1. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 1 International Workshop on Heavy Ion Physics at LHC Global Polarization of QGP in AA Collision Liang Zuo-tang Shandong University References: Z. Liang and X.N. Wang, Phys. Rev. Lett. 94, 102301 (2005); Phys. Lett. B629, 20 (2005); J. Gao, S. Chen, W. Deng, Z. Liang, Q. Wang, X.N. Wang, Phys. Rev. C77, 044902 (2008).

2. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 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 Measurements at RHIC Outlook for LHC Summary

3. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 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. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 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. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 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. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 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. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 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. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 8 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 Hard sphere nuclear matter distribution Landau fireball model: equal p z of partons produced at a given x.

9. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 9 Gradient in p z -distribution along x -direction Hard sphere vs Woods-Saxon Landau fireball model: equal p z of partons produced at a given x.

10. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 10 Gradient in p z -distribution along x -direction Bjorken Scaling limit: a parton interacts only with other partons within the same region of width Δy. Results from HIJING

11. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 11 Local Orbital Angular Momentum for b =R A,  x =1fm impact parameter of the two partons has a preferred direction ( ) !

12. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 12 Questions What do we expect to see if such partons interact with each other? 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 sQGP?

13. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 13 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

14. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 14 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

15. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 15 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

16. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 16 Quantitative results with QCD at finite temperature - Quark polarization P q temperature See next talk by Q. Wang

17. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 17 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

18. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 18 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 Λ longitudinal polarization

19. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 19 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

20. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 20 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

21. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 21 Vector meson spin alignment Polarization of vector meson is described by Spin density matrix: : probability for third component m=1,-1 or 0 Unpolarized: ρ 00 can be measured and the spin of vector is aligned if

22. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 22 Consequence II: Vector meson spin alignment In analog to Fragmentation scenario Recombination scenario

23. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 23 More recent theoretical studies 1) Barbara Betz, Miklos Gyulassy, Giorgio Torrieri, “Polarization probes of vorticity in heavy ion collisions”, Phys.Rev.C76:044901,2007. arXiv:0708.0035 [nucl-th] 2) Andreas Ipp, Antonino Di Piazza, Jorg Evers, Christoph H. Keitel, “Photon polarization as a probe for quark-gluon plasma dynamics” arXiv:0710.5700 [hep-ph] 3) F. Becattini, F. Piccinini, J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy”, Phys.Rev.C77:024906,2008. arXiv:0711.1253 [nucl-th] 4) Shou-wan Chen, Jian Deng, Jian-hua Gao, Qun Wang, “ A General derivation of differential cross-section in quark-quark scatterings at fixed impact parameter”. arXiv:0801.2296 [hep-ph] ……………………….. See also next talk by Q. Wang

24. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 24 Polarization of photon Andreas Ipp, Antonino Di Piazza, Jorg Evers, Christoph H. Keitel, “Photon polarization as a probe for quark-gluon plasma dynamics” arXiv:0710.5700 [hep-ph]

25. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 25 Ideal rotating quark gas F. Becattini, F. Piccinini, J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy”, Phys.Rev.C77:024906,2008; arXiv:0711.1253 [nucl-th]

26. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 26 International Workshop on Heavy Ion Physics at LHC Measurements already carried out at RHIC

27. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 27 Can we measure such polarization? Determination of hyperon polarization Spin self-analyzing parity violating weak decay H  B+M. E.g.:   p  - ; α=0.642. angle between direction of motion of B and polarization direction of H in the REST frame of H. polarization of H.

28. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 28 Experimental studies at RHIC Lambda polarization Ilya Selyuzhenkov for STAR: QM2005; SQM2006; CIPANP 2006; QM2006; Xi’An 2006; STAR Paper, Phys.Rev.C76:024915,2007. arXiv:0705.1691 [nucl-ex]

29. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 29 Measurement of Vector meson spin alignment Polarization of vector meson is described by Consider the decay process of V into 2 spin 0 mesons: V  M 1 +M 2, again in the rest frame of V, the decay amplitude is given by: Spin density matrix: Angular distribution:

30. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 30 Measurement of Vector meson spin alignment No need to determine the direction of reaction plane! Vector meson: strong decay V  M 1 +M 2. Integrated over  *,

31. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 31 Experimental studies at RHIC Vector meson spin alignment J. Chen for STAR, QM2006, J.Phys.G34:S331-S336,2007. Z. Tang for STAR, Xi’An 2006. High Ener. Phys. & Nucl. Phys. STAR Paper, 0801.1927[Nucl-ex]

32. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 32 RHIC vs LHC Global orbital angular momentum of the colliding system LHC RHIC

33. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 33 RHIC vs LHC Local orbital angular momentum of two partons at  x =1fm LHC RHIC Landau fireball model

34. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 34 Outlook at LHC Gradient in p z -distribution along x -direction LHC RHIC Landau fireball model

35. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 35 RHIC vs LHC: Quark Polarization For b =R A, Much More Significant at LHC! RHIC: LHC: Near the peak region! RHIC LHC (Landau fireball model)

36. Wuhan Workshop 2008 年 5 月 21-24 日 Wuhan 梁作堂 (Liang Zuo-tang) 山东大学 36 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 and quarks and anti-quarks can be polarized in that direction due to spin-orbital interaction in QCD. Many consequences, first data are obtained at RHIC. The effects should be more significant at LHC. Thank you for your attention!