Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 1 International Workshop on Heavy Ion Physics at LHC Global Polarization of QGP in AA

Wuhan Workshop　2008年5月21-24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 1

International Workshop on Heavy Ion Physics at LHC Global Polarization of QGP in AA Collision

Liang Zuo-tang Shandong University

References: Z. Liang and X.N. Wang, Phys. Rev. Lett. 94, 102301 (2005); Phys. Lett. B629, 20 (2005); J. Gao, S. Chen, W. Deng, Z. Liang, Q. Wang, X.N. Wang, Phys. Rev. C77, 044902 (2008) .


Outline

Introduction Global polarization of quarks and anti-quarks Direct consequences: I. Hyperon polarization II. Vector meson spin alignmentMeasurements at RHICOutlook for LHC Summary


IntroductionIntroduction

1989: Proton’s spin crisis; Since 1970s: Hyperon polarization in unpolarized p+p/AH+X; Since 1970s: Single-spin left-right asymmetry in p()+p+X; Since 1970s: Spin analyzing power in p()+pp+p; Spin transfer in fragmentation process; J/ polarization in p+p J/+X; … … …

Spin effects usually provide us with useful information on reaction mechanism and often surprises. Many examples … … … …


IntroductionIntroduction

Do spin physics in AA collisions without polarizing A ?

heavy ion collider

polarized pp collider

heavy ion physics

spin physics

spin physics in heavy ion collisions ?RH

IC


Global Orbital Angular Momentum

Yb

Huge orbital angular momentum of the colliding system.reaction plane: can be determined by measuring v2 and v1.

normal of the reaction plane

impact parameter|| bp

bpn

in

inre

-L

y in

unit

of 1

05b/RA


Global orbital angular momentum

Gradient in pz-distribution along the x-direction

x

zimpact parameter b


Gradient in pz-distribution along x-direction

GeVscsp 22.2)(2/0

Au+Au at 200AGeV

p z(x,b

) in

unit

of p

0

GeV/fm68.0/2 0 ARpdp

z\dx in

uni

t of 2

p 0\RA



GeVscsp 22.2)(2/0

Au+Au at 200AGeV

p z(x,b

) in

unit

of p

0

GeV/fm68.0/2 0 ARpdp

z\dx in

uni

t of 2

p 0\RA

Hard sphere nuclear matter distribution

Landau fireball model: equal pz of partons produced at a given x.



Hard sphere vs Woods-SaxonLandau fireball model: equal pz of partons produced at a given x.



Bjorken Scaling limit: a parton interacts only with other partons within the same region of width Δy.

Results from HIJING


Local Orbital Angular Momentum

x

xdxdp

p zz

7.1 xpL zy

for b =RA, x=1fm

Tximpact parameter of t

he two partons Tx

has a preferred direction ( ) !b


Questions

What do we expect to see if such partons interact with each other?

Can such a local orbital angular momentum be transferred to the polarization of quark or anti-quark through the interactions between the partons in a sQGP?


Quark scattering with fixed reaction plane

Scattering amplitude in momentum space ),(, EqM Ti

spin independent part

Differential cross section w.r.t. the impact parameter

spin dependent part

Tx

),(),(21

)2()2(*

,,)(

2

2

2

2

2 EqMEkMekdqd

xdd

TTxqkiTT

Tii

i

TTT

Txdd

2

T

unp

xdd

2

Quark polarization after the scattering: unpqP /

a 2-dimensional Fourier transformation to impact parameter space

average over the preferred directions Tx


Qualitative results

),(4 20

22 TDsT

T

unp xKcxd

d

Static potential model with “small angle approximation”

Both have exactly the same form !

)()(4)(

)( 102

2 TDTDsTq

DT

T

xKxKcmEE

pxpn

xdd

Bessel functions

)(2222 Tsqq

TTT

unp xFcxd

dxd

dxd

d

QCD at finite temperature with HTL(hard thermal loop) gluon propagator

)( )( 2222 TsqqT

TTT

xFcxpnxd

dxd

dxd

d

scalar functions of xT

spin direction of the quark after the scattering


Qualitative results

)(2 T

T

xpnxd

dΔ

has a preferred direction

Tx

b has a preferred

directionTxp

bpn inre

re

TT

nnxd

dΔ

xd

dΔ

at 22max

a polarization of quark in the direction opposite to the normal of the reaction plane!

normal of the AA-reaction plane


Quantitative results with QCD at finite temperature

- Quar

k po

lariz

atio

n P q

:T temperature

Tpz /

See next talk by Q. Wang


A new picture of QGP in non-central AA collisions

fp

p

Tx

ren

The scattered quark acquiresa negative polarization in thenormal direction of the reaction plane! global polarization


Direct consequences

XVHqqZee )or (0Compare to:

global polarization of quarks & anti-quarks

polarization of hadrons

hadronization

OPAL XKee 0*

00 : probability for the third component of the spin of K*0 to take zero.

00=1/3: unpolarized

In a non-central AA collision:

Vector meson spin alignment Λ longitudinal polarization


Consequence I: Hyperon polarizationRecombination scenario q1

+q2+q3

H

ssdudu PPPPPP

Hyperon

PH Ps

PH in the case that Pq = Ps

Pq Pq Pq Pq

We expect . , ssqdudu PPPPPPP

.' and ' allfor s HsHPP qH

In the case that

2

2

4334

qsq

qssq

PPPPPPP

2

2

4334

ssq

qsqs

PPPPPPP

)1(3)5(

2

2

s

ss

PPP


Consequence I: Hyperon polarization

Fragmentation scenario q H + X.

Hyperon

PH

PH in the case of Pq =Ps

PH in the case of Pq =Ps and ns =fs

ss

ss

fnPn2 )2(3

4

ss

ssqs

fnPnPf

)2(34

ss

qsss

fnPfPn

3sP

qss

s Pfn

n2 q

ss

ss Pfn

nf)2(3

4

qss

ss Pfn

fn)2(3

4

3sP

3qP

QGP in quarksfor :1:1:: ssdu nNNN

ionfragmentat in produced quarksfor :1:1:: ssdu fNNN

3qP

3qP

3qP


Vector meson spin alignment

Polarization of vector meson is described by

1001111

111011

100001

111011

||

gVSpin density matrix:

: probability for third component m=1,-1 or 0001111 ,,

Unpolarized: 3/1001111

ρ00 can be measured and the spin of vector is aligned if 3/100


Consequence II: Vector meson spin alignment

XVqXVq or

XVqXVqfragV or for 3/1)(

,31

2

2)(

00q

qfrag

PP

,31

31

2

2

2

2)*(

00s

s

ss

s

q

q

ss

srecK

PP

fnn

PP

fnf

In analog to XKqqZee *0

5.0

for 3/1)(00 VqqrecV

,31

2

2)(

00q

qrec

PP

,31)*(

00sq

sqrecK

PPPP

ρ

Fragmentation scenario

Recombination scenario Vqq 21


More recent theoretical studies1) Barbara Betz, Miklos Gyulassy, Giorgio Torrieri, “Polarization probes of vorticity in heavy ion collisions”, Phys.Rev.C76:044901,2007. arXiv:0708.0035 [nucl-th] 2) Andreas Ipp, Antonino Di Piazza, Jorg Evers, Christoph H. Keitel, “Photon polarization as a probe for quark-gluon plasma dynamics”

arXiv:0710.5700 [hep-ph] 3) F. Becattini, F. Piccinini, J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy”, Phys.

Rev.C77:024906,2008. arXiv:0711.1253 [nucl-th] 4) Shou-wan Chen, Jian Deng, Jian-hua Gao, Qun Wang, “ A General derivation of differential cross-section in quark-quark scatterings at fixe

d impact parameter”. arXiv:0801.2296 [hep-ph] ………………………..

See also next talk by Q. Wang


Polarization of photon

Andreas Ipp, Antonino Di Piazza, Jorg Evers, Christoph H. Keitel, “Photon polarization as a probe for quark-gluon plasma dynamics” arXiv:0710.5700 [hep-ph]


Ideal rotating quark gas

F. Becattini, F. Piccinini, J. Rizzo, “Angular momentum conservation in heavy ion collisions at ver

y high energy”, Phys.Rev.C77:024906,2008; arXiv:0711.1253 [nucl-th]


International Workshop on Heavy Ion Physics at LHC

Measurements already carried out at RHIC


Can we measure such polarization?Determination of hyperon polarization

)cos1(41 *

* HP

ddN

Spin self-analyzing parity violating weak decay HB+M.

E.g.: p -; α=0.642.

angle between direction of motion of B and polarization direction of H in the REST frame of H.

polarization of H.


Experimental studies at RHICLambda polarization

Ilya Selyuzhenkov for STAR: QM2005; SQM2006; CIPANP 2006; QM2006; Xi’An 2006;

STAR Paper, Phys.Rev.C76:024915,2007. arXiv:0705.1691 [nucl-ex]


Measurement of Vector meson spin alignment

Polarization of vector meson is described by

pUUpNpUUpgNddN V |ˆˆ||ˆ||ˆ|*

Consider the decay process of V into 2 spin 0 mesons: VM1+M2 , again in the rest frame of V, the decay amplitude is given by:

111011

100001

111011

||

gVSpin density matrix:

Angular distribution:

mlpconstmsUmlmlpmsUppA VV ,|*,|ˆ|,,|*,|ˆ|**)(

pUmsmsmsmsUpN VVV

VVmm

|ˆ|',',||,,|ˆ|

',

)( Vsl


Measurement of Vector meson spin alignment

No need to determine the direction of reaction plane!

Vector meson: strong decay VM1+M2.*2

0000* cos)13()1[(83

VV

ddN

)ImsinRe(cos2sin2 0,1*

0,1** VV

)ImsinRe(cos2sin2 0,1*

0,1** VV

)]Im2sinRe2(cossin2 1,1*

1,1**2 VV

Integrated over ]cos)13()1[(43

cos*2

0000*

VV

ddN


Experimental studies at RHIC

Vector meson spin alignment

J. Chen for STAR, QM2006, J.Phys.G34:S331-S336,2007.

Z. Tang for STAR, Xi’An 2006. High Ener. Phys. & Nucl. Phys.

STAR Paper, 0801.1927[Nucl-ex]


RHIC vs LHC

Global orbital angular momentum of the colliding system

LHCRHIC


RHIC vs LHCLocal orbital angular momentum of two partons at x=1fm

LHCRHIC

Landau fireball model


Outlook at LHC


GeVscsp 22.2)(2/0

LHCRHIC

RHICLHC pscsp ,0,0 9~)(2/

Landau fireball model


RHIC vs LHC: Quark Polarization

,4.0~ GeVT

x

,17.0~ GeVpz

For b =RA ,

Tpz /

Much More Significant at LHC!

! 8.1~)/(3.4~)/( RHICzLHCz TpTp RHICzLHCz pp ,, 6~

43.0~/ TpzRHIC:LHC: RHICLHC TT 3/13~

Near the peak region!

RHIC

LHC

(Landau fireball model)mx /1~


Summary A great advantage to study spin effects in non-central AA-collisions i

s: the reaction plane can be determined experimentally by measuring v1 and v2.

There exists a huge orbital angular momentum of the colliding system w.r.t. the reaction plane and quarks and anti-quarks can be polarized in that direction due to spin-orbital interaction in QCD.

Many consequences, first data are obtained at RHIC. The effects should be more significant at LHC.

Thank you for your attention!

Documents

Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 1 International Workshop on Heavy Ion Physics at LHC Global Polarization of QGP in AA