1. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 1 For The 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006) Globally polarized QGP in non-central AA collisions at high energies References: Z. Liang and X.N. Wang, Phys. Rev. Lett. 94, 102301 (2005); Phys. Lett. B629, 20 (2005); Gao Jian-hua et al, …… in preparation. Liang Zuo-tang Shandong University

2. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 2 Outline Introduction Global polarization of quarks and anti-quarks Direct consequences: I. Hyperon polarization II. Vector meson spin alignment Summary and outlook

3. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 3 Introduction  1989: Proton’s spin crisis;  Since 1970s: Hyperon polarization in unpolarized p+p/A  H+X;  Since 1970s: Single-spin left-right asymmetry in p(  )+p  +X;  Since 1970s: Spin analyzing power in p(  )+p  p+p;  Spin transfer in fragmentation process;  J/  polarization in p+p  J/  +X;  … … … Spin effects usually provide us with useful information on reaction mechanism and often surprises. Many examples … … … …

4. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 4 Introduction Do spin physics in AA collisions without polarizing A ? heavy ion collider polarized pp collider heavy ion physics spin physics spin physics in heavy ion collisions ? RHIC

5. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 5 Global Orbital Angular Momentum Y Huge orbital angular momentum of the colliding system. reaction plane: can be determined by measuring v 2 and v 1. normal of the reaction plane impact parameter - L y in unit of 10 5 b/R A

6. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 6 Global orbital angular momentum Gradient in p z -distribution along the x -direction x z impact parameter

7. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 7 Gradient in p z -distribution along x -direction Au+Au at 200AGeV p z ( x,b ) in unit of p 0 dp z \dx in unit of 2 p 0 \R A

8. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 8 Local Orbital Angular Momentum for b =R A,  x =1fm impact parameter of the two partons has a preferred direction ( ) !

9. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 9 Question Can such a local orbital angular momentum be transferred to the polarization of quark or anti-quark through the interactions between the partons in a QGP?

10. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 10 Quark scattering with fixed reaction plane Scattering amplitude in momentum space spin independent part Differential cross section w.r.t. the impact parameter spin dependent part Quark polarization after the scattering: a 2-dimensional Fourier transformation to impact parameter space average over the preferred directions

11. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 11 Qualitative results Static potential model with “small angle approximation” Both have exactly the same form ! Bessel functions QCD at finite temperature with HTL(hard thermal loop) gluon propagator scalar functions of x T spin direction of the quark after the scattering

12. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 12 Qualitative results has a preferred direction has a preferred direction a polarization of quark in the direction opposite to the normal of the reaction plane! normal of the AA -reaction plane

13. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 13 Quantitative results with QCD at finite temperature More details about the calculations will be given in the talk by Gao Jian-hua in Xi’An. - Quark polarization P q temperature

14. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 14 A new picture of QGP in non-central AA collisions The scattered quark acquires a negative polarization in the normal direction of the reaction plane! global polarization

15. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 15 Direct consequences Compare to: global polarization of quarks & anti-quarks polarization of hadrons hadronization OPAL  00 : probability for the third component of the spin of K* 0 to take zero.  00 =1/3: unpolarized In a non-central AA collision: Vector meson spin alignment

16. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 16 Consequence I: Hyperon polarization Recombination scenario q 1  + q 2  + q 3   H  Hyperon  PHPH PsPs P H in the case that P q = P s PqPq PqPq PqPq PqPq We expect In the case that

17. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 17 Consequence I: Hyperon polarization Fragmentation scenario q   H + X. Hyperon  PHPH P H in the case of P q =P s P H in the case of P q =P s and n s =f s

18. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 18 Consequence I: Hyperon polarization Some of the expected qualitative features The same for hyperons and anti-hyperons. (Approximately) the same for different hyperons. No polarization at b=0, increases approximately linearly with b.

19. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 19 Consequence II: Vector meson spin alignment In analog to Fragmentation scenario Recombination scenario

20. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 20 Experimental studies at RHIC See e.g., next talk. Also: special session at the Xi’An workshop.

21. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 21 Still many open questions More realistic calculations by taking longitudinal as well as transverse flows into account; Influence from final state interaction between hadrons; Influence of orbital angular momenta in hadronization; Relation to hyperon polarization w.r.t. production plane; Other measurable consequences; … … …

22. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 22 Summary A great advantage to study spin effects in non-central AA -collisions is: the reaction plane can be determined experimentally by measuring v 1 and v 2. There exists a huge orbital angular momentum of the colliding system w.r.t. the reaction plane. Quarks and anti-quarks are polarized in the opposite direction as the normal of the reaction plane due to spin-orbital interaction in QCD. Many consequences, many open questions … …

23. QM2006 2006 年 11 月 14-21 日 Shanghai, China 梁作堂 (Liang Zuo-tang) 山东大学 23 Outlook ………………………  A possible method to study the role of orbital angular momentum in high energy spin physics.  An effective way to study spin-orbital interaction in QCD?  A new window to look at the properties of QGP? Thank you for your attention!