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Introduction to the physics of the Quark-Gluon Plasma and the relativistic heavy-ion collisions Villa Gualino-Torino, 7-3-2011 Matter under extreme conditions… Fermi Notes on Thermodynamics QGP Eleven Science Questions for the New Century NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES… No. 7 - What Are the New States of Matter at Exceedingly High Density and Temperature? QGP is at T>1012K and r > 1040 cm-3 Let’s start from 100 years ago … 1911 - Rutherford discovered the Nucleus In ’30 started the study of a new force: Nuclear Force between nucleons Bashing nucleons with increasing energy … p p p,n,L,S,D,.. It became clear that nucleons and more generally hadrons are made of quarks exchanging gluons p,r,w,f,K, .. In 1974 the theory of the strong interaction was written down and called Quantum Chromodynamics Quantum Chromodynamics 1 a ψi mi ψi ψi Fa Fa ψi γ i gAa 2 4 a i 1 nf LQCD Fa Aa Aa i f abc Ab Ac electric charge Similar to QED but 3 charges + gauge invariance imply that the gauge field (gluons) self-interact: - Asymptotic freedom - Confinement colour charge Two regimes: - Q>>LQCD one can use perturbative QCD (pQCD) - Q ~LQCD , Q >LQCD non perturbative methods : lattice QCD (lQCD) and effective lagrangian approach Quark-Gluon Plasma Inside nuclei strong interaction manifest in an extremely non-perturbative regime (LQCD~ 1 fm-1) and quarks are not the relevant degrees of freedom Several arguments already in the ’70-’80 lead to think that at some temperature and/or density quarks “can roam freely in a medium”-> QGP 1) ASYMPTOTIC FREEDOM At large T there are interaction q2 ~ (3T)2 and the coupling is weak 2) OVERLAP (percolation) Hadrons Overlap does not allow to identify the hadrons itself: T0 ~ 150 MeV 3) BAG PRESSURE MODELING Pressure of pion gas smaller than the quark gas one: T0 ~ 150 MeV 4) HAGERDON LIMITING TEMPERATURE Hadron gas partition function has a singularity at T0 ~ 160 MeV Hagerdon’s limiting temperature From the Hadronic side increasing temperature leads to the production of higher mass hadronic states, but the density of states grows exponentially with the mass Partition functon for a gas o particle with density of states r(m) m>>T Hagerdon, Nuovo Cimento (1965): T0 is a limiting temperature for hadronic systems Cabibbo-Parisi, PLB59(1975): Divergency of the partition function has to be associated with a phase transition of hadronic matter to quark-gluon matter Quark-antiQuark free energy in lQCD We cannot observe quarks, but at large T we can envisage a weakly interacting gas of quarks and gluons Asymptotic value Charm Quarks String breaking vacuum lQCD Kaczmarek et al., PPS 129,560(2004) Order Parameters of the Phase Transition Polyakov Loop lQCD L Tr e Chiral Condensate T~170 MeV T~170 MeV ig 0 A0 ( x ,t ) d Tre H int qq (250 MeV )3 0 What is the order of the phase transition? [Ratti] The basic relations of reference Ideally our reference is a gas of non-interacting massless quarks and gluons x d.o.f x d.o.f Multiplied by degrees of freedom dq+q=2*2*3*Nf =24-30 , dg=8*2 From lattice QCD SB T 4 p 2 7 d d qq g 30 8 RHIC Enhancement of the degrees of freedom towards the QGP c 0.7 GeV / fm3 Tc 175 15 MeV Stefan-Boltzmann limit not reached by 20 % for : QGP as a weak interacting gas?! B=0 In Ads/CFT this can be a very strong Interaction measure interacting system [Cotrone] LHC No interaction means also =3p (for a massless gas) QGP in the Early Universe Evolution • 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~ 10-5s) • Quark and gluons Bang Degrees of freedom in the Universe T4 g(T) g (T ) g (T ) 2 4e 4 3 3p ... 16 g 31.5uds 21cb ... D.J.Schwartz, Ann. Phys. 2004 Quark-Gluon Plasma How to produce a matter with >>1 GeV/fm3 lasting for > 1 fm/c in a volume much larger than an hadron? Let’s bash again at higher energy… High Energy Heavy Ion Collision Facilities Accelerator Lab. Ebeam [AGeV] s AGeV Contrac tion AGS (’80s) BNL 10 (*) 4.5 2 SPS (94-…) CERN 160(*) 17.3 9 RHIC (00-…) BNL 100 +100 200 100 LHC (09-…) CERN 2750+2750 5500 Fixed target sNN 2 mEbeam Collider sNN 2 Ebeam 2 s NN ( p A pB ) 2 ECMS γ CM E s m m 2750 Max energy density complete stopping 3 s N part 3sN part E max CM 3 VA 4p R 4p mR3 RHIC -> max~ 102 GeV/fm3 LHC -> emax~ 3 103 GeV/fm3 LHC Exploring the phase diagram RHIC RHIC SPS nuclei new medium created from the energy deposited B=0 (quark=antiquarks) Hotter-denser-longer increasing Ebeam Increasing beam energy -> transparency Energy distributed in a larger volume How to make simple estimates? Time – 5-15 fm/c = 15-45ys~10-22s Statistical Model analysis Temperature Chemical Potential T Yield Mass Quantum Numbers F. Becattini Hagerdon limiting temperature AGS (BNL) SPS(CERN) RHIC (BNL) Energy Density and Temperature Estimate I | Dy | 0.5 Particle streaming from origin z v z tanh yz t dz cosh y dy Energy density a la Bjorken: DE E DN m T DN 1 dET ε0 2 DV A T Dz πR τ 0 Dy pR 2 0 dy theory estimate experiments RHIC ~0.6-1 fm/c dET/dy ~ 720 GeV We can estimate the initial 0 RHIC ~ 5 8 GeV/fm3 Is this correct? Energy Density and Temperature Estimate II Entropy Conservation S sV cost s0 0 s T03 0 T 1D expansion T0 T 3 0 0 4/3 0 But this means that the previous estimate cannot be correct because it supposes that ~ 1, but to conserve entropy ~ 4/3 1 dET f ε 2 pR 0 dy 0 1/ 4 30 T0 2 0 p g 1/ 3 Bjorken 2 10 15 GeV fm3 8 12 10 1/ 4 fm1 1.7 fm1 335MeV Estimate of QGP lifetime (0~0.6 fm/c at RHIC) T0 RHIC - T=2Tc > QGP=0.6*23 =5 fm/c 0 Tc LHC - T=3.5 Tc > QGP=0.4*3.53 =15 fm/c 3 QGP So with uRHIC 0>>c QGP>1fm/c V> 103 fm3 Different stages of the Little Bang System expands and cools down 2 Freeze-out ~20 fm/c Hadron Gas t 2 z 2 1/ 2 cost Phase Transition ~5 fm/c Plasma-phase ~0.6 fm/c Pre-Equilibrium <0.2 fm/c Soft and Hard probes SOFT (pT ~LQCD,T) driven by non perturbative QCD Hadron yields, collective modes of the bulk, strangeness enhancement, fluctuations, thermal radiation, dilepton enhancement HARD (pT >> LQCD) Early production, pQCD applicable, comparable with pp, pA jet quenching, heavy quarks, quarkonia, hard photons 95% of particles The Several Probes [Romatschke], [Snellings],[Beraudo] Initial Conditions Quark-Gluon Plasma Hadronization BULK (pT~T) CGC (x<<1) Gluon saturation [Albacete] MINIJETS (pT>>T,LQCD) [Bruna] Heavy Quarks (mq>>T,LQCD) [Arnaldi] Microscopic Mechanism Matters! [Becattini] [Blume] Initial Condition – “exotic” non equilibrium CGC Bulk – Hydrodynamics BUT finite viscosities (h,z) Minijets – perturbative QCD BUT strong Jet-Bulk “talk” Heavy Quarks – Brownian motion (?) BUT strongly dragged by the Bulk Quarkonia – Are suppressed (only resonances?) or regenerated Hadronization – Microscopic mechanism can modify QGP observables RHIC LHC Dominance of QGP phase (QGP> 10 fm/c) Vanishing hadronic contamination? A new QGP phase: perturbative plasma? Larger h/s we get close to the pQCD estimates? Hopefully with several other surprises… Very large yield of heavy quarkthe (m >>T ) and jets (p >>T) Enjoy School! Increasing relevance of non-equilibrated “objects”! q T Existence of a primordial non-equilibrium phase Color Glass Condensate (CGC) as high-energy limit of QCD? Collective Expansion of the Bulk v2/ measures efficiency in converting the eccentricity from Coordinate to Momentum space z y x x y2 x2 y x 2 2 c2 s=dP/d EoS v2 p x2 p y2 p x2 p y2 The fluid with lowest ever observed h/s Viscosity h/s For the first time close to ideal Hydrodynamics h/s viscosity QGP Transverse Density [fm-2] Color Glass Condensate initial conditions? dN/d2pT Parton distr. funct Ideal Sketch Qsat(s) At small x (pT) dense gluon matter Gluons of small x (pT) -> larger size >1/Qs overlap and the gluon dostribution stops growing pT y x e s pT At RHIC Q2 ~ 2 GeV2 At LHC Q2 ~ ? 2 What is the impact xg ( x , Q ) 2 2 1/ 3 Qsat ( s) s (Q ) A 2 of a different intial condition? pR Jet Quenching y x Suppression of minijets Jet triggered angular correl. near Suppression should increase with density and temperature. Allows a further measure of energy density. It is due to gluon radiation? Jet energy loss produce mach cones? Medium away Heavy Quarks dragged by the medium? - mc,b >> LQCD produced by pQCD processes (out of equil.) - 0 << QGP they go through all the QGP lifetime -mc,b >> T0 no thermal production A better test of pQCD scattering and energy loss: - mQ>>mq small drag from the bulk Indirect measurement from semileptonic decay (D->Ke) came as a surprise: Strong suppression Large elliptic Flow Quarkonia Suppression? QQ Quarkonium dissoved by charge screening: Thermometer V eff e mD r r rQQ 1 1 mD gT cc, J/Y, cb, Y, … More binding smaller radius higher temperature Suppression at SPS! More suppression at RHIC because of high the higher temperature?! and even more at LHC? Hadronization Modified Baryon/Mesons Quark number scaling Meson p+p PHENIX, PRL89(2003) Use medium and not vacuum -> Quark coalescence More easy to produce baryons! v 2,M (p1T ) 2v pT 2,q (p T /2) V2 v 2,B (pnT ) 3v n 2,q (p T /3) dN M f a (ra , pa ) f b (rb , pb ) M rab , qab d 3 P a ,b Hadronization is modified Dynamical quarks are visible Fries-Greco-Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008) Hadronization Modified Baryon/Mesons Quark number scaling p+p v2q fitted from v2p GKL PHENIX, PRL89(2003) dN q pT dpT dφ dN q pT dpT 1 2v 2 cos(2 ) dN q dN H ( pT ) 2 ( pT n) 2 d pT d pT n Coalescence scaling Enhancement of v2 v 2,M (p T1) 2v p2,Tq (p T /2) V2 v 2,B (p Tn) 3v n2,q (p T /3) Dynamical quarks are visible Collective flows