher beam intensities, Z = -1 – 92 (protons up to uranium, antiprotons), up to 35 GeV/nucleon 2007begin of construction 2012first experiments 2014 completion

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

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

22. 22 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables 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 Mandelstam variables: energy-momentum four-vectors

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

24. 24 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables  s for Fixed-Target and Collider Experiments Target Fixed-Target-Experiment: 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 m p, therefore

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

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

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

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

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

30. 30 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables Invariant Mass Consider decay of a particle with mass M into two daughter particles Example:  0 - Decay M (GeV/c 2 ) counts Background of  -pairs, which don‘t originate from the same  0 decay Signal: Number of entries over combinatorial background (Peak width determined by energy resolution of the detector) Momentum of the  0 Invariant Mass: