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Search for the Quark-Gluon Plasma in Heavy Ion Collision V. Greco Outline Introduction: definitons & concepts - Quark-Gluon Plasma (QGP) - Heavy-Ion-Collisions (HIC) Theory and Experiments - probes of QGP in HIC - what we have found till now! Introduction I Goals of the Ultra-RHIC program: Production of high energy density matter better understanding of the origin of the masses of ordinary nuclei Produce matter where confinement -> deconf QGP and hadronization Structure of the nucleon how quantum numbers arise (charge spin, baryon number) Big Bang • e. m. decouple (T~ 1eV , t ~ 3.105 ys) “thermal freeze-out “ • but matter opaque to e.m. radiation • Atomic nuclei (T~100 KeV, t ~200s) “chemical freeze-out” • Hadronization (T~ 0.2 GeV, t~ 10-2s) • Quark and gluons We’ll never see what happened t < 3 .105 ys (hidden behind the curtain of the cosmic microwave background) Bang HIC can do it! Little Bang From high rB regime to high T regime AGS SPS RHIC 2 sNN ( pA pB )2 ECMS We do not observe hadronic systems with T> 170 MeV (Hagerdon prediction) Different stages of the Little Bang N D N “Elastic” finite Dt Freeze-out Hadron Gas Phase Transition Plasma-phase Pre-Equilibrium Euristic QGP phase transition Free massless gas E g 3 4 gtot g g 78 ( g q g q ) d p p f ( p) gtot T 3 0 V (2 ) 30 g g 16 , g q gq Nc N s N f Bag Model (cosm. cost.) EH C PH B V 4R 4 P 0 RH Pressure exceeds the Bag pressure -> quark liberation 37 2 904 1/ 4 B1/4 ~ 210 MeV Tc T 2 B B > Tc~ 145 MeV 90 37 1/ 4 Extension to finite mB , mI Phase Transition Def. Phase transition of order n-th means the n-th derivative of the free energy F is discontinous F T FT I order Mixed phase V F CV 2 T 2 II order Critical behavior Cross over Not a mixed phase, but a continous modification of the matter between the two phases Quantum ChromoDynamics 1 m m a ψi γ m i gAa ψi mi ψi ψi Fam Fam 2 4 a i 1 nf Fa Aa Aa i f abc Ab Ac m m m m m Similar to QED, but much richer structure: SU(3) gauge symmetry in color space Confinement Approximate Chiral Symmetry in the light sector broken in the vacuum. Chiral Symmetry Restoration UA(1) ciral Scale Invariance broken by quantum effects Chiral Symmetry SU C (3) SU A (3) SU V (3) UV (1) U A (1) L,R (1 5 ) L , R e i Lj ,R j L , R QCD is nearly invariant under rotation among u,d,s associate Axial and Vector currents are conserved qq (250 MeV )3 Eight goldstone Bosons (,K,h) Absence of parity doublets Mass (MeV) Constituent quark masses > explicit breaking of chiral simmetry a1 (1260) f1 (1285) s (4001200) r (770) (140) w (782) P-S V-A splitting In the physical vacuum Lattice QCD QCD can be solved in a discretized space ! Z D Ama ( x)D ( x) D ( x) e i d d 3 x L A , , 0 i d 4 x L A, , to evaluate ZLattice D Am ( xthe)Dalgorithm ( x) D ( x) eZ in the QCDais Space-time -> static at finite temperature iHt ie 1 / TeH Dynamics -> Statistics time dim. regulate the temperature ψ(n) U (n, n mˆ ) exp (ig t a Ama (n)) Gluon field Continuum limit 1 1 1 4 2 2 m a 0 S 2 Tr U m (n) 2 Tr expia g Fm (n) d x F F m p p closed 2g 2g 4 p It is less trivial than it seems, Ex.: fermion action, determinant Lattice QCD Prospectives Quark –gluon plasma properties (vs density and temperature) Hadron properties (mass, spin, ) vacuum QCD structure (istantons ..) CKM matrix elements (f,fk,fc,fB) CPU time is very large quark loops is very time consuming (mq=∞ > no quark loops = “quenched approximation”) lattice spacing a > 0 baryon chemical potential Limitations No real time processes Scattering Non equilibrium Physical understanding Effective models are always necessary !!! ( Polyakov Loop ig 0 A0 ( x ,t ) d L Tr e ) Tr(e a 3 a a a H int d y J m ( y) Am ( y) ig A0 ( x ) 2 J m ( y) ig a a 2 H int ) -static quark -only gluon dynamics ( y x )(1,0,0,0) L 0 H int confinement If quark mass is not infinite and quark loops are present L is not really an order parameter ! Lattice QCD Polyakov Loop Chiral Condensate • Coincident transitions: deconfinement and chiral symmetry restoration it is seen to hold also vs quark mass Phase Transition to Quark-Gluon Plasma Enhancement of the degrees of freedom towards the QGP 0.7 GeV / fm 3 Tc 173 15 MeV Quantum-massless non interacting qq 2 7 4 g 6n f 16 T 30 4 Gap in the energy density (I0 order or cross over ?) Definitions and concepts in HIC Kinematics Observables Language of experimentalist The RHIC Experiments Au+Au STAR Soft and Hard SOFT (npQCD) string fragmentation in e+e , pp … or (pT<2 GeV) string melting in AA (AMPT, HIJING, NEXUS…) QGP HARD minijets from first NN collisions Indipendent Fragmentation : pQCD + phenomenology • Small momentum transfer • Bulk particle production – How ? How many ? How are distributed? • Only phenomenological descriptions available (pQCD doesn’t work) 99% of particles Collision Geometry - “Centrality” Spectators Participants S. Modiuswescki 15 fm 0 b N_part For a given b, Glauber model 0 fm predicts N part 394 and Nbinary Kinematical observables 1 E pz Additive like Galilean velocity y z ln 2 E pz y j / CM y j / LAB yLAB / CM Transverse mass 1/ 2 mT (m 2 pT2 ) E mT cosh y , pz mT sinh y z Angle respect z beam axis 1 | p | pz h ln tan( / 2) ln 2 | p | pz Rapidity -pseudorapidity dN m2 dN 1 2 2 dhdpT mT cosh y dydpT Energy Density | Dy | 0.5 Energy density a la Bjorken: dET 1 dET ε A T dz πR 2 τ dy Particle streaming from origin z v z tanh yz t dz cosh y dy R 1.18 A 7 fm τSPS 1 fm/c Estimate for RHIC: dET/dy ~ 720 GeV Time estimate from hydro: 0.6 fm/c ~ 8 GeV/fm 3 1/3 τ RHIC 0.4 1 fm/c Tinitial ~ 300-350 MeV Collective Flow I: Radial Observable in the spectra, that have a slope due to temperature folded with Radial flow expansion <T> due to the pressure. Absence 1 Non Relativist ic p T m , Tsl Tf m v T 2 1 vT Ultra Relativist ic p T >> m, Tsl Tf 1 vT Slope for hadrons with different masses allow to separate thermal from collective flow Tf ~ (120 ± 10) MeV <T> ~ (0.5 ± 0.05) 2 Collective flow II: Elliptic Flow Perform a Fourier decomposition of the momentum space particle distributions in the x-y plane dN dN 1 2 v n cos(n ) dpT d dpT n z y x Anisotropic Flow Measure of the Pressure gradient Good probe of early pressure v2 is the 2nd harmonic Fourier coeff. of the distribution of particles. px2 p y2 v2 cos2 2 px p y2 Statistical Model Temperature Yield Maximum entropy principle Mass Chemical Potential Quantum Numbers There is a dynamical evolution that Leads to such values of Temp. & abundances? Hydro add radial flow, freeze-out hypersurface for describing the differential spectrum Yes, but what is Hydro? Maximum Entropy Principle d 3 pd 3 x f ln f (1 f ) ln(1 f ) S 3 k DV (2 ) E > dw Ei fi i B > dw Bi fi All processes costrained by the conservation laws i S > dw si fi i Maximizing S with this constraints the solution is the statistical thermal equilibrium The apparent “equilibrium” is not achieved kinetically but statistically ! HYDRODYNAMICS Local conservation Laws 5 partial diff. eq. for 6 fields (p,e,n,u) + Equation of State p(e,nB) m mT ( x) 0 T m ( x) e( x) p( x)u m ( x)u ( x) p( x) g m m m jB ( x) 0 jBm ( x) nB ( x)u m ( x) No details about collision dynamics (mean free path >0) Another level of Knoweledge Follow distribution function time evolution: Initial non-equilibrium gluon phase > final chemical and thermal equlibrated system How hydrodynamical behavior is reached Relevance of npQCD cross section Description of the QCD field dynamics Transport Theory f q , g (r , p, t ) Follow distribution function time evolution From the initial non-equilibrium gluon phase f p r f rU p f I coll Non-relativistically t m drifting mean field collision 2 2 m 2 2 f f )W 23 4 (1p 2 p p Relativistically Ipcoll ( f f 1 2I 1234 f I3 4 I 1 2... 3 p4 ) m 1 2 3 coll coll coll gg>ggg g>gg To be treated: - Multiparticle collision (elastic and inelastic) - Quantum transport theory (off-shell effect, … ) - Mean field or condensate dynamics at High density Transport Spectra still appear thermal Hydro Elliptic Flow rapidity rapidity • Chemical equilibrium with a limiting Tc ~170MeV • Thermal equilibrium with collective behavior - Tth ~120 MeV and <T>~ 0.5 • Early thermalization ( < 1fm/c, ~ 10 GeV) - very large v2 We have not just crashed 400 balls to get fireworks, but we have created a transient state of plasma A deeper and dynamical knowledge of the system is still pending! Outline II Probes of QGP in HIC What we have find till now! strangeness enhancement jet quenching coalescence J/ suppression What we have learned ? Glauber model N Binary Collisions Participants b (fm)