6/24/2007 SQM07 @ Levoca 1

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

STAR

• Introduction

• Results

– spin alignment w.r.t. reaction plane

– spin alignment w.r.t. production plane

• Conclusions

2

Global Angular Momentum and Hadron Polarization

x

y

beam

reaction plane

L

The participant matter may have a large angular momentum to begin with in non-central A+A collisions –1) 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

• 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 and X.N. Wang, Phys. Rev. Lett. 94 (2005) 102301

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Z.T. Liang nucl-th/0705.2852

“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

4

Spin-Orbital Coupling Quark Polarization

Z.T. Liang nucl-th/0705.2852

• 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

STAR

5

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.

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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 AlignmentSTAR

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) havethe same probabilities (1/3) – spin alignment ?

-- sz = +1, -1 states are degenerate (cos2 dependence)-- phi mesons do not have decay feeddown contributions

7

Data SetAu+Au Year 2004 Running, ~23 M Min-Bias Events

p+p Year 2001 Running, ~6 M Min-Bias Events

8

Analysis details (φ-meson)

Correct ρooobs for the “reaction

plane resolution” to obtain ρ00.

Correct the dN(pT)/d(cosθ*) with

detector acceptance and tracking efficiency.

]cos)13()1[(4

3 *20000 Norm

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

Using mixed event method to get the raw dN(pT)/dcos(θ*) distribution.

φK+K-

STAR Preliminary

9

pT dependence

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STAR

There is no significant spin alignment observed for vector mesons –

model prediction for spin alignment is also small – difficult to observe !

K*0 (0.8<pT<5.0 GeV/c): ρ00 = 0.33 +- 0.04 +- 0.12φ (0.4<pT<5.0 GeV/c): ρ00 = 0.34 +- 0.02 +- 0.03

STAR Preliminary

10

Centrality dependenceSTAR

No strong centrality dependence has been observed

-- presumably the spin-orbital coupling may be too small

to polarize the quarks with strong centrality dependence !

STAR Preliminary

11

Spin alignment w.r.t. the production plane

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• 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, 034023 (2003).

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STAR

12

pT dependence

pT<2.0 GeV/c

ρ00(K*) = 0.43 +- 0.04 +- 0.08 ; ρ00(φ) = 0.42 +- 0.02 +- 0.04

pT>2.0 Gev/c

ρ00(K*) = 0.38 +- 0.04 +- 0.06 ; ρ00(φ) = 0.38 +- 0.03 +- 0.05

In p+p, ρ00(φ) = 0.40 +- 0.04 +- 0.06

STAR

STAR Preliminary

13

Comparison between different system

K*0 PLB 412 (1997) 210

XKqqZee 0*

DELPHI Col. PLB 406 (1997) 271

GeVpp 200@PRL 95, 202001 (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

STAR

14

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.

STAR