Color Instabilities in Quark-Gluon Plasma Stanisaw Mrwczyski Jan - - PowerPoint PPT Presentation

1

Color Instabilities in Quark-Gluon Plasma

Jan Kochanowski University, Kielce, Poland & Institute for Nuclear Studies, Warsaw, Poland

Stanisław Mrówczyński

2

• ver 30 years
• St. Mrówczyński,

Stream instabilities of the quark-gluon plasma, Physica Letters B 214, 587 (1988), Erratum B 656, 273 (2007)

• St. Mrówczyński,

Plasma Instability at the initial stage of ultrarelativistic heavy-ion collisions, Physics Letters B 314, 118 (1993)

• St. Mrówczyński and M. Thoma,

Hard loop approach to anisotropic systems, Physical Review D 62, 036011 (2000)

• St. Mrówczyński, B. Schenke and M. Strickland,

Color instabilities in the quark-gluon plasma, Physics Reports 682, 1 (2017)

 

1)

2) 5) 17)



3

Elementary Physics Story

• n Color Instabilities

in Quark-Gluon Plasma

4

Hadrons, Quarks & Gluons

baryons mesons

 

q q q , ,

 

q q, , , , , K      , , , , , , , ,

*

     N p n

5

Confinement

Electrodynamics Chromodynamics    

2 2

e e E r V r r r     r

Gauss law

   

4 4 g g E r V r r        4 E g      r   const

2

1 1 , 0, 8 8 D E u ED E            

• K. Kogut & L. Susskind, Phys. Rev, D 9, 3501 (1974)

H.B. Nielsen & P. Olesen, Nucl. Phys. B 61, 45 (1973)

energy density

6

Confinement cont.

 

V r r

2

2

q

m c

Coulomb linear The potential is studied in spectroscopy of heavy quarkonia.

7

Asymptotic Freedom

1 1 c t c t              D B B E D H

    D E B H

Sourceless Maxwell equations in a medium

2 2 2 2 2 2

c t c t                         E B

c 

phase velocity of EM wave



in vacuum

1  

 

2 2 2 QCD

12 ( ) 33 2 ln

f

Q s Q N 



          

Color charge vanishes at small distances

8

Asymptotic Freedom cont.

1  

1  

paramagnetic



1   1  

diamagnetic



1  

dielectric paraelectric charges are screened charges are antiscreened! Quarks of spin ½ produce diamagnetic effect Gluons of spin 1 produce paramagnetic effect

Gluons win!

• G. ’t Hooft, unpublished
• N. K. Nielsen, Am. J. Phys. 49, 1171 (1981)

9

Creation of Quark-Gluon Plasma

compression of nuclear matter heating up hadron gas

3

~ T 

hadron density 1 fm

3

0.12 fm 



 natural system of units:

B

c k   

m T

 

normal nuclear density

10

Hadron Gas Quark-Gluon Plasma

Color Superconductor

B

 T

~ 180 MeV baryon density

nuclei



3

fm 12 .





B



critical point

Phase diagram of strongly interacting matter

11

T

density of molecules

critical point

gas liquid gas & liquid supercritical vapor solid





triple point

 T

Schematic phase diagram of water

12

Relativistic heavy-ion collisions

before after

t z

equilibration hadronization freeze-out free hadrons quarks & gluons hadrons

time

An important role of boost invariance

2 2

t z   

13

Quark-Gluon Plasma vs. EM Plasma

Quark-Gluon Plasma Electromagnetic Plasma

Underlying Microscopic Theory

QCD QED

Elementarny Interactions Constituents Fermions

quarks, antiquarks electrons, positrons

Massless Gauge Bosons

gluons photons

• massive ions

Coupling



e e

137 1 4

2

    e

1 1 . 4 ) (

2 2

     g Q

g

q q

g

g g g g g g

14

Ultrarelativistic Quark-Gluon Plasma

T mq 

Plasma constituents – quarks & gluons – are massless! Temperature T is often the only dimensional parameter.

3

~ T 

density:

1

~ l T 

inter-particle spacing:

4

~ T 

energy density:

4

~ p T

pressure:

15

Weakly Coupled Quark-Gluon Plasma

Plasma from the earliest stage of relativistic heavy-ion collisions is assumed to be weakly coupled.

 

2 2 2 QCD

12 ( ) 33 2 ln

f

Q s Q N 



           Asymptotic freedom formula: Dimensional argument:

1 / 4

Q    - energy density

16

Plasma manifests collective behavior

gT mD

D

1 ~ 1  

screening length Debye sphere

1 if 1 1 ~ , ~ , 1 ~ 3 4

3 3 3 3 3

    g g V n T n T g V

D D D

In a weakly coupled plasma, there are many particles in a Debye sphere!

r e r V

D

r  

~ ) (

) (r V r

D



Coulomb screened

17

Screening length

( ) ( ) V e    r r

Poisson equation

( )

( ) 1

eV T

e  



       

r

r

( )

( ) ( ) 1 1 1

eV T

eV eV e T T



     

r

r r 

( ) e V T  r

2

( ) ( ) ( ) e V e V T       r r r

2 2 2

( ) ( ) ( ) ~

D

m x D

d V x m V x V x e dx



 

1 ~

D D

m e eT T    

Debye mass

charge density ( ) r 

r

3 0 ~ T



18

Plasma oscillations

E

charge fluctuation

) ) ( cos( ) , (       r k k E r E t t

( ) ~

p

gT    k

plasma or Langmuir frequency

 k

19

Plasma frequency

x x

E e x  

s

Q  

Gauss theorem

ES  

E  E  E 

s

Q e Sx  

flux charge

M x F  

M mSl  

l

Equation of motion

F QE 

electric field mass force charge Q

e Sl  

2 p

x x    

p

e m   

~

p

gT 

Harmonic oscillator Quark-gluon plasma

e g 

3

~ T 

~ m T

plasma frequency

  

20

Landau damping

) cos( ) , ( kx t E x t E x    k v  

 Resonance energy transfer from electric field to particles with v = vφ

21

Instabilities

) ( ) ( t A A t A   

stationary state fluctuation

t

t A



  e ) (

 

Instability

) (t A A

unstable configuration

) (t A A

stable configuration

22

Plasma instabilities

instabilities in configuration space – hydrodynamic instabilities instabilities in momentum space – kinetic instabilities

instabilities due to non-equilibrium momentum distribution

      T E f exp ~ ) (

not is

p

23

Kinetic instabilities

longitudinal modes –

) (

e ~ , ||

kr

E k

  



t i

transverse modes –

) (

e ~ ,

kr

j E k

  

 

t i

E – electric field, k – wave vector, ρ – charge density, j – current

Which modes are relevant for QGP from relativistic heavy-ion collisions?

24

Logitudinal modes

x

p

) , , (

z y x

p p p f

plasma beam

unstable configuration

Energy is transferred from particles to fields.

25

Logitudinal modes

E px

x

k 

) , , (

z y x

p p p f

particle deceleration particle acceleration

E px

x

k 

) , , (

z y x

p p p f

particle deceleration particle acceleration

x

k 

E p x

• phase velocity of the electric field wave,
• particle’s velocity

Electric field decays - damping Electric field grows - instability

26

Parton momentum distribution in AA collisions

Longitudinal unstable modes are irrelevant for relativistic heavy-ion collisions. Momentum distribution has a single maximum and monotonously decreases in every direction.

y

p

x

p

e ˆ

There are unstable transverse modes.

27

Evolution of Parton Momentum Distribution

L

p

T

p

time

• blate

L

p

T

p

prolate

28

Seeds of instability

) ( ) ( ) 2 ( 2 1 ) ( ) (

) 3 ( 2 3 3 2 1

  



t f E p p p d x j x j

p ab b a

v x p   

   

but current fluctuations are finite

1 1 1

( , ) x t  x

Direction of the momentum surplus

) ( 

 x

ja

 2 2 2

( , ) x t  x

1 2 1 2

( , ) x t t    x x



29

Mechanism of filamentation



v v

F F



v v

F F

z

j

y

B



B v F   q

j B   

Lorentz force Ampere’s law

z

y x

30

Time scale & collisional damping

 

4 hard ~

ln 1/ g g T 

Parton-parton scattering

hard scattering: q ~ T collec collec collec

1 1 ~ ~ ~ t gT gT t  

Time scale of collective phenomena

q

soft scattering: q ~ gT

2 hard soft collec

1 g       

The instabilities are fast! Frequency of collisions

 

2 soft ~

ln 1/ g g T 

31

Growth of instabilities – 1+1 numerical simulations

SU(2) Hard Loop Dynamics

• A. Rebhan, P. Romatschke & M. Strickland, Phys. Rev. Lett. 94, 102303 (2005)

γ* - maximal growth rate

) | (| ) (

iso z

p f f    p p

10  

Anisotropic particle’s momentum distribution

) , ( z t A A

a a    1+1 dimensions

transverse magnetic

total Scaled field energy density





   

iso 2 2

) ( dp p df dpp m

s D

Strong anisotropy

32

What is the role of instabilities in nuclear collisions?

Instabilities speed up equilibration of quark-gluon plasma

33

Isotropization - particles

j F



  F p dt





B

Direction of the momentum surplus

34

Isotropization – numerical simulation

Classical system of colored particles & fields

) ( ) 2 (

3 3

p f E p p p d T

j i ij 

 

(Tyy+Tzz)/2 Txx

Isotropy:

2 / ) (

zz yy xx

T T T  

• A. Dumitru & Y. Nara, Phys. Lett. B 621, 89 (2005).

35

Isotropization - fields

Direction of the momentum surplus

k E B P ~ ~

fields a a 

E k 



B

36

Transport in unstable plasma

L

p

T

p

• blate

fastest unstable mode Test particle in unstable plasma

37

Collisional energy loss or gain

2 2

1

D

dE g m dx 

• M. Carrington, K. Deja and St. Mrówczyński, Phys. Rev. C 92, 044914 (2015)

D

m t

equilibrium value:

2 2

1 0.1

D

dE g m dx  

2   

Initial conditions are crucially important!

38

Raditive energy loss

• M. Carrington, St. Mrówczyński and B. Schenke, Phys. Rev. C 95, 024906 (2017),
• A. Dumitru, Y. Nara, B. Schenke and M. Strickland, Phys. Rev. C 78, 024909 (2008)

4    3    2    12    equilibrium plasma

D

m t

2 2

2 ˆ

D T

q g m p

equilibrium value:

2 2

2 ˆ 0.1

D T

q g m p 

ˆ

s

dE qL dx   

Radiative energy loss:

ˆ q - momentum broadening

39

Conclusions

Non-equilibrium QGP can be unstable Unstable transverse modes are relevant for AA collisions Instabilities drive equilibration Unstable QGP is highly opaque and anisotropic medium