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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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 2
Outline
Introduction Global polarization of quarks and anti-quarks Direct consequences:
I. Hyperon polarization
II. Vector meson spin alignment
Summary and outlook
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 3
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 … … … …
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 4
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 5
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 6
Global orbital angular momentum
Gradient in pz-distribution along the x-direction
x
zimpact parameter b
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 7
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 8
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 9
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?
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 10
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 11
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 12
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 13
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 14
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 15
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 16
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 17
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
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 18
Consequence I: Hyperon polarization
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 19
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
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 20
Experimental studies at RHIC
See e.g., next talk.
Also: special session at the Xi’An workshop.
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 21
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;
… … …
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 22
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 … …
QM2006 2006年11月14-21日 Shanghai, China 梁作堂(Liang Zuo-tang) 山东大学 23
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!