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You can find this page at nuclear.ucdavis/~cebra/classes/phys224/phys224c.html

You can find this page at http://nuclear.ucdavis.edu/~cebra/classes/phys224/phys224c.html QUARTER: Fall 2008 LECTURES: 432 Phys/Geo, TR 2:10 to 3:30 INSTRUCTOR: Daniel Cebra, 539 P/G, 752-4592, cebra@physics.ucdavis.edu GRADERS: none TEXT: No required text. The following could be useful:

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You can find this page at nuclear.ucdavis/~cebra/classes/phys224/phys224c.html

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  1. You can find this page at http://nuclear.ucdavis.edu/~cebra/classes/phys224/phys224c.html QUARTER: Fall 2008LECTURES: 432 Phys/Geo, TR 2:10 to 3:30 INSTRUCTOR: Daniel Cebra, 539 P/G, 752-4592, cebra@physics.ucdavis.edu GRADERS: none TEXT:No required text. The following could be useful: R.L Vogt Ultrarelativistic Heavy Ion Collisions C.Y. Wong Introduction to High-Energy Heavy-Ion CollisionsL.P. Csernai Introduction to Relativistic Heavy Ion CollisionsJ. Letessier and J. Rafelski Hadrons and Quark-Gluon Plasma HOMEWORK: There will be presentations assigned through the quarter.EXAM:There will be no exams for this courseGRADE DETERMINATION:Grade will be determined presentations and class participationOFFICE HOURS:Cebra (any time) Course Overview: The class will be taught as a seminar class. We will alternate between lectures to overview the concepts with readings and discussions of critical papers in the field. There will be no homework assignments, no exams. Students are read the discussion papers ahead and to come prepared for presentations.

  2. Course Outline • Overview and Historical Perspective • Hagedorn Bootstrap Model • Bjorken energy density • Basic Kinematics • Quantum Chromodynamics • Asymptotic freedom • Confinement • Chirality • Drell-yan • Initial Conditions and First Collisions • Glauber Model --- pre-collision and initial geometry (impact parameter) • Color-Glass Condensate • Parton Cascade --- • Quark-Gluon Plasma Formation and Evolution • Lattice QCD • Hydrodynamics • Elliptic flow • Probes of the Dense Partonic Phase • J/y Suppression and open charm • Upsilon • Jets • Direct Photons • Di-Leptons • Hadronization • Recombination vs. Fragmentation • Chemical Equilibrium, Chemical freeze-out • Strangeness enhancement • Thermal Freeze-out • Pion production/Entropy • Radial Flow • HBT • Implications • Big Bang Cosmology • BBN • Supernovae • Neutron, Strange, and Quark Stars

  3. Broad Historic Developments 1896 Discovery of Radioactivity (Becquerel) 1911 Nuclear Atom (Rutherford) 1932 Discovery of the neutron (Chadwick) 1935 Meson Hypothesis (Yukawa) 1939 Liquid-Drop model of nucear fission (Bohr and Wheeler) 1947 Discovery of the pion (Powell) 1949 Nuclear Shell Model (Mayer and Jensen) 1953 Strangeness Hypothesis (Gell-Mann and Nishjima) 1953 First production of strange particles (Brookhaven) 1955 Discovery of the anti-proton (Chamberlain and Segre) 1964 Quark model of hadrons (Gell-Mann and Zweig) 1967 Electroweak model proposed (Weinberg and Salam) 1970 Charm hypothesis (Glashow) 1974 Discovery of the J/y (Ricther, Ting) 1977 U Discovered and bottom inferred (Lederman) 1980 First Quark Matter meeting (Darmstadt, Germany) 1983 W and Z discovered (Rubbia) 1983 Isabelle cancelled 1984 RHIC Proposal 1986 Heavy-ion operations at the AGS and SPS 1992 Au beams at the AGS and Pb beams at the SPS 1995 Top quark observed (Fermilab) 2000 Au+Au operations at RHIC 2009? Pb+Pb operations at the LHC Physics 224C – Lecture 1 -- Cebra

  4. A brief history of relativistic heavy-ion facilities LBNL – Bevalac (1980 – 1992) [Au 0.1 to 1.15 AGeV] EOS --- TPC: DLS --- DiLepton spectrometer GSI – SIS () [] TAPS: KaoS: FoPi BNL – AGS (1986-1995) [Si, 1994 Au 10 AGeV, 8, 6, 4, 2] E802/866/917; E810/891; E877; E878; E864; E895; E896 CERN – SPS (1986-present) [O 60, 200 AGeV (1986-87); S 200 AGeV (1987-1992): Pb 158, 80, 40, 30, 20 AGeV (1994-2000), In] HELIOS(NA34); NA35/NA49/NA61(Shine); NA36; NA38/NA50/NA60; NA44; CERES(NA45); NA52 WA85/WA94/WA97/NA57; WA80/WA9898 BNL – RHIC (2000-present) [Au+Au 130, 200, 62.4, 19.6, d+Au 200, Cu+Cu 200, 62.4, 22, p+p 200, 450] STAR PHENIX Phobos BRAHMS pp2pp CERN – LHC (2009?)[Pb+Pb] ALICE CMS ATLAS Physics 224C – Lecture 1 -- Cebra

  5. Quark-Gluon Plasma Physics 224C – Lecture 1 -- Cebra

  6. Motivation for Relativistic Heavy Ion Collisions Two big connections: cosmology and QCD

  7. The phase diagram of QCD Early universe quark-gluon plasma critical point ? Tc Temperature colour superconductor hadron gas nucleon gas nuclei CFL r0 Neutron stars vacuum baryon density

  8. Evolution of Forces in Nature

  9. Going back in time… Age Energy Matter in universe 0 1019 GeV grand unified theory of all forces 10-35 s 1014 GeV 1st phase transition (strong: q,g + electroweak: g, l,n) 10-10s 102 GeV2nd phase transition (strong: q,g + electro: g + weak: l,n) 10-5 s 0.2 GeV 3rd phase transition (strong:hadrons + electro:g + weak: l,n) 3 min. 0.1 MeV nuclei 6*105 years 0.3 eV atoms Now (1.5*109 years) 3*10-4 eV = 3 K RHIC, LHC & FAIR RIA & FAIR

  10. Connection to Cosmology • Baryogenesis ? • Dark Matter Formation ? • Is matter generation in cosmic medium (plasma) different than matter generation in vacuum ?

  11. Sakharov (1967) – three conditions for baryogenesis Baryon number violation C- and CP-symmetry violation Interactions out of thermal equilibrium Currently, there is no experimental evidence of particle interactions where the conservation of baryon number is broken: all observed particle reactions have equal baryon number before and after. Mathematically, the commutator of the baryon number quantum operator with the Standard Model hamiltonian is zero: [B,H] = BH - HB = 0. This suggests physics beyond the Standard Model The second condition — violation of CP-symmetry — was discovered in 1964 (direct CP-violation, that is violation of CP-symmetry in a decay process, was discovered later, in 1999). If CPT-symmetry is assumed, violation of CP-symmetry demands violation of time inversion symmetry, or T-symmetry. The last condition states that the rate of a reaction which generates baryon-asymmetry must be less than the rate of expansion of the universe. In this situation the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation.

  12. Dark Matter in RHI collisions ? Possibly (not like dark energy) The basic parameters: mass, charge

  13. Basic Thermodynamics Hot Sudden expansion, fluid fills empty space without loss of energy. dE = 0 PdV > 0 thereforedS > 0 Hot Hot Gradual expansion (equilibrium maintained), fluid loses energy through PdV work. dE = -PdV thereforedS = 0 Hot Isentropic Adiabatic Cool

  14. Nuclear Equation of State

  15. Nuclear Equation of State

  16. Golden Rule 2: All entropy is in relativistic species Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out) Golden Rule 1: Entropy per co-moving volume is conserved Golden Rule 3: All chemical potentials are negligible Golden Rule 4:

  17. 1 Billion oK 1 Trillion oK g*S Start with light particles, no strong nuclear force

  18. 1 Billion oK 1 Trillion oK g*S Previous Plot Now add hadrons = feel strong nuclear force

  19. 1 Billion oK 1 Trillion oK g*S Previous Plots Keep adding more hadrons….

  20. How many hadrons? Density of hadron mass states dN/dM increases exponentially with mass. Broniowski, et.al. 2004 TH ~ 21012oK Prior to the 1970’s this was explained in several ways theoretically Statistical Bootstrap Hadrons made of hadrons made of hadrons… Regge TrajectoriesStretchy rotators, first string theory

  21. Rolf Hagedorn German Hadron bootstrap model and limiting temperature (1965) Hagedorn Limiting Temperature Ordinary statistical mechanics For thermal hadron gas (somewhat crudely): Energy diverges as T --> TH Maximum achievable temperature? “…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977)

  22. What do I mean “Bjorken”? Boost-invariant Increasing E y y dN/dy’ “Inside-out” & 1 dimensional 0 y’=y-ybeam

  23. Impact of “Bjorken” X X dN/dy distribution is flat over a large region except “near the target”. v2 is independent of y over a large region except “near the target”. (2d-hydro.) pT(y) described by 1d or 2d-hydro. Usual HBT interpretation starts from a boost-invariant source. T(t) described by 1d-hydro. Simple energy density formula

  24. Notations We’ll be using the following notations: proper time and rapidity

  25. Most General Boost Invariant Energy-Momentum Tensor The most general boost-invariant energy-momentum tensor for a high energy collision of two very large nuclei is (at x3 =0) which, due to gives There are 3 extreme limits.

  26. Limit I: “Free Streaming” Free streaming is characterized by the following “2d” energy-momentum tensor: such that and • The total energy E~ e t is conserved, as expected for • non-interacting particles.

  27. Limit II: Bjorken Hydrodynamics In the case of ideal hydrodynamics, the energy-momentum tensor is symmetric in all three spatial directions (isotropization): such that Using the ideal gas equation of state, , yields Bjorken, ‘83 • The total energy E~ e t is not conserved, while the total entropy S is conserved.

  28. If then, as , one gets . Most General Boost Invariant Energy-Momentum Tensor Deviations from the scaling of energy density, like are due to longitudinal pressure , which does work in the longitudinal direction modifying the energy density scaling with tau. • Non-zero positive longitudinal pressure and isotropization ↔ deviations from

  29. Limit III: Color Glass at Early Times In CGC at very early times (Lappi, ’06) we get, at the leading log level, such that, since Energy-momentum tensor is

  30. D. Gross QCD to the rescue! H.D. Politzer F. Wilczek Replace Hadrons (messy and numerous) by Quarks and Gluons (simple and few) American QCD Asymptotic Freedom (1973) e/T4  g*S Thermal QCD ”QGP”(Lattice) “In 1972 the early universe seemed hopelessly opaque…conditions of ultrahigh temperatures…produce a theoretically intractable mess. But asymptotic freedom renders ultrahigh temperatures friendly…” Frank Wilczek, Nobel Lecture (RMP 05) Hadron gas Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556,2003

  31. Nobel prize for Physics 2005 “Before [QCD] we could not go back further than 200,000 years after the Big Bang. Today…since QCD simplifies at high energy, we can extrapolate to very early times when nucleons melted…to form a quark-gluon plasma.” David Gross, Nobel Lecture (RMP 05) g*S Thermal QCD -- i.e. quarks and gluons -- makes the very early universe tractable; but where is the experimental proof? n Decoupling Nucleosynthesis e+e- Annihilation Heavy quarks and bosons freeze out QCD Transition Mesons freeze out Kolb & Turner, “The Early Universe”

  32. The main features of Quantum Chromodynamics • Confinement • At large distances the effective coupling between quarks is large, resulting in confinement. • Free quarks are not observed in nature. • Asymptotic freedom • At short distances the effective coupling between quarks decreases logarithmically. • Under such conditions quarks and gluons appear to be quasi-free. • (Hidden) chiral symmetry • Connected with the quark masses • When confined quarks have a large dynamical mass - constituent mass • In the small coupling limit (some) quarks have small mass - current mass

  33. Quarks and Gluons

  34. Basic Building Blocks ala Halzen and Martin

  35. Quark properties ala Wong

  36. What do we know about quark masses ? Why are quark current masses so different ? Can there be stable (dark) matter based on heavy quarks ?

  37. Elementary Particle Generations

  38. Some particle properties

  39. Elemenary particles summary

  40. Comparing QCD with QED (Halzen & Martin)

  41. Quark and Gluon Field Theory == QCD (I)

  42. Quark and Gluon Field Theory == QCD (II)

  43. Quark and Gluon Field Theory == QCD (III) • Boson mediating the q-qbar interaction is the gluon. • Why 8 and not 9 combinations ? (analogy to flavor octet of mesons) • R-Bbar, R-Gbar, B-Gbar, B-Rbar, G-Rbar, G-BBar • 1/sqrt(2) (R-Rbar - B-Bbar) • 1/sqrt(6) (R-Rbar + B-Bbar – 2G-Gbar) • Not: 1/sqrt(3) (R-Rbar + G-Gbar + B-Bbar) (not net color)

  44. Hadrons

  45. QCD – a non-Abelian Gauge Theory

  46. Particle Classifications

  47. Quarks

  48. Theoretical and computational (lattice) QCD In vacuum: - asymptotically free quarks have current mass - confined quarks have constituent mass - baryonic mass is sum of valence quark constituent masses Masses can be computed as a function of the evolving coupling Strength or the ‘level of asymptotic freedom’, i.e. dynamic masses. But the universe was not a vacuum at the time of hadronization, it was likely a plasma of quarks and gluons. Is the mass generation mechanism the same ?

  49. Confinement Represented by Bag Model

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