# Presentation: 892870

## Quark Matter Formation in Heavy Ion Collisions  

**collision****	****hard scattering****	****	****	****	****jets, heavy flavor**
**	****	**** ****	****	****	**

**Quark Matter Formation in Heavy Ion Collisions  **

- Axel Drees

## Understanding the Time Evolution

**Studying “bulk” matter:**
**Global Observables****  **
**	****N****ch****,  ********E****T******** **
**	******** ********, S ...**
**Yields & Ratios of identified hadrons**
**	******** ****T****ch****, ********B****, ********S**** ...**
**Particle Spectra**
**	******** ****T****fo****, flow, source size ...**

- STAR preliminary

**Transverse momentum spectrum of charged particles**

- Axel Drees

## Use transverse energy production:
“Highly relativistic nucleus-nucleus collisions: The central rapidity region”,
		J.D. Bjorken, Phys. Rev. D27, 140 (1983).

Assumes
~ longitudinal expansion 
~ boost invariance “central rapidity plateau”

Then

**“*****Highly relativistic nucleus-nucleus collisions: The central rapidity region*****”,**
**	****	****J.D. Bjorken, Phys. Rev. **_**D27**_**, 140 (1983).**
**Assumes**
**~ longitudinal expansion **
**~ boost invariance “central rapidity plateau”**
**  **
** **
**Then**
**    **
**   **

**Estimating the Initial Energy Density**

**Radius of nucleus **
**	****R~ 6.5 fm**

**Element of longitudinally **
**expanding reaction volume:**

****** ****is formation time ~ 1fm**

- Axel Drees

## Initial Energy Density at RHIC

**	****	**

**“****Bjorken estimate” **
**    ****relates E****T**** to energy density:**

*Phys. Rev. Lett. 87, 52301 (2001)*

**initial energy density (formation time  ********0****=1 fm): **
**	**** ****RHIC****	****Au-Au****	******** ****i**** ~ 4.6 GeV/fm****3****	********    15 GeV/fm****3**
**	**** ****SPS****	****Pb-Pb****	******** ****i**** ~ 3.0 GeV/fm****3**

**Increase by ~1.15 from **
**130 GeV to 200 GeV**

**more realistic formation time ~0.3 fm at RHIC**

**~30 times normal nuclear density****~1.5 to 2 times higher than at SPS (********s = 17 GeV)**

- Axel Drees

**Notes:**
Zunaechstmal transversaler energie fluss. Diese ergebnisse wurden in PRL publiziert.

Transversale energie ist die energie die senkrecht zur strahlachse emmittiert wird. dies ist der differenzielle wq als fkt von et. fuer die centralsten Kollisionen, sagen wir 2% vom geometrischen wq werden etwa 580 GeV in einer rapiditaets einheit abgestrahlt. 

mit hilfe einer beruehmten abschaetzung von Bjorken kann diese transversale energie dichte in primaere energiedichte umgerechnet werden. Dazu braucht man noch eine formationszeit - die zeit zu der das system termaliziert. 

Typisherweise verwendet man am SPS 1 fm. Mit der gleichen formationszeit waere die energie dichte am RHIC 
fuer 130 GeV schwerpunkts energie 4.6 GeV/fm3. 

Tatsaechlich sind aber die parton dichten in den einlaufenden protonen und neutronen groesser bei hoeheren strahlenergien, Damit mussen die mittleren freien weglaengen kleiner werden und somit kann tau o.2 fm sein
was zu etwa  20 GeV/fm3 fuehrt. 

## Converting Energy Density to Temperature

**Converting Energy Density to Temperature**

**	**** ****AGS****	******** ****i**** ~ 1.4 GeV/fm****3**** ****	****	****T****i**** ~ 175 MeV**
**	**** ****SPS****	******** ****i**** ~ 3    GeV/fm****3**** ****	****	****T****i**** ~ 220 MeV**
**                 ****RHIC****	******** ****i**** ~ 5 - 15 GeV/fm****3****	****T****i**** ~ 250-350 MeV**

**based on lattice QCD results, ignoring density effects**

**~ 5 times larger than ********c******** **
**~ 2 times larger than T****C**** **

**Lattice QCD estimate:**
**	****T****C**** ~ 155-175 MeV    **
** ****	********C**** ~ 0.3-1.0 GeV/fm****3**** **

- Axel Drees

## Charged Particle Multiplicity Density

**dN****ch****/d******

****

**19.6 GeV**

**130 GeV**

**200 GeV**

**PHOBOS *****Preliminary***

**Central**

**Peripheral**

*Total* multiplicity per participant pair scales with Npart

****

- Axel Drees

## Centrality Dependence of Multiplicity at RHIC

**Centrality Dependence of Multiplicity at RHIC**

**PHOBOS Au+Au |********|<1**

- 19.6 GeV
- preliminary

**130 GeV**

**200 GeV**

- hard and soft scaling:

-  hard processes are important even for Nch ?

- Kharzeev and Nardi PLB 507, 121 (2001)

- Axel Drees

**Notes:**
pp not in fit   
 fix point 1.5 off beam-rapidity

## Alternative Picture: Gluon Saturation

**Saturation condition  ******** ~ 1   ****Q****S****2**** ~ ********S**** A xG****A****(x,Q****2****) ****/**** ********R****2**** ~ A****1/3**

**Alternative Picture: Gluon Saturation**

**Probe J interacting with partons in nucleus A:**
**Probe J senses partons with momentum **
**fraction x over longitudinal size:****	****	****	****  parton covers transverse size:****	****	**** ****	**
******parton cross section******
**     ****	****	****dimension of A:**

-  see e.g. D. Kharzeev, nucl-th/0107033 & ref.

**With parton density in transverse plane:                        ******** ~ A xG****A****(x,Q****2****) / ********R****2  ****~ A****1/3 **

**   ******** ****~  ********S****  / Q****2**** **

**Gluons in incoming nuclei overlap ******** gluon density saturate**

**limit ******** << 1****	********   incoherent  interactions  ********  preturbative  QCD****	**
**limit ******** >> 1****	********   coherent interaction        ********  dense parton system**

- Axel Drees

## Final State Multiplicity from Gluon Saturation 

**Procedure:**
**Determine scale Q****S****2**** as function of nuclear overlap**
**Q****S****2**** ~ A****1/3**** ~ N****part****1/3**
**Assume final-state multiplicities proportional to number of initial-state gluons in this saturated regime:**
**dN/d******** = c N****part**** xG****A****(x, Q****S****2****)**
**Note that DGLAP requires evolution of xG****A****(x, Q****S****2****) :**
**  ****xG****A****(x, Q****S****2****) ~ ln (Q****S****2**** / ********QCD****2****)**
**Results:**
**“****Running” of the multiplicity yield****directly from  from xG****A****(x, Q****2****)  +DGLAP**

**Logarithmic increase **
**of multiplicity with N****part**

**N****ch**** does not distinguish **
**saturation from soft+hard**

- Axel Drees

## Particle Composition and Particle Ratios

**Particle Composition and Particle Ratios**

**Large amount of high quality data****  **
******-****/********+****, ****K****-****/K****+****, ********p/p************/******** ,********/********,************/********, ********/****p****, ****K****/******** , ********/********, ********/****h****, ********K, K*/K, ...**
**RHIC, SPS, AGS ...**
**As function of N****part****, p****T**
**Example anti-particle/particle ratios at y=0 vs ********s**
**Approaches unit**
**All particles produced **
**	****in collision**
**“****pure matter” like  **
**    ****after big bang **

- Axel Drees

## Statistical Models for Particle Production

**Statistical Models for Particle Production**

**Extract T****ch**** and ********B ****: from measured ****particle ratios**

- s	: strangeness saturation factor
*n**s**	**:* number of strange quarks
*g**i**	*:* *spin-isospin freedom
- Tch	: Chemical freeze-out temperature
- B	: baryon chemical potential
*B**i*	: baryon number
*S**i*	: strangeness
*I**3**	**: *isospin projection
- I	: isospin chemical potential

- Particle density of each particle:

_*Statistical Thermal Model*_
*F. Becattini; P. Braun-Munzinger, J. Stachel, D. Magestro*
*J.Rafelski PLB(1991)333;  J.Sollfrank et al. PRC59(1999)1637*
*Assume:*
-  Ideal hadron resonance gas
-  thermally and chemically    equilibrated fireball at hadro-chemical freeze-out
*Recipe:*
-  grand canonical ensemble to describe partition function  density *n**i *of particles of species *i*
-  parameters fixed by conservation laws: volume, , strangeness chemical potential, isospin
-  input: measured particle ratios
-  output: temperature Tch and baryo-chemical potential B and strangeness saturation factor s

- Axel Drees

**Notes:**
We can have information of chemical freeze-out from statistical approach.
The system can be described by macro scopic parameters, that is, temperature, baryonic potential,
strangeness potential, and strangeness suppression factor.

## Statistical Models work well at RHIC

**T****ch**** ~ 175 MeV****	****	****chemical freeze out at phase boundary**
******B**** ~ 30-40 MeV****	****  ****	****almost net-baryon free**
** ********s **** = 1****	****	****	****strangeness equilibrated**

**Particle ratios for central collisions**

- Axel Drees

**Notes:**
Caveat - BRAHMS: 10% effect on ratios when including feed-down

## Centrality Systematics of Chemistry

- G. VanBuren and M. Kaneta (STAR)

** ****Statistical model using STAR**
**  ****data at 130 GeV at different centralities**
** ****Fits ****without (red)**** and ****with (blue)**** ******
**	****T****ch**** approximately constant**
**	********B**** *****increasing***** with centrality**
**	********s**** increasing with centrality**

- Axel Drees

**Notes:**
mu_b  increase with centrality: more baryon transport and/or antiproton absorption

## Statistical Models at other Energies

- Fit by Becattini using total yields from NA49
- hadron gas fit with partial strangeness saturation

|  | Tch [MeV] | B [MeV] |
| --- | --- | --- |
| AGS   | 125 | 540 |
| SPS    | 165 | 250 |
| RHIC   | 175 | 30 |

**Slight variations in the models, **
**but roughly:**

**Statistical models work **
**extremely well!!**

**even in pp and e+e- collisions!**

**but ********s**** < 1   i.e. strangeness is suppressed**

- Axel Drees

## Statistical Models: from AGS to RHIC

- Different implementation of statistical model
- Fact: all work well at RHIC, SPS, AGS and even at SIS energies

**At high energies T****ch**** ~ critical temperature**

**Hadrons are born into pre established equilibrium**

**phenomenological: **
**Universal freeze-out condition:**
**Average energy/particle**
******E********/********N******** ~ ********M******** + 3/2 T ~ 1 GeV**

- Axel Drees

## Strangeness Equilibration

**“****shell model type picture” for partonic degrees of  freedom**
**elementary p-p collision:**
**    ****u,d  quark levels empty**
**    ****s      quark levels large energy gap**
**    ******** ****strangeness production suppressed**
**nucleus-nucleus collisions (QGP):**
**    ****u,d  quark levels occupied**
**    ****s      quark levels large energy gap**
**    ******** ****strangeness production enhanced**

**Strangeness Equilibration**

_**Key Prediction: Strangness Euqilibration in QGP**_
-     (J.Rafelski and B.Müller, Phys.Rev.Lett. 48 (1982) 1066)

**strangeness production**
**enhanced by factor ~2**

**QGP threshold?**

- Axel Drees

**Notes:**
Im folgenden moechte ich ihen nun zeigen das auch alle schluessel vorhersagen beobachtet wurden und so ein konsistentes Bild liefer. 

Zunaechst einmal Strangness Erzeugung:

Warum man im QGP eine erhoehte s quark production erwarted kann man sich leicht in einem Schalen Bild veranschaulichen. Nehmen wir an es gibt drei potential toepfe fuer u,d,s quarks. das untereste Niveau fuer S-quarks liegt 2x die squark masse ueber denen von u und d quarks. 

In einer p-p kollision faengt man mit 6 quarks an dadurch sind nur die unteresten u-d Niveaus besetzt es gibt eine energie luecke zu s-quark niveaus sodass s-quark produktion unterdrueckt ist. 

In einer Kern Kern Kollision faengt man mit lkw ladungen von Quarks an viele der levels sind gefuellt und es kann zu einer 
umkehrung der energieschwelle fueher. s-quraks werden bevorzugt erzeugt bis niveaus gleich sind und alle in ch. gleichgewicht erzeugt werden.

Tatsaechlich beobachted man eine erhoehte production von 
strangness in kern-kern kollisionen. Hier ist der starngness anteil ss/uu+dd aufgetragen als fkt von der schwerpunktsenergie. In blau elementare kollisionen. Gruen und rot kern kern kollisionen. Bei SPS energien gibt es eine verdopplung des Stragness anteils. Detailiertere untersuchungen zeigen das Strangness nahezu in chemischem gleichgewicht ist.   

## Strangeness Equilibration

**Strangeness Equilibration**

**strangeness production through hadronic interactions:****	**
**  ****easy to produce ******** and ******** :               ********+********  ******** K+******** ****	****	****	****	****	********+******** ********+******** **
** ****hyperons (multi strange baryons and anti baryons)**
**   ****require  >100 fm/c to equilibrate**
** ****direct: ****	****	********+********+******
** ****multiple interactions:****	********+******** ******** N+********N**
**	****	****                ********N+K ********+ ********  **
**	****	****                ********+K ********+ ******
**	****	****                ********+K ******** + ********  **

**observe large hyperon enhanced:**

**WA97**

******  ****factor 20**

**hyperon enhancement not explained by hadronic interactions?**

******  ****factor 4**

**lifetime of hadronic system **
**only ~ 10 fm/c**

- Axel Drees

## But: Interpretation Remains Ambiguous

**But: Interpretation Remains Ambiguous**

**K/********  ratio at y=0 consistent with statistical model **
**correlation of baryon density and ********s **
**associated K-******** production reduced threshold or strangeness (if strangeness produced at hadronization) **

- y = 0

**4******** analysis with Wroblewski ratio: **
**	****strangeness content at hadronization**
**agreement not as good **
**trend with ********s not clear yet**

**statistical model with ********s**** = 1**

- 

******s dependence might distinguish strangeness production due to **
**statistical population of phase space   or   quark matter**

- P.Braun-Munzinger et al., Nucl.Phys A.697 (2002) 902

- P.Braun-Munzinger et al., Nucl.Phys A.697 (2002) 902

- Axel Drees

## Strange Baryon Production 

******  ****factor 20**

******  ****factor 4**

**compared to p-Be:**

**Strange Baryon Production **

**substantial enhancement of multi-strange baryons in Pb-Pb collisions **
**not equilibrated in hadronic phase (lifetime) **
**could be consistent with statistical model**
**enhancement in p-A**

- statistical model

- K.Redlich  Nucl.Phys. A.698 (2002) 95c

- WA97 & NA57:  N.Carrer et al., A.698 (2002) 118c
- NA49 compiled from C.Blume Hirschegg Workshop 2002

- preliminary

- preliminary

**issues:**
**size and N****part**** dependence of  p-A enhancement **
**threshold or smooth on set of enhancement in A-A**

**centrality dependence might distinguish strangeness production due to **
**statistical population of phase space   or   quark matter**

- Axel Drees

## Identified Particle Spectra at RHIC @ 200 GeV

- BRAHMS: 10% central
- PHOBOS: 10%
- PHENIX: 5%
- STAR: 5%

**various experiments agree well**
**different spectral shapes for particles of differing mass******** strong ****collective radial flow**

- Axel Drees

## Hydrodynamics: Modeling High-Density Scenarios

**Hydrodynamics: Modeling High-Density Scenarios**

**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)**
**EOS relates quantities like ****pressure****, temperature, chemical potential, volume, density ...**
**Works *****qualitatively***** at lower energy****but always over predicts collective****effects - infinite scattering limit****not valid there**

**lattice QCD input**

**At RHIC hydro works for first time**

- Axel Drees

## RHIC Spectra - an Explosive Source

- data: STAR, PHENIX, QM01
- model: P. Kolb, U. Heinz

**System evolution:   initial T****i ****        phase transition T****c****	****end of interactions T****f**
**	****	****	****             ****chemical freeze out      kinetic freeze out**

**cooling and expansion (collective velocity <********> of all particles)**

- Axel Drees

## Single Particle Spectra and Radial Flow

- Au+Au @ 130 GeV, central and peripheral (STAR, PHENIX):

**Hydrodynamics**
**works from central**
**to peripheral**
**collisions**
- (Heinz & Kolb
- hep-ph/0204061)

**Initial condition:*****  ************eq****** = 0.6 fm,   T******i ******(b=0)***** = 340 MeV,   ******** = 21.4 GeV/fm****3**
**Evolution:*****	******T******c****** =***** 165 MeV,   *****T******f ***** = 130 MeV**

- Axel Drees

## Mid-Rapidity mT spectra in 158 AGeV  (SPS)

- M. van Leeuwen (NA49)

- Axel Drees

## Tfo and <r> vs. s

***T******fo***** and <***********r*****> vs. ********s**

*************r *********  increases continuously**
***T******fo***** saturates around AGS energy**

- Slightly model dependent
- here:
- blastwave model
- (Kaneta/Xu)

**large pressure!!!**

- Axel Drees

**Notes:**
Next slide is T and beta systematic.
The radial flow saturate around 4GeV of root s once.
Then it glow-up at RHIC, if we focus mean values.
On the other hand, the temperature seems to be constant after AGS energy.
This behavior is predicted by Stocker et al.

To conclude beta is enhanced or not in high energy,  we need 200GeV data that will com soon
and energy scan between SPS and RHIC.

## Azimuthal Anisotropy: Elliptic Flow

**Azimuthal Anisotropy: Elliptic Flow**

**Almond shape overlap region in ****coordinate space**

**Anisotropy in**** momentum space**

*AGS*

*SPS, RHIC*

**Pressure**

- v2:  2nd harmonic Fourier coefficient in dN/d with respect to the reaction plane

- Axel Drees

## When Does Elliptic Flow Develop? 

- Equal energy density lines

*P. Kolb, J. Sollfrank, and U. Heinz*

- Mechanism is self-quenching
- Elliptic flow observable sensitive to early evolution of system

- v2

- Zhang, Gyulassy, Ko, PL B455 (1999) 45

- Au+Au at b=7 fm

- 

- 

- 

- 

- Large v2 is an indication
- of ***early*** thermalization

- Axel Drees

## Charged Particle v2 vs. Centrality

- midrapidity : |h| < 1.0

**Hydrodynamical models can describe data at low p****T ****(~2 GeV/c)           **
**Contrast to lower collision energies where hydro overpredicts elliptical flow**

*Peripheral  ****  Central*

- Axel Drees

## v2 vs pT for Charged and Identified Hadrons

**v2 vs p****T**** for Charged and Identified Hadrons**

**Hydro describes data very well**
**Transverse momentum distributions ******** transverse flow**
**v2 ******** elliptic flow**
**For different particles and as function of centrality**

**Initial condition:*****  ************eq****** = 0.6 fm,   T******i ******(b=0)***** = 340 MeV,   ******** = 21.4 GeV/fm****3**
**Evolution:*****	******T******c****** =***** 165 MeV,   *****T******f ***** = 130 MeV**

- Heinz & Kolb hep-ph/0204061

**Early equilibration quite likely!!**

- Axel Drees

- Axel Drees

## The Source Size or “HBT” Measurement

**Technique: Bose Einstein correlations**
**Introduced by Hanbury Brown-Twiss (1950’s) to measure sizes of stars**

**C(q) ~ contains sources **
**            ****shape information **

**Astronomy:  C(********t) two photon intensity as function of arrival time difference**

**Nuclear collisions: C(q) measure two boson intensity in momentum space **
**   ****	**** ****in bins of momentum difference  q****t**
**    ****	**** ****and bins of pair momentum (Y******** ,k****t****)**

- Axel Drees

## The  “HBT” Puzzle

***What is wrong with HBT?***

**Hydro calculation fail to describe HBT!**
**Very little variation with ********s ?**
**R****OUT****/R****SIDE**** ~ 1 ******** short life time ???**

- Soff, Bass, Dumitru, Phys. Rev. Lett. 86, 3981 (2001)

- Axel Drees

## Rapidity Spectra for Central Au-Au Collisions

**PHOBOS****	****     central Au-Au**

**At RHIC:**
**Particle production independent of y for –1 < y < 1 **

**rapidity ******** pseudo rapidity**

**pseudo rapidity**

- for pT   m

**BRAHMS**

**rapidity**

**boost invariance **
**near mid rapidity**

- Axel Drees

## Multiplicity per Participant in Central A-A

**Multiplicity per Participant in Central A-A**

**Increase of  multiplicity per participant in A-A compared to p-p **
**Sets in above SPS energy (********s~20 GeV)**

**SPS**

**Could indicates increased entropy?**

**Impact parameter b~0**
**~ 5% of inel. cross section**

- Axel Drees

## Leading Proton Effect in pp Collisions

**Leading Proton Effect in pp Collisions**

- Nch

**Basile et al (1980-84)**

**(ISR pp)**

**Subtract energy of leading protons to define effective energy**** **

- Axel Drees

## Nch(sNN) – Universality of Hadronization?

**pQCD e****+****e****-**** Calculation**

- Total charged particle multiplicity / participant pair

**leading proton energy converted to particle production**
******  ****multiple interactions of projectiles**
******  ****universality of hadronization?  **

- (A. Mueller,
-  1983)

- Same for all systems at same s(seff for pp)

- Axel Drees

**Notes:**
1 free parameter in fit .... lambda_QCD = 225 
PYTHIA also gives s_eff = s/2

## K-/K+ and p/p from AGS to RHIC

- I. Bearden (BRAHMS)

- Becattini caluclation using
- statistical model:
- T=170, s=1 (weak dependency)
- vary B/T  K+/K- andp/p
- K- /K+=(p/p)1/4 is
- a empirical fit to the data points
- K****K****  driven by s
- ~ exp(2s/T)
- p/p   driven by  B
- ~ exp(-2B/T)
- s = s (B)   since <S> = 0

- Axel Drees

**Notes:**
Kristoph Redlich : two different curves: AGS K/K driven by associate production / RHIC pair production

## What flows and when?

**What flows and when?**

- M. Kaneta/N. Xu (STAR)

- <pT> obtained for Tf
- and <>  (green line)

- <pT> obtained for
- Tch = Tf = 170 MeV
- and <>=0
*pp no rescattering, *
*no flow*

- STAR

- preliminary
- F. Wang

- and  also flow!
- Slightly below trend!
-     Smaller elast  
-     early decoupling 
-     should have much less flow?

***partonic***** flow?**

- Axel Drees

**Notes:**
fit k, pi, p only  ---- <pt> Boltzman for pion, K exp, p exponential, rest is exponential

## Does it flow? Fits to Omega mT spectra

- M. van Leeuwen (NA49)

- C. Suire (STAR)

- SPS/NA49

- RHIC

- STAR preliminary

- T is not well constrained !

**Need better data**

- Axel Drees