Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro1 What did we learn, and what will we learn from Hydro CIPANP 2003 New York City, May 22, 2003

Peter Kolb, CIPANP03, May 22, 2003Peter Kolb, CIPANP03, May 22, 2003 what we learn from hydro 11

What did we learn, andwhat will we learn from Hydro

CIPANP 2003New York City, May 22, 2003

Department of Physics and AstronomyState University of New YorkStony Brook, NY 11794

with support from theAlexander von Humboldt Foundation

Peter F. Kolb


Modeling the Expansion Dynamics

microscopic view macroscopic view vs

u

T

t

scattering of partons and hadrons

kinetic transport equations

collision terms

formalism:

continuity equations

energy, momentum conservation

equation of stateF. Karsch, Nucl. Phys. A 698 (2002) 1999U. Heinz, Nucl. Phys. A 685 (2001) 414


Hydrodynamic Evolution (b=0)

Equations of Motion:

+ Equation of State:

+ Initial Configuration:from an optical Glauber calculation

0 = 0.6 fm

here a resonance gas EoS for Tcrit < 165 MeVwith mixed phase and ideal gas EoS above


Evolution of Radial Flow

radial flow at fixed r as a function of time radial flow at fixed time as a function of r

+ mixed phase obstructs the generation of transverse flow+ the transverse flow profile rapidly adopts

a linear behavior vr = r with ~ 0.07 fm-1

PFK, nucl-th/0304036


Particle Spectra of Central Collisions: Au+Au @ 200 A GeV

Hydro parameters:0 = 0.6 fm/cs0 = 110 fm-3

s0/n0 = 250Tcrit=Tchem=165 MeV

Data: PHENIX: NPA715(03)151; STAR: NPA715(03)458; PHOBOS: NPA715(03)510; BRAHMS: NPA715(03)478Hydro-calculations including chemical potentials: PFK and R. Rapp, Phys. Rev. C 67 (03) 044903

Tdec=100 MeV


Single Particle Spectra: STAR collab., Nucl. Phys. A 715 (2003) 470c

Hydro calculation as in PFK and R.Rapp, Phys. Rev. C 67 (2003) 044903

The Omega resonance shows as strong transverse flow as the lighter hadrons. It appears to fully participate in the collective

expansion in the partonic as well as in the hadronic stage


Even Multistrange Particles FlowJavier Castillo for the STAR collaboration at SQM 2003

VERY PRELIMINARY

??

The Omega picks up flow from both the partonic as well as the hadronic phase and falls right on the hydro-systematics!

According to Batsouli, Kelly Gyulassy and Nagle (Phys. Lett. B 557 (2003) 26), even the D-meson spectrum is as flat as expected from hydro (however PYTHIA gives about the same result !)

See also Zhangbu Xu’s talk for 200 GeV, Tuesday May 20


Still more exotic: Mesons with Heavy Quarks

PHENIX collab: Phys. Rev. Lett. 88 (2002) 192303S.Batsouli, S.Kelly, M.Gyulassy, J.L.Nagle, Phys. Lett. B 557 (2003) 26

Single electron spectra from charm decay can be described by PYTHIA, as well as by assuming transverse flow of D and B mesons.

Elliptic flow will make a clear statement!

(And such measurements are coming!)


Transverse Momentum and Trans. EnergyPHENIX collab., Nucl. Phys. A 715 (2003) 151c PHENIX collab., Nucl. Phys. A 715 (2003) 151c

Transverse momenta as function of centrality are wellunder control as long as the collisions are not too peripheral.

Transverse energy agrees for all centralities.


Evolution of Non-Central Collisions

spatial eccentricity

momentumanisotropy

evolution of the energy densityinitial energy density distribution

PFK, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909(here b=7 fm)

initial energy density distribution


Elliptic Flow at RHIC (130):Heinz, PFK, NPA 702(02)269; Huovinen et al. PLB 503(01)58;

Teaney et al. PRL 68(01)4783; Hirano, PRC 65(01)011901

Mass, momentum and centrality dependence are well described up to pT ~ 2 GeV and b ~ 7 fm

Over 99 % of the emitted particles follow hydro systematics

ST

AR

col

lab.

, PR

L 8

7 (2

001)

182

301

ST

AR

, J.

Phy

s. G

28

(200

2) 2

0


Elliptic flow requires Rapid ThermalizationPFK, J. Sollfrank and U. Heinz, PRC 62 (2000) 054909

Free flow for an interval t changes the initial distribution function .For massless particles in the transverse plane ( ):

Reduced spatial anisotropy

as , the elliptic flow is reduced accordingly. With typical dimensions of non-central collisions, one obtains a reduction of 30 % for t = 2 fm/c.


Elliptic Flow requires Strong RescatteringPFK et al., PLB 500 (2001) 232; D. Molnar and M. Gyulassy, NPA 698 (2002) 379

Cross-sections and/or gluon densities of at some 10 to 80 times the perturbative estimates are required to deliver sufficient anisotropies.

At larger pT the experimental results (as well as the parton cascade) saturate, indicating insufficient thermalization of the rapidly escaping particles to allow for a hydrodynamic description.


Sensitivity on the Equation of State

Teaney, Lauret, Shuryak, nucl-th/0110037PFK and U. Heinz, nucl-ex/0204061

The data favor an equation of state with a soft phase and a latent heat e between 0.8 and 1.6 GeV/fm3


Elliptic Flow at Finite RapidityT. Hirano and K. Tsuda, nucl-th/020868

Boost invariance and thermodynamic concepts seem to be justified

over a pseudo-rapidity interval from -1.5 < 1.5

Observables at larger rapidities:

hold pre-equilibrium information ( directed flow!) operate at higher B ( close to the critical point!)

---

J.B

ower

s, K

.Raj

agop

al, h

ep-p

h/02

0916

8


Hydrodynamics is THE TOOL to study the thermodynamic properties (i.e. the equation of state) of nuclear matter under extreme conditions

Elliptic flow is THE OBSERVABLE to study the thermodynamic features of the equation of state from the earliest stages of the collision

The data suggest rapid thermalization and favor an equation of state with a soft region of width e~ 1 GeV/fm3

Summary 1: What Have we Learned


with the prerequisites for a hydrodynamic description given, and the many precise results on soft observables we can:

Which particles flow? Multistrange? Charm?

Summary 2: What Will we still Learn

study the degree and breakdown of thermalization

(in b, pT, sNN), and quantify viscosity effects (i.e

fundamentals of QCD and hadronic physics)

get more quantitative to extract information on the equation of state (even at varying chemical potential)

The bulk of the system follows hydrodynamics. Use this information as background for rarer observables and hard processes to answer:

How does the dog wag its tail ? (see M. Gyulassy’s talk)

Documents

Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro1 What did we learn, and what will we learn from Hydro CIPANP 2003 New York City, May 22, 2003