International Workshop on Heavy Ion Physics at LHC

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. B 629, 20 (2005); J. Gao, S. Chen, W. Deng, Z. Liang, Q. Wang, X. N. Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 1

Outline n Introduction n Global polarization of quarks and antiquarks n Direct consequences: I. Hyperon polarization II. Vector meson spin alignment n. Measurements at RHIC n. Outlook for LHC n. Summary Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 2

Introduction Spin effects usually provide us with useful information on reaction mechanism and often surprises. Many examples … … Ø 1989: Proton’s spin crisis; Ø Since 1970 s: Hyperon polarization in unpolarized p+p/A H+X; Ø Since 1970 s: Single-spin left-right asymmetry in p( )+p +X; Ø Since 1970 s: Spin analyzing power in p( )+p p+p; Ø Spin transfer in fragmentation process; Ø J/ polarization in p+p J/ +X; Ø … … … Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 3

RHIC Introduction heavy ion collider heavy ion physics polarized pp collider spin physics in heavy ion collisions ? Do spin physics in AA collisions without polarizing A ? Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 4

Global Orbital Angular Momentum -Ly in unit of 105 Huge orbital angular momentum of the colliding system. reaction plane: can be determined by measuring v 2 and v 1. impact parameter b/RA Y normal of the reaction plane 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 Gradient in pz-distribution along the xdirection x impact parameter Wuhan Workshop　2008年 5月21 -24日 Wuhan z 梁作堂(Liang Zuo-tang) 山东大学 6

Au+Au at 200 AGe. V dpzdx in unit of 2 p 0RA pz(x, b) in unit of p 0 Gradient in pz-distribution along xdirection Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 7

Au+Au at 200 AGe. V l Hard sphere nuclear matter distribution l Landau fireball model: equal pz of partons produced at a given x. dpzdx in unit of 2 p 0RA pz(x, b) in unit of p 0 Gradient in pz-distribution along xdirection Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 8

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

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

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

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 s. QGP? Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 12

Quark scattering with fixed reaction plane Scattering amplitude in momentum space a 2 -dimensional Fourier transformation to impact parameter space Differential cross section w. r. t. the impact parameter average over the preferred directions spin independent part spin dependent part Quark polarization after the scattering: Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 13

Qualitative results Static potential model with “small angle approximation” Bessel functions spin direction of the quark after the scattering QCD at finite temperature with HTL(hard thermal loop) gluon scalar functions of x. T Both have exactly the same form ! Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 14

Qualitative results normal of the AA-reaction plane has a preferred direction preferred direction a polarization of quark in the direction opposite to the normal of the reaction plane! Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 15

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

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

Direct consequences In a non-central AA collision: global polarization of quarks & anti. Compare quarks to: Λ longitudinal polarization hadronizatio n polarizatio n of hadrons 00 : probability for the third component of the spin of K*0 to take zero. OPA L Vector meson spin alignment 00=1/3: unpolarized Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 18

Consequence I: Hyperon polarization Recombination scenario q 1 +q 2 +q 3 H We expect Hyperon PH Ps PH in the case that Pq = Ps Pq Pq Pq In the case that 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 Fragmentation scenario q H + X. Hyperon PH PH in the case of Pq =Ps and ns =fs Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 20

Vector meson spin alignment Polarization of vector meson is described by Spin density matrix: : probability for third component m=1, -1 or 0 Unpolarize d: ρ00 can be measured and the spin of vector is aligned if Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 21

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

More recent theoretical studies 1) Barbara Betz, Miklos Gyulassy, Giorgio Torrieri, “Polarization probes of vorticity in heavy ion collisions”, Phys. Rev. C 76: 044901, 2007. ar. Xiv: 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” ar. Xiv: 0710. 5700 [hep-ph] 3) F. Becattini, F. Piccinini, J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy”, Phys. Rev. C 77: 024906, 2008. ar. Xiv: 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”. ar. Xiv: 0801. 2296 [hep-ph] ……………. . See also next talk by Q. Wang Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 23

Polarization of photon Andreas Ipp, Antonino Di Piazza, Jorg Evers, Christoph H. Keitel, “Photon polarization as a probe for quark-gluon plasma dynamics” ar. Xiv: 0710. 5700 [hep-ph] Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 24

Ideal rotating quark gas F. Becattini, F. Piccinini, J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy”, Phys. Rev. C 77: 024906, 2008; ar. Xiv: 0711. 1253 [nucl-th] Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 25

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

Can we measure such polarization? Determination of hyperon polarization Spin self-analyzing parity violating weak decay H B+M. polarization of H. E. g. : p -; Wuhan Workshop　2008年 5月21 -24日 Wuhan α=0. 642. angle between direction of motion of B and polarization direction of H in the REST frame of H. 梁作堂(Liang Zuo-tang) 山东大学 27

Experimental studies at RHIC Lambda polarization Ilya Selyuzhenkov for STAR: QM 2005; SQM 2006; CIPANP 2006; QM 2006; Xi’An 2006; STAR Paper, Phys. Rev. C 76: 024915, 200 7. ar. Xiv: 0705. 1691 [nucl-ex] Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 28

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

Experimental studies at RHIC Vector meson spin alignment ü J. Chen for STAR, QM 2006, J. Phys. G 34: S 331 S 336, 2007. ü Z. Tang for STAR, Xi’An 2006. High Ener. Phys. & Nucl. Phys. Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 31

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

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

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

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

Summary n n 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. n Many consequences, first data are obtained at RHIC. n The effects should be more significant at LHC. Thank you for your attention! Wuhan Workshop　2008年 5月21 -24日 Wuhan 梁作堂(Liang Zuo-tang) 山东大学 36