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The Phase Diagram of Nuclear Matter Oumarou Njoya

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Outline Motivations for studying QCD phase transitions Introduction to QCD Mapping the phase diagram Experimental considerations Summary

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Motivations The Big bang Theory Neutron stars Discovery of strong force

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Forces and structures in Nature Gravity one “charge” (mass) force decreases with distance m1m1 m2m2 Electromagnetism two “charges” (+ / -) force decreases with distance +- ++ Atom

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Atomic nuclei and the “nuclear” force Nuclei composed of: protons (+ electric charge) neutrons (no electric charge) Do not fly apart!? “nuclear force” overcomes electrical repulsion determines nuclear reactions (stellar burning, bombs…) arises from fundamental strong force (#3) acts on color charge of quarks proton neutron quark

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What is QCD? Quantum chromo-dynamics A theory of the strong (or nuclear, or color) force. Closely modeled on QED but with three conserved color charges: Quarks: r, g, b Anti quarks: anti-red, anti-green, anti-blue. Quarks scatter by exchanging gluons, which carry color and anticolor.

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More QCD Only colour singlet states can exist as free particles. Hadrons are colour singlet. Mesons: Baryons: Confinement (r ~ 1fm) Chiral symmetry Having to do with quark masses Asymptotic freedom (r → 0) Strong interaction becomes weaker at high energy Relativistic hot gas

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Strong color field Energy grows with separation !!! Confinement to study structure of an atom… “white” proton nucleus electron quark quark-antiquark pair created from vacuum “white” proton (confined quarks) “white” 0 (confined quarks) Confinement: fundamental & crucial (but not well understood!) feature of strong force - colored objects (quarks) have energy in normal vacuum… QCD neutral atom

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QCD Thermodynamics Relativistic kinematics of free gas. Partition function: bosons fermions

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A simple model Ideal gas of massless pions. Stefan-Boltzmann

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From hadrons to quarks and gluons Chiral symmetry argument Massless u and d implies chirally symmetric Lagrangian. Spontaneous symmetry breaking in ground state. Symmetry conserved at high T. Expect phase transition. (akin to Curie point in a ferromagnet). Pisarski-Wilzeck: 1 st order transition Tricritical point Evidence suggests 1 st order at high T and low μ B At low T: nuclear matter

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Crossover and critical point Crossover for μ B = 0. (Lattice QCD) Critical point Coexisting phases along 1 st order line, similar to that of liquid in condensed matter physics Low-T high- μ B : ordered quark phases exist

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Locating the critical point Theoretically simple (singularity of partition function). Importance sampling and sign problem. Lattice QCD.

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Lattice QCD Quarks and gluons are studied on a discrete space-time lattice Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams) The lattice provides a natural momentum cut-off Recover the continuum limit by letting a 0 There are two order parameters pure gauge = gluons only

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Order Parameters Deconfinement measure: Palyokov loop Effective quark mass Energy density є at deconfinement

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The phase diagram of QCD Temperature baryon density Neutron stars Early universe nuclei nucleon gas hadron gas quark-gluon plasma TcTc 00 critical point ? vacuum

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Generating a deconfined state Nuclear Matter (confined) Hadronic Matter (confined) Quark Gluon Plasma deconfined ! Present understanding of Quantum Chromodynamics (QCD) heating compression deconfined color matter

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RHIC BRAHMS PHOBOS PHENIX STAR AGS TANDEMS Relativistic Heavy Ion Collider (RHIC) 1 km v = 0.99995 c = 186,000 miles/sec

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A few methods Hadron radiation Electromagnetic radiation Dissipation of a passing quarkonyum beam (fancy for Debye screening in nuclear matter) Energy loss of a passing jet.

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Hadron radiation Formed at the transition surface between hot matter and physical vacuum. At T c local hadronization occurs. Mostly pions, kaons, nucleons and anti-nucleons. Study of relative abundances gives us information about hadronization temperature.

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Electromagnetic radiation Spectra of photons and leptons provide information about the state of the medium at the time they were formed. Consider for illustration μ+μ- formation

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Summary Mapping the QCD phase diagram is important for understanding the early evolution of the universe and the physics of neutron star. QCD thermodynamics suggests a well-defined transition from hadronic matter to a plasma of deconfined quarks and gluons. The nature and the origin of the transition at high needs to be clarified further. The properties of the QGP can be explored through hard probes. Certainly, lots of new physics await discovery.

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Bibliography M. Stephanov, [arXiv:hep-lat/0701002v1] Helmut Satz, [arXiv:0903.2778v1 [hep-ph]] Peter G Jones, Introduction to QCD, rhic.physics.wayne.edu/~bellwied/classes/phy707 0/QCD-lecture.ppt Slides 5,8,17,18 were borrowed from Gang Wang (UCLA).

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Thank you!

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