Spin alignment of vector mesons (K* 0 , φ ) in Au+Au and p+p collisions at RHIC

1. STAR • Motivations • Analysis details • Results • spin alignment w.r.t. reaction plane • spin alignment w.r.t. production plane • Conclusions 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 SQM07 @ Levoca

2. beam x reaction plane y Global Angular Momentum and Hadron Polarization 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. 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/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 Z.T. Liang and X.N. Wang, Phys. Rev. Lett. 94 (2005) 102301

4. STAR 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

5. STAR or 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. • Global hyperon polarization andglobal vector meson spin alignment • Measured through decay products angular distribution w.r.t. reaction plane

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

9. STAR pT dependence STAR Preliminary K*0(0.8<pT<5.0 GeV/c): ρ00 = 0.33 +- 0.04 +- 0.12 φ (0.4<pT<5.0 GeV/c): ρ00 = 0.34 +- 0.02 +- 0.03 There is no significant spin alignment observed for vector mesons – model prediction for spin alignment is also small – difficult to observe !

10. 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. STAR production plane Spin alignment w.r.t. the production plane • 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).

12. STAR STAR Preliminary 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

13. STAR K*0 PLB 412 (1997) 210 DELPHI Col. PLB 406 (1997) 271 Comparison between different system 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

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.