Hydrodynamic Instabilityin the Quark-Gluon Plasma

Carlos E. AguiarInstituto de Física - UFRJ

C.E.A., E.S. Fraga, T. Kodama, nucl-th/0306041

Outline:

• Introduction; explosive hadronization

• Thermodynamics of the chiral phase transition

• Supercooling and spinodal decomposition

• Hydrodynamics of the chiral phase transition

• Fluid mechanical instability in the QGP

• Comments

Heavy Ion Collisions at High Energies

AuAu

Heavy Ion Collisions at High Energies

SPH calculation

z

t hadrons

10 fm/c

QGP

mixedphase

Explosive Hadronization?

22pair

2side

2out )(VRR

1R/R sideout 0 sudden emission

• HBT radii:

SPSRHIC

___ strong 1st order...... weak 1st order- - - crossover

D. Zschiesche et al. Phys. Rev. C 65 (2002) 064902

The Phase Diagram of Strongly Interacting Matter

T

922 MeV

150 MeV

QGP

Hadrons

crossover

supercooling

Lattice QCD and Freezeout States

Z. Fodor and S. D. Katz, Phys. Lett. B 534 (2002) 87, JHEP 0203 (2002) 014

RHIC

SPS

Thermodynamics of theChiral Phase Transition

Linear sigma model

)(U2

1qigiqL 05

),(,)d,u(q

hv

4)(U

22222

0

fgm,mm

m3mfv,

f2

mm,mfh q22

2222

2

222

3.3g,MeV 600m,MeV 138m,MeV 93f

Partition function

Effective potential

V

0q

3T/1

0

qqLxd)ti(dexpDDqqDTNHexpTrZ

)3/( q

ZlnV

T),T(U PV/U

• mean field approximation: <>

)(T/)E(exp1ln)2(

pdT)(U),,T(U qqq3

3

q0

2q

2 mpE 222222q ggm

Effective Potential

-20 0 20 40 60 80 100 120 (M eV)

-120

-100

-80

-60

-40

-20

U (

Me

V/fm

3 ) T = 105 M eV

118 M eV

130 M eV

= 500 M eV

-20 0 20 40 60 80 100 120 (M eV)

-50

-40

-30

-20

-10

0

U (

MeV

/fm

3 )

T = 41 M eV

49.9 M eV

57 M eV

63.5 M eV

69 M eV

= 800 M eV

crossover1st order

Supercooling and Spinodal Decomposition

-20 0 20 40 60 80 100 120 (M eV)

-120

-100

-80

-60

-40

-20

U (

Me

V/fm

3 ) T = 105 M eV

118 M eV

130 M eV

= 500 M eV

-20 0 20 40 60 80 100 120 (M eV)

-50

-40

-30

-20

-10

0

U (

MeV

/fm

3 )

T = 41 M eV

49.9 M eV

57 M eV

63.5 M eV

69 M eV

= 800 M eV

crossover1st order

Pressure and Chiral Field

4 0 5 0 6 0 7 0tem perature (M eV)

2 0

3 0

4 0

5 0

pre

ssur

e (M

eV

/fm3 )

0 40 80 120 160tem perature (M eV)

0

20

40

60

80

100

sigm

a fi

eld

(M

eV

)

= 800 M eV

sh

sc

First order

Mesons

2

22

2

22 U

m,U

m

0 40 80 120 160T (M eV)

0

200

400

600

800

m

(M

eV)

0 40 80 120 160T (M eV)

0

200

400

600

800

m

(MeV

)

= 800 M eV

First order

Pressure and Chiral FieldCrossover

0 40 80 120 160 200tem perature (M eV)

0

200

400

600

pres

sure

(M

eV/f

m3)

0 40 80 120 160 200tem perature (M eV)

0

20

40

60

80

100

sigm

a fie

ld (

MeV

)

= 500 M eV

Mesons

Crossover

0 40 80 120 160 200T (M eV)

0

200

400

600

800

m

(M

eV)

0 40 80 120 160 200T (M eV)

0

200

400

600

800

m

(MeV

)

= 500 M eV

Chiral Phase Diagram

400 600 800 1000chem ical potentia l (M eV)

0

40

80

120te

mpe

ratu

re (

MeV

)

chiralsymmetry

broken chiralsymmetry

spinodalline

T-n Diagram

0 0.1 0.2 0.3

baryon density (1 /fm 3)

0

40

80

120te

mpe

ratu

re (

MeV

)

spinodal

chiralsymmetry

brokensymmetry

Hydrodynamics of the Chiral Phase Transition

),s,n(2

1xdA 4

nTsUdensityenergy ),s,n(

1uu

0)us(

0)un(

constraints: baryon number conservation entropy conservation flow velocity normalization

Action:

Chiral Hydrodynamics

),,T(UR

Pguu)P(T

R

RT

0)un(

0)us(

Wave Motion

Perturbation ofequilibrium:

k//v1

Linearizedequations:

)k,(K

0

),n/s,(PP

0

),n/s,(RR

101222 vRw

kmk

0mk 1222

1122 RkvkP

xKi10 e)x(

xKi10 euu)x(u

00 )P(w

Chiral and Sound Modes

220

22222 kRwmkkP

Dispersion relation

Long wavelengths

22

202

s km

RwP

22 m

sound waves:

chiral waves:

Hydrodynamic Instability

0m

RwP

2

20

If

then s2 < 0, and the sound modes become

unstable, growing exponentially instead of propagating. This instability occurs before the chiral spinodal line (m

2 = 0) is reached.More importantly, the crossover region (m

2 0) is unstable.

Hydrodynamic Instability in the QGP

0 200 400 600 800 1000chem ical potentia l (M eV)

0

40

80

120

160te

mp

erat

ure

(M

eV)

instabilityline

spinodal

Instability Line in the T-n Plane

0 0.1 0.2 0.3

baryon density (1 /fm 3)

0

40

80

120

160te

mpe

ratu

re (

MeV

)instability

line

In summary:

• The nonequilibrium chiral condensate changes qualitatively the hydrodynamical behavior of the QGP

• Explosive hadronization doesn’t need spinodal decomposition, and can occur even in the crossover region.

Final comments:

• This is a very general effect; it doesn’t depend on specific aspects of the sigma model.

• The instability develops even for very slow cooling, contrary to spinodal decomposition.

• Finite size effects may be important in nuclei: min ~ 5 fm at the critical point

• Implications for the hadronization process in: heavy ion collisions (?) early universe (!)