Workshop on Quark-gluon Thermalization Vienna, August 10-12, 2005

In collaboration with Zuo-tang Liang

Xin-Nian Wang/LBNL

Thermalization and Globally Polarized QGP in Non-central Heavy-ion Collisions

Instability and Cerenkov Radiation

Phys. Rev. Lett. 94 (2005)102301

Direct Signs for Thermalization

<pT> from away jets

<pT> from medium decay

Leadinghadrons

Medium

Fuqiang Wang

Global Orbital Angular Momentum

xz

y

Low-energy nuclear collisions:

Stiff EOSP~ E

Rotationand deformed nuclei

xz

y

p

A

0-2 2-4 4

Global Orbital Angular Momentum

xz

y

xz

y

High-energy Nuclear Collisions

Nuclei Are Spherical !

3D distribution of multiplicity and

Momentum

Heinz & Kolb’04Adil & Gyulassy’5

Transverse Gradient of Shear Velocity

,P TpartdN

dx

Distribution of number of participant projectile ortarget nucleons

( , )2

( )

Ppart

Pp

Tpart

Tpartart

z

dN

dxd

ds

p x bN

N

dxdN

dxxs

dc

Collectivelongitudinalmomentumper producedparton

x

zb

Local Orbital Angular Momentum

(x-b

/2)/

RA

zz

dpp x

dx

2 zy z

dpL x p x

dx 0 0.34 GeV/fm

2 ( ) A

dp s

dx c s R

x

Quark Scattering with fixed Ly

, ( ) ( ) ( ) ( )2i iT f T

igM q u p A q u p

E

02 2

1( )T

T

A qq

2 2

2

2 2 2 2 2,

1 1( )

(2 ) 2 ( )i

TT T

d gM q C

d q q

Screened static potential model:

20 0 ( ) ( )( ) ( ) 1

2 2 ( )T T

T Tq

g q k n pI A q A k i

E E m

: final quark spin

xT

p

n

pf

2 2( ) †

, ,2 2 2

1( ) ( )

(2 ) (2 ) 2T T T

i i

i

i k q xT TT T T

T

d d q d kC e M q M k

d x

I

Quark Polarization

2 202 2 2

4 ( )T s TT T T

d d dC K x

d x d x d x

4 ( )qq

pP

E E m

Unpolarized cross section:

20 12 2 2

ˆ( )4 ( ) ( )

( )T

T s T TT T T q

d d d p x nC K x K x

d x d x d x E E m

Polarized cross section:

0 0.34 GeV/fm2 ( ) A

dp s

dx c s R

( ) 45 at RHICc s 1

0.5 GeVx

0. 3qP

Semi-central: b=RA

xT

p

n

pf

A New Picture of A+A

Spin-orbital coupling

2

nonrelativistic limit: ( , )

8

q

qq

m p

pP

m

4 ( )qq

pP

E E m

02

1

LSq

dVE L s

dr r m

200

1,

dV pE L

r dr

0

LSq

EP

E

xT

p

n

pf

Consequences

Single-spin asymmetry:

Polarized thermal dilepton, J/Hyperons and vector mesons

Directed flow?

Enhanced /, /pratio

Constituent Quark Recombination

sP P 2

2

4 3

3 4q s s q

q s q

P P P PP

P P P

2

2

4 3

3 4s q q s

q s s

P P P PP

P P P

2

2

5

3(1 )s

ss

PP P

P

Polarization of valence quarks + relative orbital angular momentum

Polarization of constituent quarks

0

0

1/ 2

1/ 6 2

1/ 6 2

u d u d s

s s u s s s s u

u d s u d u d s

Constituent quark model:

(l=0, color anti-symmetric)

Features of Global Hyperon Polarization

• Hyperons & anti-hyperons are similarly polarized

• PH=0 in central and increases with b

• Pq 0 for pT>> p0z, PH finite for moderate pT due to hard-soft recombination

• Contribution from directed flow at large y

Other effects

1( ) (( () () ) )

2f fM u p kS q V qk u p

P>0 P<0

Hadronic scattering:

Thoughts for the Brave…

N1

N2

N2> N1

v2 in p+A collisions?

Summary

• Shear velocity gradient leads to global polarization if there is interaction across transverse direction due to thermalization

• A new picture of QGP structure in heavy-ion collisions:– Hyperon polarization, vector meson spin

alignment, contribution to v2

• Future work: – Quantitative evaluation of hadronic interaction – Spin transport: spintronics of strong interaction