Wolfgang CassingWolfgang Cassing

Erice 22.09.08Erice 22.09.08

Parton dynamics and hadronizationParton dynamics and hadronizationfrom the sQGPfrom the sQGP

Compressing and heating hadronic matter:Compressing and heating hadronic matter:

sQGPsQGP

Questions:Questions:

•What are the What are the transport propertiestransport properties of the of the sQGPsQGP??

•How may the How may the hadronization hadronization (partons (partons hadrons) occur? hadrons) occur?

From hadrons to partonsFrom hadrons to partons

We We need need a a consistent transport model withconsistent transport model with

explicit explicit parton-parton interactionsparton-parton interactions (i.e. between quarks and gluons) (i.e. between quarks and gluons) explicit explicit phase transitionphase transition from hadronic to partonic degrees of from hadronic to partonic degrees of freedomfreedomQCD EoS for the partonic phaseQCD EoS for the partonic phase

PParton-arton-HHadron-adron-SString-tring-DDynamics (ynamics (PHSDPHSD))

QGP phase described by input from theQGP phase described by input from the

DDynamical ynamical QQuasiuasiPParticle article MModelodel (DQPMDQPM)

Transport theoryTransport theory: off-shell Kadanoff-Baym equations for the : off-shell Kadanoff-Baym equations for the Green-functions GGreen-functions G<<

hh(x,p) in phase-space representation (x,p) in phase-space representation

for thefor the partonic partonic andand hadronic phase hadronic phase

Interacting quasiparticlesInteracting quasiparticles

Entropy density of interacting bosons and fermionsEntropy density of interacting bosons and fermions (G. Baym 1998):(G. Baym 1998):

gluonsgluons

quarksquarks

antiquarksantiquarks

with with ddgg = 16 = 16 for 8 transverse gluons and for 8 transverse gluons and ddqq = 18 = 18 for quarks with 3 colors, 3 for quarks with 3 colors, 3

flavors and 2 spin projectionsflavors and 2 spin projections

Gluon propagator: Gluon propagator: ΔΔ-1-1 =P =P22 - Π - Π gluon self-energy: gluon self-energy: Π=MΠ=M22-i2γ-i2γggωω

Quark propagator Quark propagator SSqq-1-1 = P = P22 - Σ - Σqq quark self-energy: quark self-energy: ΣΣqq=m=m22-i2γ-i2γqqωω

Simple approximations Simple approximations DQPM: DQPM:

cf. talk by B. Kämpfer

The Dynamical QuasiParticle Model (DQPM)The Dynamical QuasiParticle Model (DQPM)

Spectral functions forSpectral functions for partonic degrees of freedom partonic degrees of freedom (g, (g, q, qq, qbarbar):):

quark mass:quark mass:

gluon width:gluon width:

quark width:quark width:

with with E2(p)= p2 + M2 - γ2

NNcc = 3 = 3

Peshier, Cassing, PRL 94 (2005) 172301;Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

new:

new !

new !

The running coupling gThe running coupling g22

3 parameters:3 parameters: TTss/T/Tcc=0.46; c=28.8; =0.46; c=28.8; =2.42=2.42

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

2.5

T/TC

N=8

S(T)

Quasiparticle propertiesQuasiparticle properties (N(Nff=3; T=3; Tcc = 0.185 GeV) = 0.185 GeV)

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1 2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

gluons

g

. TC/T

M. TC/T

[GeV

]

T/TC

quarks

q

. TC/T

m. TC/T

T/TC

lQCD

Fit to lattice (lQCD) entropy density:Fit to lattice (lQCD) entropy density:

huge widthhuge widthfor gluons !for gluons !

large widthlarge widthfor quarks !for quarks !

Differential quark ‚density‘Differential quark ‚density‘

Example:Example:

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

Quarks: I(,p)T=1.05 T

C

time-like

space-likep=

p [GeV/c]

[G

eV]

1E-5

2.8E-5

4.6E-5

6.4E-5

8.2E-5

1E-4

0 1 2 3 4 50

1

2

3

4

5p=Quarks: I(,p)

T=3 TC

time-like

space-like

p [GeV/c]

[G

eV]

5E-4

1.4E-3

2.3E-3

3.2E-3

4.1E-3

5E-3

Large space-likeLarge space-like contributions for broad quasiparticles ! contributions for broad quasiparticles !

Time-like and space-like energy densitiesTime-like and space-like energy densities

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

T00

T00

T00

TC=0.185 GeV

ener

gy d

ensi

ty(T

C/T

)4 [G

eV f

m-3] gluons

T/TC

T00

T00

T00

TC=0.185 GeV

quarks

T/TC

space-like energy densities dominate except close to Tc ! space-like parts are identified with potential energy densities!

x:x: gluons, quarks, antiquarks gluons, quarks, antiquarks

Potential energy per time-like partonPotential energy per time-like parton

Potential energy:Potential energy:

Plasma parameters:Plasma parameters:

1 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1 100

1

2

3

4

5

6

=<

V>

/<T

kin>

Vqq

/Nq

+. T

C/T

Vgg

/Ng

+. T

C/T

# [G

eV]

T/TC

gluons

quarks

T/TC

Partonic liquid should persist at Partonic liquid should persist at LHC !LHC !

huge !huge !

liquidliquid

gasgas_________________

Potential energy versus parton densityPotential energy versus parton density

Potential energy:Potential energy:

Parton density:Parton density: Gluon fraction:Gluon fraction:

1 10 100 10000

1

2

3

4

5

6

7

8

9

10

1 10 100 1000

0.18

0.20

0.22

0.24

0.26

0.28

0.30

fit

glu

on f

ract

ion

V/P

P [fm-3]

# [G

eV]

P [fm-3]

fit

PHSDPHSD

Self-energies of time-like partonsSelf-energies of time-like partons

1 10 100 10000

5

10

15

20

10 100 10001.8

1.9

2.0

2.1

2.2

2.3

rati

o

Uq

Ug

P [fm-3]

U [

GeV

]

P [fm-3]

Ug/U

q

gluonsgluons

quarksquarks

PHSDPHSD

Effective 2-body interactions of time-like partonsEffective 2-body interactions of time-like partons

22ndnd derivatives of derivatives ofinteraction densitiesinteraction densities

1 10 100 1000

-0.4

-0.2

0.0

0.2

0.4

0.6

10 100 10000

1

2

3

4

5

6

7

qq

gg

qg

P [fm-3]

inte

ract

ion

stre

nght

[G

eV f

m3 ]

P [fm-3]

qg

/qq

gg

/qq

effective interactions turn strongly attractive below 2.2 fmeffective interactions turn strongly attractive below 2.2 fm -3-3 ! ! PHSDPHSD

9/4

Transport properties of hot glueTransport properties of hot glue

viscosity ratio to entropy density:viscosity ratio to entropy density:

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.1

1pQCD

1/4 T = 2 T

C

Nf=0

/s

g [GeV]

Why do we need broad quasiparticles?

PHSD: PHSD: the partonic phasethe partonic phase

Partonic phase:Partonic phase: Degrees of freedom:Degrees of freedom: quarks and gluons (= quarks and gluons (= ‚dynamical quasiparticles‘)‚dynamical quasiparticles‘) (+ hadrons)(+ hadrons) Properties of partons:Properties of partons:

off-shell spectral functionsoff-shell spectral functions (width, mass) defined by DQPM (width, mass) defined by DQPM EoS of partonic phase: EoS of partonic phase: from lattice QCD from lattice QCD (or DQPM)(or DQPM)

• elastic parton-parton interactions:elastic parton-parton interactions: using the effective cross sections from the DQPM

• inelastic parton-parton interactions:inelastic parton-parton interactions: quark+antiquark (flavor neutral) <=> gluon (colored) gluon + gluon <=> gluon (possible due to large spectral width) quark + antiquark (color neutral) <=> hadron resonances Note: inelastic reactions are described by Breit-Wigner cross sections determined by the spectral properties of constituents (q,qbar,g) !

• off-shell parton propagation:off-shell parton propagation: with with self-generated potentials Uself-generated potentials Uqq, U, Ugg Cassing, E.B. arXiv:0808.0022 [hep-ph] PRCCassing, E.B. arXiv:0808.0022 [hep-ph] PRC

Cassing, arXiv:0808.0715 [nucl-th] EPJCassing, arXiv:0808.0715 [nucl-th] EPJ

PHSD: hadronizationPHSD: hadronization

HadronizationHadronization happens:happens:

• when the when the effective interactions become attractiveeffective interactions become attractive <= from <= from DQPMDQPM

• for for parton densitiesparton densities 1 < 1 < P P < 2.2 fm< 2.2 fm-3 -3 ::

gluons gluons q + qbar q + qbar q + qbar q + qbar meson meson q + q +q q + q +q baryon baryon

<= from DQPM<= from DQPMand recomb. modeland recomb. model

Note:Note: nucleon: nucleon: parton density parton density PP

= N= Nq q / V/ VNN=3 / 2.5 fm=3 / 2.5 fm33=1.2 fm=1.2 fm-3-3

meson:meson: parton density parton density PPmm

= N= Nq q / V/ Vmm = 2 / 1.2 fm= 2 / 1.2 fm33=1.66 fm=1.66 fm-3-3

Parton-parton recombination rate Parton-parton recombination rate = probability to form bound state = probability to form bound state during fixed time-interval during fixed time-interval t in volume t in volume VV::

ΔVji,

2Pqq

4

|ρV|fluxΔV

1

ΔVΔt

Pd

Matrix element increases drastically for Matrix element increases drastically for PP->0 => ->0 => => => hadronization successful !hadronization successful !

Based on DQPM: Based on DQPM: massive, off-shell quarks and gluons massive, off-shell quarks and gluons with broad spectralwith broad spectral functions hadronize tofunctions hadronize to off-shell mesons and baryons:off-shell mesons and baryons:

2Pqq

|ρV| 0ρ

4

P|

ΔVΔt

Pd

Hadronization rate

Local off-shell transition rate: (meson formation)

using

Wm: Gaussian in phase space

Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008

PHSD: hadronization (continued)PHSD: hadronization (continued)

Conservation lows:Conservation lows: 4-momentum conservation4-momentum conservation invariant mass and momentum of meson invariant mass and momentum of meson flavor current conservationflavor current conservation quark-antiquark content of meson quark-antiquark content of meson color + anticolor color + anticolor color neutralitycolor neutrality

• large parton masses large parton masses dominant production of vector mesons dominant production of vector mesons or baryon resonances (of finite/large width)or baryon resonances (of finite/large width)• resonance state (or string)resonance state (or string) is determined by the weight of its is determined by the weight of its spectral functionspectral function at given invariant mass M at given invariant mass M

• hadronic resonances are propagated in HSD (and finally decay to thehadronic resonances are propagated in HSD (and finally decay to the groundstates by emission of pions, kaons, etc.) groundstates by emission of pions, kaons, etc.) Since the partons are Since the partons are massive the formed states are very heavy (strings)massive the formed states are very heavy (strings) entropy productionentropy production in the hadronization phase !in the hadronization phase !

Hadronic phase:Hadronic phase:

hadron-string interactions –> hadron-string interactions –> off-shell transport in HSDoff-shell transport in HSD

Expanding partonic fireball IExpanding partonic fireball I

Initial condition:Initial condition: Partonic fireball at Partonic fireball at temperature 1.7 Ttemperature 1.7 Tcc with with

ellipsoidal gaussian shape in coordinate spaceellipsoidal gaussian shape in coordinate space

0 2 4 6 8 10 12

0

500

1000

1500

2000

2500

3000

V

Em

TP

EB +B

Etot

ener

gy [

a.u.

]

time [fm/c]

0 2 4 6 8 10 12

0

200

400

600

800

1000

1200

1400

1600

gluonsB +B

q +q

mesons

num

ber

time [fm/c]

Eccentricity:Eccentricity: ε = (σε = (σyy22 – σ – σxx

22)/(σ)/(σyy22 + σ + σxx

22))

ε = 0

energy conservationenergy conservation partons and hadronspartons and hadrons

More hadrons in the final state than initial partons !More hadrons in the final state than initial partons !

Expanding fireball IIExpanding fireball II

2 4 6 8 10

2

4

6

8

10 time: 1 fm/c

z

x

0

2.500

5.000

7.500

10.00

12.50

15.00

17.50

20.00

22.50

25.00

2 4 6 8 10

2

4

6

8

10 time: 3 fm/c

z

x

0

2.000

4.000

6.000

8.000

10.00

12.00

14.00

16.00

18.00

20.00

2 4 6 8 10

2

4

6

8

10 time: 5 fm/c

z

x

0

0.8000

1.600

2.400

3.200

4.000

4.800

5.600

6.400

7.200

8.000

2 4 6 8 10

2

4

6

8

10 time: 1 fm/c

z

x

0

12.00

24.00

36.00

48.00

60.00

72.00

84.00

96.00

108.0

120.0

2 4 6 8 10

2

4

6

8

10 time: 3 fm/c

z

x0

25.00

50.00

75.00

100.0

125.0

150.0

175.0

200.0

225.0

250.0

2 4 6 8 10

2

4

6

8

10 time: 5 fm/c

zx

0

25.00

50.00

75.00

100.0

125.0

150.0

175.0

200.0

225.0

250.0

Time-evolution of parton densityTime-evolution of parton density

Time-evolution of hadron densityTime-evolution of hadron density

Expanding grid: Expanding grid: Δz(t) = ΔzΔz(t) = Δz00(1+a t) !(1+a t) !

-8.75 fm

-8.75 fm

8.75 fm

8.75 fm

10 fm 12 fm

10 fm 12 fm

8.75 fm

Dynamical informationDynamical information

effective cross sectionseffective cross sections from the DQPM from the DQPMversus parton densityversus parton density

become low at high parton densitybecome low at high parton densitybut interaction rate slightly increases but interaction rate slightly increases with parton density!with parton density!

gluon decay rategluon decay rate to q+qbar to q+qbarroughly equal to glue roughly equal to glue formation rateformation rate

Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008

Hadronization versus the Statistical Model

mass distributions for color neutral ‚mesons‘ and ‚baryons‘ mass distributions for color neutral ‚mesons‘ and ‚baryons‘ after parton fusionafter parton fusion: (rotating color dipoles)

Comparison of particle ratios with the statistical model (SM):Comparison of particle ratios with the statistical model (SM):

These ‚prehadrons‘ decayThese ‚prehadrons‘ decayaccording to JETSET toaccording to JETSET to0-, 1-,1+ mesons and 0-, 1-,1+ mesons and the baryon octet/decoupletthe baryon octet/decouplet

A. Andronic 08

Expanding fireball III – collective aspectsExpanding fireball III – collective aspects

Elliptic flow vElliptic flow v22 is defined by an anisotropy in momentum space: is defined by an anisotropy in momentum space:

vv22 = (p = (pxx22 – p – pyy

22))//(p(pxx22 + p + pyy

22))

Initially: vInitially: v22 = 0 = 0 study final v study final v22 versus initial eccentricity versus initial eccentricity ε !ε !

vv22//ε = const. ε = const.

indicates hydrodynamic flow !indicates hydrodynamic flow !

This is expected sinceThis is expected since η/s is η/s is small in the DQPMsmall in the DQPM

ε = (σε = (σyy22 – σ – σxx

22)/(σ)/(σyy22 + σ + σxx

22))

Reminder: Collective flow: vReminder: Collective flow: v22 excitation function excitation function

vv2 2 excitation function from string-hadronic transport models : excitation function from string-hadronic transport models :

Proton vProton v22 at at low energylow energy very sensitive to the very sensitive to the nucleon potential !nucleon potential ! Cascade Cascade codes fail to describe the exp. data !codes fail to describe the exp. data !

vv22 is determined by attractive/repulsive potentials ! is determined by attractive/repulsive potentials !

cascade

Expanding fireball II: Differential elliptic flowExpanding fireball II: Differential elliptic flow

Time evolution of v2: Quark number scaling v2/nq:

parton vparton v22 is generated to a is generated to a

large extentlarge extent by the repulsive by the repulsivepartonic forces !partonic forces !

meson to baryon v2 indicatesquark number scaling !

Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008

Summary

• The dynamical quasiparticle model (DQPM)The dynamical quasiparticle model (DQPM) defines the transport defines the transport input for PHSD (in line with lattice QCD)!input for PHSD (in line with lattice QCD)!

• PHSDPHSD provides a consistent description of provides a consistent description of off-shell parton dynamicsoff-shell parton dynamics;;the repulsive mean fields generate a sizeable partonic flow! the repulsive mean fields generate a sizeable partonic flow!

• The dynamical The dynamical hadronizationhadronization in PHSD yields particle ratios close to in PHSD yields particle ratios close to the (GC) statistical model at a temperature of about 170 MeV!the (GC) statistical model at a temperature of about 170 MeV!

• The The elliptic flow velliptic flow v22 scales with the initial eccentricity in space as in scales with the initial eccentricity in space as in

ideal hydrodynamics! ideal hydrodynamics!

• The The scaled elliptic flowscaled elliptic flow of mesons and baryons is approximately the of mesons and baryons is approximately the same as a function of the scaled transverse kinetic energy, but is smaller same as a function of the scaled transverse kinetic energy, but is smaller than the parton vthan the parton v22(p(pTT) and ) and suggests quark-number scaling!suggests quark-number scaling!

Thanks toThanks to

Elena BratkovskayaElena Bratkovskaya

Sascha JuchemSascha Juchem

Andre PeshierAndre Peshier