1. STAR
Spin alignment of vector mesons (K*0, φ) in Au+Au and p+p collisions at RHIC
Jin Hui Chen
Shanghai Institute of Applied Physics and UCLA
For the STAR Collaboration
Introduction
Results
spin alignment w.r.t. reaction plane
spin alignment w.r.t. production plane
Conclusions
6/24/2007
Levoca

2. Global Angular Momentum and Hadron Polarizationx y
beam
reaction plane L
The participant matter may have a large angular momentum
to begin with in non-central A+A collisions –
are quarks from the dense matter created polarized (with a
preferred spin direction)?
spin-orbital coupling
2) are vector mesons from polarized dense quark blob polarized?
hadronization dynamics

3. A Theoretical Estimate on Orbital Angular Momentum
STAR
A Theoretical Estimate on Orbital Angular Momentum
Large orbital angular momentum
possessed in non-central Au+Au
collisions[2,3]:
“The local angular momentum for the
two neighboring parton is larger than the
spin of a quark”
A clear b dependence.
Z.T. Liang nucl-th/
“Global polarization is essentially a local
manifestation of the global angular momentum of the colliding system through interaction of spin-orbit coupling in QCD”
global hyperon polarization and global vector meson spin alignment
Z.T. Liang and X.N. Wang, Phys. Rev. Lett. 94 (2005)

4. Spin-Orbital Coupling  Quark Polarization
STAR
Spin-Orbital Coupling  Quark Polarization
Z.T. Liang nucl-th/
Features of Possible Global Polarization:
For non-central collisions, it should have a finite value, at small pT
in central rapidity;
It should increase with b;
It should vanish in central collisions

5. Hadronization does not wash out quark polarization
STAR
Hadronization does not wash out quark polarization
Global spin alignment is sensitive to different hadronization scenarios in different kinematic region[1]
Coalescence (ρ00<1/3)
Fragmentation (ρ00>1/3)
[1] Z.T. Liang and X.N. Wang, Phys. Lett. B 629 (2005) 20. or
Global hyperon polarization and global vector meson spin alignment
Measured through decay products angular distribution w.r.t. reaction plane

6. Hyperon Polarization vs Vector Meson Spin Alignment
STAR
Hyperon Polarization vs Vector Meson Spin Alignment
Hyperon spin ½, -- is the hyperon spin up or down (sz=+1/2 or -1/2) ?
-- define an absolute direction (up or down)
-- feed down from other multi-strange hyperons
Vector mesons spin = 1, -- do the three components (sz=+1,0,-1) have
the same probabilities (1/3) – spin alignment ?
-- sz = +1, -1 states are degenerate (cos2q dependence)
-- phi mesons do not have decay feeddown contributions

7. Data Set
Au+Au Year 2004 Running, ~23 M Min-Bias Events
p+p Year 2001 Running, ~6 M Min-Bias Events

8. Analysis details (φ-meson)
STAR
Analysis details (φ-meson)
Using mixed event method to
get the raw dN(pT)/dcos(θ*)
distribution.
φK+K-
Correct the dN(pT)/d(cosθ*) with detector acceptance and tracking efficiency.
Fitting dN(pT)/d(cosθ*) with
to get the ρ00obs.
Au+Au (20-60%) w.r.t. reaction plane
0.8<pT<1.2 GeV/c
STAR Preliminary
Correct ρooobs for the “reaction
plane resolution” to obtain ρ00.

9. pT dependence STAR Preliminary
K*0 (0.8<pT<5.0 GeV/c): ρ00 =
φ (0.4<pT<5.0 GeV/c): ρ00 =
There is no significant spin alignment observed for vector mesons –
model prediction for spin alignment is also small – difficult to observe !

10. Centrality dependence
STAR
Centrality dependence
STAR Preliminary
No strong centrality dependence has been observed
-- presumably the spin-orbital coupling may be too small
to polarize the quarks with strong centrality dependence !

11. Spin alignment w.r.t. the production plane
STAR
Hyperons are transversely polarized
G. Bunce et. al. PRL 36, 1113 (1976); P.T. Cox et. al. PRL 46, 877 (1981); C. Wilkinson et. al. PRL 58, 855 (1987); B.E. Bonner et. al. PRL 62, 1591 (1989); J. Duryea et. al. PRL 67, 1193 (1991)…
It’s related to particle formation dynamics or to intrinsic quark transverse spin distribution
B. Andersson et. al. PLB 85, 417 (1979); J. Szwed PLB 105, 403 (1981); R. Barni et. al. PLB 296, 251 (1992); J. Soffer et. al. PRL 68, 907 (1992)
It may be closely related to the AN
Z. Liang and C. Boros PRL 79, 3608(1997); Q.Xu and Z. Liang PRD 68, (2003).
production plane

12. pT dependence STAR Preliminary pT<2.0 GeV/c
ρ00(K*) = ; ρ00(φ) =
pT>2.0 Gev/c
ρ00(K*) = ; ρ00(φ) =
In p+p, ρ00(φ) =

13. Comparison between different system
STAR
Comparison between different system
DELPHI Col. PLB 406 (1997) 271
K*0 PLB 412 (1997) 210
PRL 95, (2005)
At small xp region, ρ00 are consistent with 1/3 from ee, pp, to AuAu collisions
It’s consistent with the null AN observation at central rapidity from RHIC

14. STAR
Conclusions
With respect to the reaction plane, ρ00(pT) are consistent within 1/3 within statistical and systematic uncertainty for vector meson in the measured pT up to 5 GeV/c and are independent of collision centrality and transverse momentum.
 Vector mesons in the measured kinematic region appear not to be produced with a strong global spin alignment despite the presence of a large orbital angular momentum for the system created in non-central Au+Au collisions.
With respect to the production plane, ρ00(pT) is less than 2 standard deviation above 1/3 and is similar to the results from p+p collisions.
 Vector mesons in the measured pT region at mid-rapidity don’t seem to carry a significant polarization through production dynamics.