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 SQM07 @ Levoca

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 – 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

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/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

Spin-Orbital Coupling  Quark Polarization STAR 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

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

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

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

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.

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 !

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 !

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, 034023 (2003). production plane

pT dependence STAR Preliminary 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

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