qm2006 2006 年 11 月 14-21 日 shanghai, china 梁作堂 (liang zuo-tang) 山东大学 1 for the...

QM2006 　2006年11月14-21日 Shanghai, China　梁作堂(Liang Zuo-tang) 山东大学 1

For The 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006)

Globally polarized QGP in non-central AA collisions at high energies

References: Z. Liang and X.N. Wang, Phys. Rev. Lett. 94, 102301 (2005); Phys. Lett. B629, 20 (2005); Gao Jian-hua et al, …… in preparation.

Liang Zuo-tang Shandong University


Outline

Introduction Global polarization of quarks and anti-quarks Direct consequences:

I. Hyperon polarization

II. Vector meson spin alignment

Summary and outlook


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 ?R

HIC


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 ARp

dpz\d

x in

unit

of 2

p 0\RA


Local Orbital Angular Momentum

x

xdx

dpp z

z

7.1 xpL zy

for b =RA, x=1fm

Tximpact parameter of t

he two partons Tx

has a preferred direction ( ) !b


Question

Can such a local orbital angular momentum

be transferred to the polarization of quark or

anti-quark through the interactions between t

he partons in a QGP?


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

),(),(2

1

)2()2(*

,,)(

2

2

2

2

2 EqMEkMekdqd

xd

dTT

xqkiTT

Tii

i

TTT

Txd

d2

T

unp

xd

d2

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

2

2 TDsTT

unp xKcxd

d

Static potential model with “small angle approximation”

Both have exactly the same form !

)()(4)(

)( 102

2 TDTDsTq

DT

T

xKxKcmEE

pxpn

xd

d

Bessel functions

)(2

222 TsqqTTT

unp xFcxd

d

xd

d

xd

d

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

)( )( 2

222 TsqqTTTT

xFcxpnxd

d

xd

d

xd

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

Tp /More details about the calculations will be given in the talk by Gao Jian-hua in Xi’An.

- Qua

rk p

olar

izat

ion

P q

:T temperature


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 (0

Compare 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


Consequence I: Hyperon polarization

Recombination scenario q1+q2

+q3H

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

43

34

qsq

qssq

PPP

PPPP

2

2

43

34

ssq

qsqs

PPP

PPPP

)1(3

)5(2

2

s

ss

P

PP



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

fn

Pn

2 )2(3

4

ss

ssqs

fn

PnPf

)2(3

4

ss

qsss

fn

PfPn

3sP

qss

s Pfn

n

2 qss

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



Some of the expected qualitative features

The same for hyperons and anti-hyperons.

(Approximately) the same for different hyperons.

No polarization at b=0, increases approximately linearly with b.

Tp


Consequence II: Vector meson spin alignment

XVqXVq or

XVqXVqfragV or for 3/1)(

,3

12

2)(

00q

qfrag

P

P

,3

1

3

12

2

2

2)*(

00s

s

ss

s

q

q

ss

srecK

P

P

fn

n

P

P

fn

f

In analog to XKqqZee *0

5.0

for 3/1)(00 VqqrecV

,3

12

2)(

00q

qrec

P

P

,3

1)*(00

sq

sqrecK

PP

PPρ

Fragmentation scenario

Recombination scenario Vqq 21


Experimental studies at RHIC

See e.g., next talk.

Also: special session at the Xi’An workshop.


Still many open questions More realistic calculations by taking longitudinal as well a

s transverse flows into account;

Influence from final state interaction between hadrons;

Influence of orbital angular momenta in hadronization;

Relation to hyperon polarization w.r.t. production plane;

Other measurable consequences;

… … …


Summary

A great advantage to study spin effects in non-central AA-collisions is: 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.

Quarks and anti-quarks are polarized in the opposite direction as the normal of the reaction plane due to spin-orbital interaction in QCD.

Many consequences, many open questions … …


Outlook

………………………

A possible method to study the role of orbital angular momentum in high energy spin physics.

An effective way to study spin-orbital interaction in QCD?

A new window to look at the properties of QGP?

Thank you for your attention!

qm2006 2006 年 11 月 14-21 日 shanghai, china 梁作堂 (liang zuo-tang) 山东大学 1 for the...

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