Modern Nuclear Physics with RHIC: Recreating the Creation of the Universe Rene Bellwied Wayne State University Lecture 1: Why and How ? Lecture 1: Why and How ? Lecture 2: Bulk plasma matter ? Lecture 2: Bulk plasma matter ? (soft particle production) Lecture 3: Probing the plasma Lecture 3: Probing the plasma (via hard probes)

What is our mission ? Discover the QGP Find transition behavior between an excited hadronic gas and another phase Characterize the states of matter Do we have a hot dense partonic phase and how long does it live ? Characterize medium in terms of density, temperature and time Is the medium equilibrated (thermal, chemical)

The idea of two phase transitionsDeconfinement The quarks and gluons deconfine because energy or parton density gets too high (best visualized in the bag model). Chiral symmetry restoration Massive hadrons in the hadron gas are massless partons in the plasma. Mass breaks chiral symmetry, therefore it has to be restored in the plasma What is the mechanism of hadronization ? How do hadrons obtain their mass ? (link to LHC and HERA physics)

What do we measure in a collider experiment ? particles come from the vertex. They have to traverse certain detectors but should not change their properties when traversing the inner detectors particles come from the vertex. They have to traverse certain detectors but should not change their properties when traversing the inner detectors DETECT but don’t DEFLECT !!! DETECT but don’t DEFLECT !!! inner detectors have to be very thin (low radiation length): easy with gas (TPC), challenge with solid state materials (Silicon). inner detectors have to be very thin (low radiation length): easy with gas (TPC), challenge with solid state materials (Silicon). Measurements: - momentum and charge via high resolution tracking in SVT and TPC in magnetic field (and FTPC) - PID via dE/dx in SVT and TPC and time of flight in TOFand Cerenkov light in RICH - PID of decay particles via impactparameter from SVT and TPC Measurements: - momentum and charge via high resolution tracking in SVT and TPC in magnetic field (and FTPC) - PID via dE/dx in SVT and TPC and time of flight in TOFand Cerenkov light in RICH - PID of decay particles via impactparameter from SVT and TPC particles should stop in the outermost detector particles should stop in the outermost detector Outer detector has to be thick and of high radiation length (e.g. Pb/Scint calorimeter) Outer detector has to be thick and of high radiation length (e.g. Pb/Scint calorimeter) Measurements:- deposited energy for event and specific particles - e/h separation via shower profile - photon via shower profile Measurements:- deposited energy for event and specific particles - e/h separation via shower profile - photon via shower profile

What do we have to check ? If there was a transition to a different phase, then this phase could only last very shortly. The only evidence we have to check is the collision debris. If there was a transition to a different phase, then this phase could only last very shortly. The only evidence we have to check is the collision debris. Check the make-up of the debris: Check the make-up of the debris:  which particles have been formed ?  how many of them ?  are they emitted statistically (Boltzmann distribution) ?  what are their kinematics (speed, momentum, angular distributions) ?  are they correlated in coordinate or momentum space ?  do they move collectively ?  do some of them ‘melt’ ?

Signatures of the QGP phase Phase transitions are signaled thermodynamically by a ‘step function’ when plotting temperature vs. entropy (i.e. # of degrees of freedom). The temperature (or energy) is used to increase the number of degrees of freedom rather than heat the existing form of matter. In the simplest approximation the number of degrees of freedom should scale with the particle multiplicity. At the step some signatures drop and some signatures rise Phase transitions are signaled thermodynamically by a ‘step function’ when plotting temperature vs. entropy (i.e. # of degrees of freedom). The temperature (or energy) is used to increase the number of degrees of freedom rather than heat the existing form of matter. In the simplest approximation the number of degrees of freedom should scale with the particle multiplicity. At the step some signatures drop and some signatures rise For more detail see for example: J. Harris and B. Müller, Annu, Rev. Nucl. Part. Sci : (

Evidence: Some particles are suppressed If the phase is very dense (QGP) than certain particles get absorbed If the phase is very dense (QGP) than certain particles get absorbed ? If things are produced in pairs then one might make it out and the other one not. Central Au + Au Peripheral Au + Au STAR Preliminary If things require the fusion of very heavy rare quarks they might be suppressed in a dense medium

Evidence: Some particles are enhanced Remember dark matter ? Well, we didn’t find clumps of it yet, but we found increased production of strange quark particles Remember dark matter ? Well, we didn’t find clumps of it yet, but we found increased production of strange quark particles

How do we know what happened ? We have to compare to a system that did definitely not go through a phase transition (a reference collision) We have to compare to a system that did definitely not go through a phase transition (a reference collision) Two options: Two options:  A proton-proton collision compared to a Gold- Gold collision does not generate a big enough volume to generate a plasma phase  A peripheral Gold-Gold collision compared to a central one does not generate enough energy and volume to generate a plasma phase

Kinematic variables of choice Rapidity y = ln (E+p z /E-p z ) = lorentz invariant ‘velocity’ Transverse momentum p t = sqrt (p x 2 +p y 2 ) y = y=-1y=1 y=2.2 y=3.7

0.) Global observables A.) particle production B.) particle spectra C.) particle flow D.) particle correlations

Lattice QCD Quarks and gluons are studied on a discrete space-time lattice 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) Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams) There are two order parameters There are two order parameters (F. Karsch, hep-lat/ )  /T 4 T/T c Lattice Results T c (N f =2)=173  8 MeV T c (N f =3)=154  8 MeV GeV/fm 3 75 T = MeV  ~ GeV/fm 3

R2R2 Assessing the Initial Energy Density: Calorimetry Central Au+Au (Pb+Pb) Collisions: 17 GeV:  BJ  3.2 GeV/fm 3  GeV  BJ  4.6 GeV/fm GeV:  BJ  5.0 GeV/fm 3 Bjorken-Formula for Energy Density: PRD 27, 140 (1983) – watch out for typo (factor 2) Time it takes to thermalize system (  0 ~ 1 fm/c) ~6.5 fm Note:   (RHIC) <   (SPS) commonly use 1 fm/c in both cases

Assessing the Initial Energy Density: Tracking Bjorken-Formula for Energy Density: Gives interestingly always slightly smaller values than with calorimetry (~15% in NA49 and STAR).

The Problem with  BJ   BJ is not necessarily a “thermalized” energy density  no direct relation to lattice value  requires boost invariance    is not well defined and model dependent  usually 1fm/c taken for SPS  0.2 – 0.6 fm/c at RHIC ?  system performs work p·dV   real >  BJ  from simple thermodynamic assumptions  roughly factor 2  roughly factor 2 Lattice  c   Bj  ~ 4.6 GeV/fm 3  Bj  ~ 23.0 GeV/fm 3

Boost invariance based on rapidity distributions

So what is  now ? At RHIC energies, central Au+Au collisions: At RHIC energies, central Au+Au collisions: 1. From Bjorken estimates via E T and N ch :  > 5 GeV/fm 3 2. From energy loss of high-p T particles:  ≈ 15 GeV/fm 3 3. From Hydromodels with thermalization:  center ≈ 25 GeV/fm 3 All are rough estimates and model dependent (EOS,     ?), no information about thermalization or deconfinement. Methods not completely comparable All are rough estimates and model dependent (EOS,     ?), no information about thermalization or deconfinement. Methods not completely comparable But are without doubt good enough to support that  >>  C ≈ 1 GeV/fm 3 But are without doubt good enough to support that  >>  C ≈ 1 GeV/fm 3

How do we use hadrons ? Discovery probes: CERN: Strangeness enhancement/equilibration RHIC: Elliptic flow RHIC: Hadronic jet quenching Characterization probes: Chemical and kinetic properties HBT and resonance production for timescales Fluctuations for dynamic behavior

Particle Identification in STAR

Chemical freeze-out (yields & ratios)  inelastic interactions cease  particle abundances fixed (except maybe resonances) Thermal freeze-out (shapes of p T,m T spectra):  elastic interactions cease  particle dynamics fixed Basic Idea of Statistical Hadronic Models Assume thermally (constant T ch ) and chemically (constant n i ) equilibrated system Given T ch and  's (+ system size), n i 's can be calculated in a grand canonical ensemble

Particle production: Statistical models do well We get a chemical freeze-out temperature and a baryochemical potential out of the fit

Ratios that constrain model parameters

Statistical Hadronic Models : Misconceptions Model says nothing about how system reaches chemical equilibrium Model says nothing about when system reaches chemical equilibrium Model makes no predictions of dynamical quantities Some models use a strangeness suppression factor, others not Model does not make assumptions about a partonic phase; However the model findings can complement other studies of the phase diagram (e.g. Lattice-QCD)

Thermalization in Elementary Collisions ? Beccatini, Heinz, Z.Phys. C76 (1997) 269 Seems to work rather well ?!

Thermalization in Elementary Collisions ? Is a process which leads to multiparticle production thermal? Is a process which leads to multiparticle production thermal?  Any mechanism for producing hadrons which evenly populates the free particle phase space will mimic a microcanonical ensemble.  Relative probability to find a given number of particles is given by the ratio of the phase-space volumes P n /P n’ =  n (E)/  n’ (E)  given by statistics only. Difference between MCE and CE vanishes as the size of the system N increases. This type of “thermal” behavior requires no rescattering and no interactions. The collisions simply serve as a mechanism to populate phase space without ever reaching thermal or chemical equilibrium In RHI we are looking for large collective effects.

Statistics  Thermodynamics Ensemble of events constitutes a statistical ensemble T and µ are simply Lagrange multipliers “Phase Space Dominance” A+A We can talk about pressure T and µ are more than Lagrange multipliers p+p

Are thermal models boring ? Good success with thermal models in e+e-, pp, and AA collisions. Thermal models generally make tell us nothing about QGP, but (e.g. PBM et al., nucl-th/ ): Elementary particle collisions: canonical description, i.e. local quantum number conservation (e.g.strangeness) over small volume. Just Lagrange multipliers, not indicators of thermalization. Heavy ion collisions: grand-canonical description, i.e. percolation of strangeness over large volumes, most likely in deconfined phase if chemical freeze-out is close to phase boundary.

T systematics it looks like Hagedorn was right! it looks like Hagedorn was right!  if the resonance mass spectrum grows exponentially (and this seems to be the case), there is a maximum possible temperature for a system of hadrons  indeed, we don’t seem to be able to get a system of hadrons with a temperature beyond T max ~ 170 MeV! filled: AA open: elementary [Satz: Nucl.Phys. A715 (2003) 3c]

Does the thermal model always work ?  Particle ratios well described by T ch = 160  10 MeV,  B = 24  5 MeV  Resonance ratios change from pp to Au+Au  Hadronic Re-scatterings! Data – Fit (  ) Ratio

Strange resonances in medium Short life time [fm/c] K* <  *<  (1520) <  4 < 6 < 13 < 40 Red: before chemical freeze out Blue: after chemical freeze out Medium effects on resonance and their decay products before (inelastic) and after chemical freeze out (elastic). Rescattering vs. Regeneration ?

Resonance  Production in p+p and Au+Au Thermal model [1]: T = 177 MeV  B = 29 MeV [1] P. Braun-Munzinger et.al., PLB 518(2001) 41 D.Magestro, private communication [2] Marcus Bleicher and Jörg Aichelin Phys. Lett. B530 (2002) M. Bleicher, private communication Rescattering and regeneration is needed ! UrQMD [2] Life time [fm/c] :  (1020) = 40  (1520) = 13 K(892) = 4  ++ = 1.7

Resonance yields consistent with a hadronic re-scattering stage Generation/suppression according to x-sections p  **   K*    p K K p      More  Less K*  Chemical freeze-out K K  Ok   p  K K*/K  Less  * Preliminary

Strangeness: Two historic QGP predictions restoration of  symmetry -> increased production of s restoration of  symmetry -> increased production of s  mass of strange quark in QGP expected to go back to current value (m S ~ 150 MeV ~ Tc)  copious production of ss pairs, mostly by gg fusion [Rafelski: Phys. Rep. 88 (1982) 331] [Rafelski-Müller: P. R. Lett. 48 (1982) 1066] deconfinement  stronger effect for multi-strange deconfinement  stronger effect for multi-strange  by using uncorrelated s quarks produced in independent partonic reactions, faster and more copious than in hadronic phase  strangeness enhancement increasing with strangeness content [Koch, Müller & Rafelski: Phys. Rep. 142 (1986) 167] Strangeness production depends strongly on baryon density (i.e. stopping vs. transparency, finite baryo-chemical potential)

Strangeness enhancement in B/B ratios Baryon over antibaryon production can be a QGP signature as long as the baryochemical potential is high (Rafelski & Koch, Z.Phys. 1988) Baryon over antibaryon production can be a QGP signature as long as the baryochemical potential is high (Rafelski & Koch, Z.Phys. 1988) With diminishing baryochemical potential (increasing transparency) the ratios approach unity with or without QGP, and thus only probe the net baryon density at RHIC.

New RHIC data of baryon ratios The ratios for pp and AA at 130 and 200 GeV are almost indistinguishable. The baryochemical potentials drop from SPS to RHIC by almost an order of magnitude to ~50 MeV at 130 GeV and ~20 MeV at 200 GeV. BRAHMS, PRL nucl-ex/ STAR p+p 200 GeV

Strangeness enhancement: Wroblewski factor evolution Wroblewski factor dependent on T and  B dominated by Kaons Lines of constant S / = 1 GeV I. Increase in strange/non-strange particle ratios II. Maximum is reached III. Ratios decrease (Strange baryons affected more strongly than strange mesons) Peaks at 30 A GeV in AA collisions due to strong  B dependence mesons baryons hidden strangeness mesons PBM et al., hep-ph/ total See P.Senger’s talk

Strangeness enhancement K/  – the benchmark for abundant strangeness production: K/  – the benchmark for abundant strangeness production: K/  K+/K+/ [GeV]

The SPS ‘discovery plot’ (WA97/NA57) Unusual strangeness enhancement N(wounded)

The switch from canonical to grand-canonical (Tounsi,Redlich, hep-ph/ , hep-ph/ ) The strangeness enhancement factors at the SPS (WA97) can be explained not as an enhancement in AA but a suppression in pp. The pp phase space for particle production is small. The volume is small and the volume term will dominate the ensemble (canonical (local)). The grand-canonical approach works for central AA collisions, but because the enhancements are quoted relative to pp they are due to a canonical suppression of strangeness in pp.

Strangeness enhancement factors at RHIC  N part -scaling in Au-Au at RHIC -> lack of N part scaling = no thermalization ? Alternatives: no strangeness saturation in peripheral collisions (  s = 1) non-thermal jet contributions rise with centrality Grandcanonical prediction

Identified particle spectra : p, p, K -,+,  -,+, K 0 s and 

Identified Particle Spectra for 200 GeV BRAHMS: 10% central PHOBOS: 10% PHENIX: 5% STAR: 5% The spectral shape gives us: The spectral shape gives us:  Kinetic freeze-out temperatures  Transverse flow The stronger the flow the less appropriate are simple exponential fits: The stronger the flow the less appropriate are simple exponential fits:  Hydrodynamic models (e.g. Heinz et al., Shuryak et al.)  Hydro-like parameters (Blastwave) Blastwave parameterization e.g.: Blastwave parameterization e.g.:  Ref. : E.Schnedermann et al, PRC48 (1993) 2462 Explains: spectra, flow & HBT

“Thermal” Spectra Invariant spectrum of particles radiated by a thermal source: where:m T = (m 2 +p T 2 ) ½ transverse mass (Note: requires knowledge of mass)  = b  b + s  s grand canonical chem. potential Ttemperature of source Neglect quantum statistics (small effect) and integrating over rapidity gives: R. Hagedorn, Supplemento al Nuovo Cimento Vol. III, No.2 (1965) At mid-rapidity E = m T cosh y = m T and hence: “Boltzmann”

“Thermal” Spectra (flow aside) N.B. Constituent quark and parton recombination models yield exponential spectra with partons following a pQCD power-law distribution. (Biro, Müller, hep-ph/ )  T is not related to actual “temperature” but reflects pQCD parameter p 0 and n. Describes many spectra well over several orders of magnitude with almost uniform slope 1/T usually fails at low-p T (  flow) most certainly will fail at high-p T (  power-law)

“Thermal” spectra and radial expansion (flow) Different spectral shapes for particles of differing mass  strong collective radial flow Spectral shape is determined by more than a simple T at a minimum T,  T mTmT 1/m T dN/dm T light heavy T purely thermal source explosive source T,  mTmT 1/m T dN/dm T light heavy

Thermal + Flow: “Traditional” Approach 1. Fit Data  T2. Plot T(m)  T th,  T  is the transverse expansion velocity. With respect to T use kinetic energy term ½ m  2 This yields a common thermal freezeout temperature and a common . Assume common flow pattern and common temperature T th

Hydrodynamics in High-Density Scenarios Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles) Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles) Equations given by continuity, conservation laws, and Equation of State (EOS) Equations given by continuity, conservation laws, and Equation of State (EOS) EOS relates quantities like pressure, temperature, chemical potential, volume = direct access to underlying physics EOS relates quantities like pressure, temperature, chemical potential, volume = direct access to underlying physics Kolb, Sollfrank & Heinz, hep-ph/

Hydromodels can describe m T (p T ) spectra Good agreement with hydrodynamic prediction at RHIC & SPS (2d only) RHIC: T th ~ 100 MeV,   T  ~ 0.55 c

Blastwave: a hydrodynamic inspired description of spectra R ss Ref. : Schnedermann, Sollfrank & Heinz, PRC48 (1993) 2462 Spectrum of longitudinal and transverse boosted thermal source: Static Freeze-out picture, No dynamical evolution to freezeout

The Blastwave Function Increasing T has similar effect on a spectrum as increasing  s Flow profile (n) matters at lower m T ! Need high quality data down to low-m T

Heavy (strange ?) particles show deviations in basic thermal parametrizations STAR preliminary

Blastwave fits Source is assumed to be: In local thermal equilibrium Strongly boosted , K, p: Common thermal freeze-out at T~90 MeV and ~0.60 c  : Shows different thermal freeze-out behavior: Higher temperature Lower transverse flow  Probe earlier stage of the collision, one at which transverse flow has already developed  If created at an early partonic stage it must show significant elliptic flow (v 2 ) Au+Au  s NN =200 GeV STAR Preliminary  68.3% CL  95.5% CL  99.7% CL

Blastwave vs. Hydrodynamics T dec = 100 MeV Kolb and Rapp, PRC 67 (2003) Mike Lisa (QM04): Use it don’t abuse it ! Only use a static freeze-out parametrization when the dynamic model doesn’t work !!

Collective Radial Expansion  r   increases continuously T th  saturates around AGS energy Strong collective radial expansion at RHIC  high pressure  high rescattering rate  Thermalization likely Slightly model dependent here: Blastwave model From fits to , K, p spectra:

Elliptic Flow (in the transverse plane) for a mid-peripheral collision Dashed lines: hard sphere radii of nuclei Reaction plane In-plane Out-of-plane Y X Re-interactions  FLOW Re-interactions among what? Hadrons, partons or both? In other words, what equation of state? Flow

v 2 measurements (Miklos’ Favorite) Multistrange v2 establishes partonic collectivity ?

Lifetime and centrality dependence from  (1520) /  and K(892)/K Model includes: Temperature at chemical freeze-out Lifetime between chemical and thermal freeze-out By comparing two particle ratios (no regeneration) results between : T= 160 MeV =>  > 4 fm/c (lower limit !!!)  = 0 fm/c => T= MeV  (1520)/  =   K*/K - = 0.20  0.03 at 0-10% most central Au+Au G. Torrieri and J. Rafelski, Phys. Lett. B509 (2001) 239 Life time: K(892) = 4 fm/c  (1520) = 13 fm/c preliminary More resonance measurements are needed to verify the model and lifetimes Blast wave fit of ,K,p (T kin +  T chem   ~ 6 fm/c Based on entropy:  t ~ (T ch /T kin – 1) R/  s  does not change much with centrality because slight  T reduction is compensated by slower expansion velocity  in peripheral collisions.

Time scales according to STAR data dN/dt 1 fm/c 5 fm/c 10 fm/c20 fm/c time Chemical freeze out Kinetic freeze out Balance function (require flow) Resonance survival Rlong (and HBT wrt reaction plane) Rout, Rside hadronization initial state pre-equilibrium QGP and hydrodynamic expansion hadronic phase and freeze-out

 Initial energy density high enough to produce a QGP    10 GeV/fm 3 (model dependent)  High gluon density dN/dy ~ 800  1200 dN/dy ~ 800  1200  Proof for high density matter but not for QGP Summary: global observables

Statistical thermal models appear to work well at SPS and RHIC Statistical thermal models appear to work well at SPS and RHIC  Chemical freeze-out is close to T C  Hadrons appear to be born into equilibrium at RHIC (SPS) into equilibrium at RHIC (SPS)  Shows that what we observe is consistent with thermalization consistent with thermalization  Thermal freeze-out is common for all particles if radial flow for all particles if radial flow is taken into account. is taken into account. T and   are correlated T and   are correlated  Fact that you derive T,  T is no direct proof but it is consistent with thermalization no direct proof but it is consistent with thermalization Summary of particle identified observables

Conclusion  There is no “ “ in bulk matter properties  However:  So far all pieces point indeed to QGP formation - collective flow & radial & radial - thermal behavior - high energy density - strange particle production enhancement elliptic