# Presentation: 315876

## Experimental Probes of QGP(Part I)

*Student Lecture, QM 2004, Oakland, CA*
*January 11, 2004*
*Thomas Ullrich, BNL*

## A Discovery

- Pluto

- Charon

## Is it a Planet ?

- Kuiper Belt
-  suggested 1951
-  confirmed 1992
- ~ 30,000 objects
- larger than 100 km

- Historically Pluto has been classified as a planet
- Some  think Pluto better classified as a large asteroid or comet
- Some consider it to be the largest of the Kuiper Belt objects

## A Matter of Definition ...

_**POSITION STATEMENT ON THE DEFINITION OF A "PLANET"**_
**WORKING GROUP ON EXTRASOLAR PLANETS (WGESP) OF THE INTERNATIONAL ASTRONOMICAL UNION **
- Created: February 28, 2001
- Last Modified: February 28, 2003
- Rather than try to construct a detailed definition of a planet which is designed to cover all future possibilities, the WGESP has agreed to restrict itself to developing a working definition applicable to the cases where there already are claimed detections, e.g., the radial velocity surveys of  companions to (mostly) solar-type stars, and the imaging surveys for free-floating objects in young star clusters. As new claims are made in the future, the WGESP will weigh their individual merits and circumstances, and will try to fit the new objects into the WGESP definition of a "planet",  revising this definition as necessary. This is a gradualist approach with an evolving definition, guided by the observations that will decide all in the end.
- Emphasizing again that this is only a working definition, subject to change as we learn more about the census of low-mass companions, the WGESP has agreed to the following statements ...

## So what is the Definition of “Quark Gluon Plasma”?

*The term plasma is generally reserved for a **system of charged particles large enough to behave collectively**. *
*The typical characteristics of a plasma are: *
* **Debye screening lengths that are short compared to the physical *
*  **size of the plasma. *
* **Large number of particles within a sphere with a radius of the Debye length.** *
* **Mean time between collisions usually are long when compared to the *
*  **period of plasma oscillations”*
- wordIQ.com

- Quark Gluon Plasma
*“**A **deconfined** system of strongly interaction matter (quarks and*
* **gluons) in **thermal equilibrium** at high temperatures and/or *
*densities.”*
*	**	**	**	**	**	*based on common wisdom

- No working group on the definition of a *Quark Gluon Plasma* (yet)

## Lattice QCD at Finite Temperature

-  Coincident transitions: deconfinement and chiral symmetry restoration
-  Recently extended to B> 0, order still unclear (1st, 2nd, crossover ?)

- F. Karsch,
- hep-ph/0103314

## Probes of the QGP – A Laundry List

- Kinematic Probes
- , p, s(T,B)
- Spectra  pT, dN/dy, dET/dy
- Particle Ratios
- Radial and Elliptic Flow
- Correlations:
- Identical and Non-Identical Particle Interferometry (HBT)
- Balance Function
- Fluctuations:
-  pT, Nch
- Electromagnetic Probes
-  Direct Photons
-  Thermal Dileptons / Leptonpairs

- Probes of Deconfinement
- Quarkonium Suppression
- Strangeness Enhancement
- Probes of Chiral Symmetry Restoration
- Medium Effects on Hadron Properties
- Disoriented Chiral Condensates
- Hard QCD Probes
- Jet Quenching
- Models/Theory
- QGP Models
- Non-QGP Models

- For more see for example: C.P. Singh, Physics Reports 236 (1993) 147-224,
- J. Harris and B. Müller, Annu, Rev. Nucl. Part. Sci. 1996 46:71-107
- (http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.nucl.46.1.71)
- and QM Proceedings

## Outline

- Chemical freezeout (Tch  Tc): inelastic scattering ceases
- Kinetic freeze-out (Tfo  Tch): elastic scattering ceases

*hard* (high-pT) probes

*soft* physics
- regime

## Are the conditions at SPS/RHIC met to form a QGP?

- QCD on Lattice (2-flavor):
- Phase transition at
*T**C** *≈ 1738 MeV, ***C* ≈ (62) *T *4
- hence ***C* ≈ 0.70  0.27 GeV/fm3
- Remember:  cold nuclear matter
***cold* ≈ u / 4/3*r*03 ≈ 0.13 GeV/fm3

- At a minimum we need to create ***C *in order to create a QGP.
- Note: this is a necessary but **not** sufficient condition
- Tevatron (Fermilab) (s = 1.8 TeV****pp) >> (Au+Au RHIC)
- Thermal Equilibrium  many constitutents  Size matters !!!

- pre-equilibrium

## Assessing the Initial Energy Density: Calorimetry

- R2

- Central Au+Au (Pb+Pb) Collisions:
- 17 GeV:	  BJ  3.2 GeV/fm3
- GeVBJ  4.6 GeV/fm3
- 200 GeV: BJ  5.0 GeV/fm3

- 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
-  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

## Other Means of Assessing Energy Density 

- Hydrodynamic Models (*more later*):
- need to fix initial conditions to describe spectra & flow
- at RHIC:   ≈ 25 GeV/fm3 at  = 0.6 fm/c in fireball _center_
- Careful
- depends on EOS
- thermalization is fundamental ingredient of  model

- spectra: data&hydro

- v2/x hydro-model

- v2/x (Phenix 130 GeV)

- Kolb,Heinz, nucl-th/0305084

- Au+Au at 130 GeV

## Yet another Means of Assessing Energy Density

- Energy loss via induced gluon bremsstrahlung
***E*  ***glue*  *dN**glue**/dy*  estimate of 

- “Jet Quenching”

- leading particle

## Yet another Means of Assessing Energy Density

- Compare Au+Au with p+p Collisions  RAA

- Nuclear
- Modification
- Factor:

- No “Effect”:
-  R < 1 at small momenta
-  R = 1 at higher momenta where
-         hard processes dominate
- Suppression:  R < 1

## Yet another Means of Assessing Energy Density

- STAR, nucl-ex/0305015

- energy
- loss

- pQCD + Shadowing + Cronin

- pQCD + Shadowing + Cronin + Energy Loss

- Deduced initial gluon density at  = 0.2 fm/c    dNglue/dy ≈ 800-1200
-   ≈ 15 GeV/fm3                                       (e.g. X.N. Wang nucl-th/0307036)

## So what is  now ?

- At RHIC energies, central Au+Au collisions:
- From Bjorken estimates via ET and Nch		 >  5 GeV/fm3
- Calculations of energy loss of high-pT particles  	 ≈  15 GeV/fm3
- Both do not tell us anything about thermalization or deconfinement
- (the proof can only come indirectly through models)
- Hydro models assuming thermalization give	center ≈  25 GeV/fm3
- All are rough estimates and model dependent (EOS,  ?)
- Methods not completely comparable
- But are without doubt good enough to support that  >> C ≈ 1 GeV/fm3

## Thermalization and Freeze-Out 

**Chemical freeze-out**
- (yields & ratios)
- inelastic interactions cease
- particle abundances fixed (except maybe resonances)
**Thermal freeze-out**
- (*shapes* of pT,mT spectra):
- elastic interactions cease
- particle dynamics fixed

- What can final-state particle yields and momenta tell us about thermal conditions at **freeze-out**?

## Statistical Models in RHI Collisions

- Where in the phase diagram is the system at chemical freeze-out?
- What values have Tch, B ?
- Statistical Thermal Models: a means to extract (Tch, B) from
-                                                  particle ratios

## The Basic Idea behind Statistical Hadronic Models

- Assume thermally (constant Tch) and chemically (constant ni) equilibrated system at chemical freeze-out
- System composed of non-interacting hadrons and resonances
- Given Tch and  's (+ system size), ni's can be calculated in a _grand canonical ensemble_
- Obey conservation laws: Baryon Number, Strangeness, Isospin
- Short-lived particles and resonances need to be taken into account

*Compare particle ratios to experimental data*

- Tch, 

- Iterate

## 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)

## Ratios which constrain model parameters

## Statistical Thermal Models work well at SPS

- Braun-Munzinger, Heppe, & Stachel, PLB 465 (1999) 15

- T = 168  2.4 MeV B = 266  5 MeV

## Statistical Thermal Models work well at RHIC

## Except ...

- Produced short lived resonances (K*, )
-  rescattering of daughters
-  regeneration effect

**Thermal model [1]:**
- T = 177 MeV
- B = 29 MeV

**Life time:**
******(1020) = 40 fm/c **
******(1520) = 13 fm/c**
**K(892)   =   4 fm/c**

-  Ratios short-lived/long-lived are smaller in Au+Au than in p+p collisions.
- Thermal model predictions are higher than data.

## Lattice QCD vs. Statistical Model

**Lattice-QCD**

**Stat.Thermal Model**

## Thermalization in Elementary Collisions ?

- Thermal Model:
-  e+e-  qq   hadronic jets ~ hadron gas = fireball  (jets = fireballs)
- Correlated jets: small systems + quantum numbers conservation  canonical form
*Recipe:*
-  Assume thermal and chemical equilibrium
-  canonical ensemble to describe partition function
-  input: measured particle yields
-  output: T, V, s      determined by fit   					(s to account for  incomplete saturation of strangeness)
- Studies performed at several s and various systems: pp , pp,  e+e-

## Thermalization in Elementary Collisions ?

*Beccatini, Heinz, Z.Phys. C76 (1997) 269*

- Seems to work rather well ?!

## Thermalization in Elementary Collisions ?

-  T  170 MeV  (good old Hagedorn temperature)
-  Tch does not (or only weakly) depends on s
-  Universal hadronization mechanism at critical values ?

*Beccatini, Heinz, *
*Z.Phys. C76 (1997) 269*

## Thermalization in Elementary Collisions ?

- 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 Pn/Pn’ = 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

- One (1) system is already statistical !
-  We can talk about pressure
-  T and μ are more than Lagrange multipliers

- p+p

## When canonical becomes more grand canonical - like

- Strangeness enhancement:
- 1. Lower energy threshold
-     Key concept is that *T**QGP* > *T**C* ~ *m**s **= *150 MeV
- Note that strangeness is conserved in the strong interaction
- 2. Larger production cross-section
- 3. Pauli blocking (finite chemical potential)

- Enhancement is expected to be more pronounced for the multi-strange baryons and their anti-particles

- pp

- AA

## When canonical becomes more “grand” canonical

- Enhancement E = yield|AA **/** Npart · yield|pA(pp)
- Small systems:
- conservation laws  canonical formulation
- conservation of quantum numbers reduces phase space available for particle production
- “*canonical suppression*”  E 
- “thermal” density nC  V0 = VN · Npart
- V0: correlation volume
- Large(r) Systems:
- n  nGC     (independent of V at some point)
- V0 increases from p+p to A+A  possibly due to:
-  equilibration in quark or hadronic matter
-  initial state multi-particle collisions
-  initial state correlations in A+A

- s       Enhancement 
- because denominator (pp/dA)
- becomes more “grand canonical”

- K. Redlich, hep-ph/0111159

## Describing and Interpreting Particle Spectra (Tth, T)

## The Powerlaw Function

- pQCD approach for Ed3/dp3
- Point-like scattering process a+b→c+d  (via vector gluon exchange) (Berman, Bjorken, Kogut 1971)
- d/dt ~ 1/s2
- Ed3/dp3 ~ pT-4	  f(xT,)
- “*Black Box model*” (Feynman, Field, Fox)
- assume arbitrarily d/dt ~ 1/(s t3)
- Ed3/dp3 ~ pT-8
*Constituent Interchange Model* and quark-fusion model
- add other subprocesses (quark-meson,quark-diquark scattering)
- n = 8 for pions
- n = 12 for baryons
- Data (pp,****pp) appears to scale *approximately* like n=8 pions and kaons and n=10-12 for protons but only in *certain regions*

## The Powerlaw Function

- p0 = 0.75

- 1.25

- 1.5

-  p0 ↑  flattens spectra
-  p0 ~  pT
-  n ↓  lifts tail
-  n ~ 1/pT
-  n, p0 strongly correlated
- often:
- use pT directly in fit
- Beware of extrapolations!
- Powerlaw using mT describes low pT region usually better

- A pQCD inspired
- phenomenological approach

- n=12

- 9

- 8

- n = 0.75, p0 = 8.3
- n = 1.2,   p0 = 11.4
- n = 1.5,   p0 = 13.5

## “Thermal” Spectra

- Invariant spectrum of particles radiated by a thermal source:

- where:	mT= (m2+pT2)1⁄2	transverse mass (Note: requires knowledge of mass)
- 	 = b b + s s	grand canonical chem. potential
- 	T		temperature 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)

- “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/0309052)
-   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-pT
-    ( flow)
-  most certainly will fail
-   at high-pT
-   ( power-law)

## “Thermal” Spectra and 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

## Thermal + Flow: “Traditional” Approach

- 1. Fit Data  *T*

- 2. Plot *T(m)*  *T**th**, ****T*

- Problem: spectra are not exponential in the first place (fit range dependence)

- Assume ***common***** **flow pattern and ***common***
- temperature Tth

## 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
- direct access to underlying physics

**lattice QCD input**

*Kolb, Sollfrank *
*& Heinz,*
*hep-ph/0006129*

## Use of Hydro Models to describe mT (pT) Spectra

- Good agreement with hydrodynamicprediction at RHIC (and SPS)
- RHIC:
- Tth~ 100 MeV
-  T  ~ 0.55 c

*Kolb, Sollfrank & Heinz,*
*hep-ph/0006129*

- EOS & initial conditions
- 
- particle mT-spectra

- Disadvantage of Hydro:
- not very “handy” for experimentalists

- Most implementations in 2D only

## Blastwave: a hydrodynamic inspired description of spectra

*Ref. : Schnedermann, Sollfrank & Heinz,*
*PRC48 (1993) 2462*

- Spectrum of longitudinal and transverse boosted thermal source:

- Handy formula that can be fit to mT (pT) spectra
- 2-parameters: Tth, s
- Note: velocity at surface (s) is the “true” parameter but often T is quoted

## The Blastwave Function

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

## 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:

## Functions, Functions, ...

- Note: “T” depends on function used
- in papers often more than one fit function quoted ...

## Summary

-   10 GeV/fm3   (model dependent)
- High gluon density
*    **dN/dy ~ *8001200
- Proof for *high density matter*
-    but not for QGP formation
- density   rescattering rate 
-      prerequisite for *thermalization*

## Summary

- Chemical freeze-out is close to TC
- Hadrons appear to be born
-     into equilibrium at RHIC (SPS)
- Shows that what we observe is
-     consistent with *thermalization*
-     but again no direct proof

## Summary

- RHIC and SPS spectra cannot be
-    consistently described without flow
- Many different functions fit
- different emphasis
- watch out: different “T”
- T and  are correlated
- Fact that you derive T,T is
-     no direct proof for *thermalization*

## Conclusion

-  There is no “             “
-  However:
- All this provides pieces of
-     a larger evolving picture
- So far all pieces *point*
-     indeed to QGP formation
- Need final proof from theory
-    Show that:
- QGP scenario describes data
- any other scenarios do not
- N.B.: Even if the new state does not fit into the definition of QGP (planet) it’s certainly “new” and expands our knowledge (like Pluto)

## Next ...

- For all the remaining signatures see Jamie Nagle’s talk ...