The Phase Diagram of Nuclear Matter Oumarou Njoya

1. The Phase Diagram of Nuclear MatterOumarou Njoya

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

3. Motivations • The Big bang Theory • Neutron stars • Discovery of strong force

4. Forces and structures in Nature Gravity one “charge” (mass)‏ force decreases with distance m1 m2 Electromagnetism two “charges” (+ / -)‏ force decreases with distance Atom + - + +

5. quark 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 neutron proton

6. 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.

7. 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

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

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

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

11. 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: 1st order transition • Tricritical point • Evidence suggests 1st order at high T and low μB • At low T: nuclear matter

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

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

14. Lattice QCD • There are two order parameters • 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 pure gauge = gluons only

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

16. The phase diagram of QCD Early universe quark-gluon plasma critical point ? Tc Temperature hadron gas nucleon gas nuclei 0 Neutron stars vacuum baryon density

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

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

19. 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.

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

21. 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

22. 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.

23. 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/phy7070/QCD-lecture.ppt • Slides 5,8,17,18 were borrowed from Gang Wang (UCLA).

24. Thank you!