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 STAR Collaboration

STAR

• Motivations

• Analysis details

• 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

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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 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

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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

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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

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

φK+K-

STAR Preliminary

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pT dependence

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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

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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

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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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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

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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

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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