# Presentation: 146431

## RHIC Physics:Adventures at the Highest Temperatures Created in the Laboratory 

**Thomas K Hemmick**
**Stony Brook University**

- W.A. Zajc

- 14-Jan-01

## Evolution of the Universe

**Quark-****Gluon****Plasma??**

- W.A. Zajc

- 14-Jan-01

## RHIC’s Experiments

**3.83 km circumference**
**Two *****independent*****  rings**
**Can collide ~any on ~any**
**AuAu, pp, dAu, CuCu**
**Top Center-of-Mass Energy:**
**500 GeV for p-p; 200 GeV/nucleon for Au-Au **
**Luminosity**
**Au-Au: 2 x 10****26**** cm****-2**** s****-1****; p-p  : 2 x 10****32**** cm****-2**** s****-1**** **

- W.A. Zajc

- 14-Jan-01

## Outline of Lecture

**Are we in the Ballpark?**
**Energy Density**
**Chemical Equilibrium**
**Kinetic Equilibrium**
**Is There a There There?**
**The Medium & The Probe**
**High Pt Suppression**
**Control Experiments: dAu, ********direct**
**What is It Like?**
**Azimuthally Anisotropic Flow**
**Hydrodynamic Limit**
**Recombination**
**Hot new results you’ll see **_**This Week**_** (shopping list)**
**Charm Spectral Modification**
**J/Y suppression(?)**
**Volcano Jet Shapes.**
**Direct Photons**

- W.A. Zajc

- 14-Jan-01

## The Ballpark

**Lattice QCD tells us that we should look for:**
****** ****> 1 GeV/fm****3**
**Lower bounds on ******** can be established by a CAREFUL analysis of transverse energy and multiplicity production**
**T > 170 MeV**
**Random motion (T) can be separated from collective motion so as to yield a measure of the final state temperature.**
**Particle abundances can be compared to simple chemical equilibrium calculations to establish a final state temperature (necessary a lower bound to initial state temperature).**
**Neither of these measures is sufficient to establish QGP formation, however both are necessary and thereby tell us whether we are “in the ballpark”.**

- W.A. Zajc

- 14-Jan-01

## : Ridiculous to Sublime

**Let’s calculate the Mass overlap Energy:**

- (in P=0 frame)

**Bjorken Energy Density Formula:**

**Energy Density defined as**

**Meaningless****Drivel**

- W.A. Zajc

- 14-Jan-01

## Initial Energy density

**Summary:**
**Two values of ********0:**
** ********form****=****ħ****/<m****T****>(********form****)  **
**	****        ≤****  ****ħ****/<m****T****>****final **** = 0.35 fm/c**
** ********therm**** ****	****≤ 1 fm/c (hydro)**
**We derive conservative *****lower limits***** on the energy density at formation and thermalization**
******(form) > 15 GeV/fm****3**** **
******(therm) > 5.4 GeV/fm****3**
**     ****in central Au+Au collision at 200 GeV**

**These values are well in excess of  ~1 GeV/fm3 obtained in lattice QCD as the energy density needed to form a deconfined phase.**

- W.A. Zajc

- 14-Jan-01

## Thermal Equilibrium

**We’ll consider two aspects of thermal predictions:**
**Chemical Equilibrium**
**Are all particle species produced at the right relative abundances?**
**Kinetic Equilibrium**
**Energetic sconsistent with common temperature plus flow velocity?**
**Choose appropriate statistical ensemble:**
**Grand Canonical Ensemble****:  In a large system with many produced particles we can implement conservation laws in an averaged sense via appropriate chemical potentials.**
**Canonical Ensemble****: in a small system, conservation laws must be implemented on an EVENT-BY-EVENT basis.  This makes for a severe restriction of available phase space resulting in the so-called “Canonical Suppression.”**
**Where is canonical required:**
**low energy HI collisions.**
**high energy e+e- or hh collisions**
**Peripheral high energy HI collisions**

- W.A. Zajc

- 14-Jan-01

## Canonical Suppression

**Canonical Suppression**

**Canonical Suppression is likely the driving force behind “strangeness enhancement”**

- W.A. Zajc

- 14-Jan-01

## Thermal yields

**The formula for the number density of all species:****here g****i**** is the degeneracy****E****2****=p****2****+m****2********B****, ********S****, ********3**** are baryon, strangeness, and isospin****                      chemical potentials respectively.**
**Given the temperature and all m, on determines the equilibrium number densities of all various species.**
**The ratios of produced particle yields between various species can be fitted to determine T, ********.**

- W.A. Zajc

- 14-Jan-01

## Slide 11

- W.A. Zajc

- 14-Jan-01

## Slide 12

- W.A. Zajc

- 14-Jan-01

## Flow I (parameterized)

**For any interacting system of particles expanding into vacuum, flow is a natural consequence.  **
**During the cascade process, one naturally develops an ordering of particles with the highest common underlying velocity at the outer edge.**
**This motion complicates the interpretation of the momentum of particles as compared to their temperature and should be subtracted.**
**Although 1****st**** principles calculations of fluid dynamics are the higher goal, simple parameterizations are nonetheless instructive.**
**Hadrons are released in the final stages of the collision and therefore measure ****“FREEZE-OUT”**

- W.A. Zajc

- 14-Jan-01

## Singles Spectra

**Peripheral:**
**Pions are concave due to feeddown.**
**K,p are exponential.**
**Yields are MASS ORDERED.**
**Central:**
**Pions still concave.**
**K exponential.**
**p flattened at left**
**Mass ordered wrong (p passes pi !!!)**

- Peripheral

- Central

- Underlying collective VELOCITIES impart more momentum to heavier species consistent with the basic trends

- W.A. Zajc

- 14-Jan-01

## Blast Wave

**Let’s consider a Thermal Boltzmann Source:**
**If this source is boosted radially with a velocity ********boost**** and evaluated at y=0:****where **
**Simple assumption: uniform sphere of radius R and boost velocity varies linearly w/ r:**

- W.A. Zajc

- 14-Jan-01

## Blast Wave Fits

**Fit AuAu spectra to blast wave model:**
******S ****(surface velocity) drops with dN/d******
**T (temperature) almost constant****.**

- T

- Blue y=0
- Red  y=1

- T

**p****T ****(GeV/c)**

- 1 and 3  contours

**y= 0**

- W.A. Zajc

- 14-Jan-01

**Notes:**
Get better plot from Eun-Joo, put equqtion down. 

## Is There a There There?

**We accelerate nuclei to high energies with the hope and intent of utilizing the beam energy to drive a phase transition to QGP.**
**The collision must not only utilize the energy effectively, but ****generate the signatures**** of the new phase for us.**
**I will make an artificial distinction as follows:**
_**Medium**_**:  The bulk of the particles; dominantly soft production and possibly exhibiting some phase.**
_**Probe**_**:  Particles whose production is calculable, measurable, and thermally incompatible with (distinct from) the medium.**
**The medium & probe paradigm will establish whether there is a there there.**

- W.A. Zajc

- 14-Jan-01

## The Probes Gallery:

- Jet Suppression

- charm/bottom dynamics

- J/ & 

- direct photons**CONTROL**

**The importance of the control measurement(s) cannot be overstated!**

- W.A. Zajc

- 14-Jan-01

## Calibrating the Probe(s)

**Calibrating the Probe(s)**

**Measurement from elementary collisions. **
**“****The tail that wags the dog” ****(M. Gyulassy)**

**p+p->********0**** + X**

- hep-ex/0305013 S.S. Adler et al.

- W.A. Zajc

- 14-Jan-01

## RAA Normalization 

**R****AA**** Normalization **

- <Nbinary>/inelp+p

- nucleon-nucleon
-   cross section

- 1. Compare Au+Au to nucleon-nucleon cross sections
- 2. Compare Au+Au central/peripheral

**Nuclear **
**Modification **
**Factor:**

- W.A. Zajc

- 14-Jan-01

**                   **

**Au-Au ********s = 200 GeV: high p****T**** suppression!**

**PRL91, 072301(2003)**

- W.A. Zajc

- 14-Jan-01

## Color Glass Condensate
Gluon fusion reduces number of scattering centers in initial state.
Theoretically attractive; limits DGLAP evolution/restores unitarity

**Color Glass Condensate**
**Gluon fusion reduces number of scattering centers in initial state.**
**Theoretically attractive; limits DGLAP evolution/restores unitarity**

- W.A. Zajc

- 14-Jan-01

## Control Experiment

**Collisions of small with large nuclei quantify all ****cold**** nuclear effects.**
**Small + Large distinguishes ****all**** initial and final state effects.**

- Medium?

- No Medium!

- W.A. Zajc

- 14-Jan-01

## NO suppression in d+Au!

- BRAHMS

- Phobos

- STAR

- PHENIX

- W.A. Zajc

- 14-Jan-01

## Second Control Experiment

**The medium should be transparent to photons.**
**These thereby probe the initial rate of pQCD production and provide independent normalization of hard collision rates.**

- W.A. Zajc

- 14-Jan-01

## pQCD Photons!

**PHENIX Preliminary ** PbGl / PbSc Combined

- AuAu 200 GeV    Central  **0-10%**

** ****Data consistent with hard scattering at pQCD rates plus suppression.**
-  **Jet Quenching again proves to be a final state effect!**

**pQCD Photons!**

- W.A. Zajc

- 14-Jan-01

## Jet Tomography

**Tomography, a fancy word for a shadow!**
**Jets are produced as back-to-back pairs.**
**One jet escapes, the other is shadowed.**
**Expectation:**
**“****Opaque” in head-on collisions.**
**“****Translucent” in partial overlap collisions.**

- X-ray pictures areshadows of bones

**Can Jet Absorption be Used to****“Take an X-ray” of our Medium?**

- W.A. Zajc

- 14-Jan-01

##  Back-to-back jets

**Away-side sensitive to precise v****2**** value.**
**Desire precision technique to disentangle v****2****.**

- STAR PRL 90, 082302 (2003)

- Central Au + Au

- Peripheral Au + Au

- near side

- away side

- peripheral

- central

- d + Au
- control

-                           0                                          3         (radians)

- W.A. Zajc

- 14-Jan-01

## Back-to-Back wrt Reaction Plane

**Suppression stronger in the out-of-plane direction.**
**Indicates suppression depends upon length of medium traversed.**

- W.A. Zajc

- 14-Jan-01

## “elliptic flow” barometer

- Origin:  spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system
- spatial anisotropy  momentum anisotropy

- v2:  2nd harmonic *Fourier coefficient* in azimuthal distribution of particles with respect to the reaction plane

- W.A. Zajc

- 14-Jan-01

## Anisotropic Flow

**Sensitive to the  initial time**
**Delays in the initiation of anisotropic flow not only change the magnitude of the flow but also the centrality dependence increasing the sensitivity of the results to the initial time.**

**Anisotropic Flow**

**Liquid Li Explodes ****into Vacuum**

**Gases explode into vacuum uniformly in all directions.**
**Liquids flow violently along the short axis and gently along the long axis.**
**We can observe the RHIC medium and decide if it is more liquid-like or gas-like**

**Position Space anisotropy (eccentricity) is transferred to a momentum space anisotropy visible to experiment**

- W.A. Zajc

- 14-Jan-01

## Fourier Expansion

**Most general expression for ANY invariant cross section uses explicit Fourier-Series for explicit ******** dependence:****here the sin terms are skipped by symmetry agruments.**
**For a symmetric system (AuAu, CuCu) at y=0, v****odd**** vanishes**
**v****4**** and higher terms are non-zero and measured but will be neglected for this discussion.**

- W.A. Zajc

- 14-Jan-01

##  Just how big is v2?

- Adler et al., nucl-ex/0206006

** ****Just how big is v****2****?**

**Yup, that’s pretty big**

- W.A. Zajc

- 14-Jan-01

## Parton Cascade Calculation of v2

**Huge cross sections!!**

- W.A. Zajc

- 14-Jan-01

## Limits of Cascade

**When the cascade calculation it taken to the point that the cross sections between colliding constituents is nearly of order of the system size, one recognizes that a binary cascade is the wrong theoretical approach to the calculation.**
**The limiting case of the cascade is a fluid mechanical or ****hydrodynamical**** calculation.**

- W.A. Zajc

- 14-Jan-01

## Basics of Hydrodynamics

- Hydrodynamic Equations

- Energy-momentum conservation

- Charge conservations (baryon, strangeness, etc...)

- For perfect fluids (neglecting viscosity),

- Energy density

- Pressure

- 4-velocity

- Within ideal hydrodynamics, pressure gradient *dP*/*dx* is the driving
- force of collective flow.
-     Collective flow is believed to reflect information about EoS!
-     Phenomenon which connects 1st principle with experiment

- Need equation of state
- (EoS)
-    *P*(*e*,*n*B)
- to close the system of eqs.
-  Hydro can be connected
- directly with lattice QCD

- Caveat: Thermalization,  << (typical system size)

- W.A. Zajc

- 14-Jan-01

## Inputs to Hydrodynamics

- Final stage:
- Free streaming particles
-  Need decoupling prescription

- Intermediate stage:
- Hydrodynamics can be valid
- if thermalization is achieved.
-  Need EoS

- Initial stage:
- Particle production and
- pre-thermalization
- beyond hydrodynamics
- Instead, initial conditions
-  for hydro simulations

*t*

*z*

- Need modeling
- (1) EoS, (2) Initial cond., and (3) Decoupling

- W.A. Zajc

- 14-Jan-01

## v2 -AND- spectra

**Hydro models:**
**Teaney**
***(w/ & w/o***
***RQMD)***
**Hirano**
***(3d)***
**Kolb**
**Huovinen**
***(w/& w/o***
***QGP)***

**nucl-ex/0410003**

- W.A. Zajc

- 14-Jan-01

## Hydro-models Score Board

**The hydro-models which include both hadronic and QGP phases reproduce the qualitative features of the measured v2(*****p******T*****) of pions, kaons, and protons.**
**These hydro-models require an early thermalization (********therm****<1fm/c) and high initial energy density ******** > 10 GeV/fm****3**
**Several of the hydro-models fail to reproduce the v2 and spectra simultaneously.**
**HBT source parameters are not reproduced by any hydrodynamic calculations.**

- The RHIC data are consistent with the so-called**“Hydrodynamic Limit”** for a non-viscous relativistic fluid

- W.A. Zajc

- 14-Jan-01

## Anomalous Particle Ratios

**Large excesses of baryons are observed at intermediate p****T****.**
**Why is this not just the flow we discussed yesterday?**
**Flow generates spectral differences based purely on mass.**
**We shall see later that this new effect depends not upon mass but valence quark count.**

- Large p/ ratio in 2-4 GeV/c

- Proton scales with Ncoll
- Mesons don’t

- W.A. Zajc

- 14-Jan-01

## Recombination Concept

-  for exponential parton spectrum, recombination is more effective than fragmentation
-  baryons are shifted to higher pt than mesons, for same quark distribution
-  understand behavior of protons!

- recombining partons:
- p1+p2=ph

- fragmenting parton:
- ph = z p, z<1

- Fragmentation:

- W.A. Zajc

- 14-Jan-01

## Recombination Models

**Duke:  **
**Pure thermal reco.**
**Oregon: **
**Fragmentation itself is recast as a recombination process.  HI collision simply adds extra thermal quarks during the process.**
**TAMU:**
**Jets and also feeddown from resonances.**

- W.A. Zajc

- 14-Jan-01

## Recombination Scaling

**Recombination Scaling**

**The nuclear modification factor when plotted for many particle species shows a bifurcation based upon ****VALENCE QUARK COUNT**** (not mass).**
**The flow patterns for all particles (except pions) are identical when scaled by ****valence quark count**

- W.A. Zajc

- 14-Jan-01

## HOT#1--RAA of charm electrons

***clear ***
***evidence for ***
***energy loss of***
***charm quarks***
***in central ***
***Au + Au!***
**(NOTE: Likely to**
**also be some**
**e****±**** from B decays)**

**R****AA**

**p****T**** (GeV/c)**

- W.A. Zajc

- 14-Jan-01

## Hot#2—Charm Flows!

**Charm flows, but not as strong as light mesons.**
**Drop of the flow strength at high p****T****. Is this due to b-quark contribution****?**
**The data favors the model that charm quark itself flows at low p****T****.**
**Charm flow supports high parton density and strong coupling in the matter. It is not a weakly coupled gas.****	**

- W.A. Zajc

- 14-Jan-01

## The first promising result of direct photon measurement at low pT from low-mass electron pair analysis.

Are these thermal photons? The rate is above pQCD calculation. The method can be used in p+p collisions.

If it is due to thermal radiation, the data can provide the first direct measurement of the initial temperature of the matter.

T0max ~ 500-600 MeV !?
	T0ave ~  300-400 MeV !?

**The first promising result of direct photon measurement at low p****T**** from low-mass electron pair analysis.**
**Are these thermal photons? The rate is above pQCD calculation. The method can be used in *****p+p***** collisions.**
**If it is due to thermal radiation, the data can provide the first direct measurement of the initial temperature of the matter.**
**T****0****max**** ~ 500-600 MeV !?**
**	****T****0****ave**** ~  300-400 MeV !?**

**Hot #3--(thermal?) photons**

- W.A. Zajc

- 14-Jan-01

## Hot#4--melt J/ and regenerate it?

**Hot#4--melt J/******** and regenerate it?**

**J/********’s are clearly suppressed beyond the cold nuclear matter effect**
**The preliminary data are consistent with the predicted suppression + re-generation at the energy density of RHIC collisions.**
**Can be tested by v****2****(J/********)?**

- W.A. Zajc

- 14-Jan-01

## Hot#5—Away-side Jet Hole

**Hot#5—Away-side Jet Hole**

**The shapes of jets are modified by the matter.**
**Mach cone?**
**Cerenkov?**
**Can the properties of the matter be measured from the shape?**
**Sound velocity**
**Di-electric constant**
**Di-jet tomography is a powerful tool to probe the matter**

**PHENIX preliminary**

- W.A. Zajc

- 14-Jan-01

## All Together Now:

- The matter may melt but regenerate J/’s

**All Together Now:**

- The matter is dense

- The matter is strongly coupled

- The matter is hot

- Can we determine
- the properties of the matter?

* **We are now working  with the theory community to extract the properties of the matter *

- The matter modifies jets

-  > 15 GeV/fm3
- dNg/dy > 1100

- Tave = 300 - 400 MeV (?)

- Vs = ?
- (dielec) = ?

**PHENIX preliminary**

- W.A. Zajc

- 14-Jan-01