1. GLOBAL POLARIZATION OF QUARKS IN NON-CENTRAL A+A COLLISIONS
AT HIGH ENERGIES
高建华
山东大学
Based on: Liang Zuo-tang and Wang Xin-Nian, Phys. Rev. Lett. 94, (2005);
Gao Jian-hua and Liang Zuo-tang , in preparation

2. Outline
Introduction
Calculation with static potential model
Calculation with HTL gluon propagator
Comparison between the two methods
Summary

3. Global Orbital Angular Momentum
Huge orbital angular momentum of the colliding system
in non-central heavy ion collisions Y

4. Collective Longitudinal Momentum
Collective longitudinal momentum per produced parton
Au+Au at 200A Gev
c(s): number of partons per NN collision

5. Local Orbital Angular Momentum

6. Formulas for Static Potential Model
Screened static potential model:
Scattering amplitude:
“Small angle approximation”:
Cross section in momentum space:

7. Analytic Results in Static Potential Model
Cross section in impact parameter space:
Spin independent part
Spin dependent part

8. Analytic Results in Static Potential Modelz x y
Integrated over the half plane above y-axis

9. “Small Angle Approximation” Not Enough at RHIC
Averaged quark polarization
Liang Zuo-tang and Wang Xin-Nian, Phys. Rev. Lett. 94, (2005)
Estimate of polarization at RHIC
Need to go beyond small angle approximation!
What differences beyond static potential model?

10. HTL Gluon Propagator
Gluon propagator in the finite temperature is given by:
HTL (hard thermal loop) approximation:

11. Nonperturbative Magnetic Mass
In the center of mass frame of qq where
HTL propagator can be reduced into :
Nonperturbative magnetic mass must be introduced
into the transverse self-energy:

12. Formulas with HTL Gluon Propagator
Scattering amplitude
Cross section in impact parameter space
Spin independent part
Spin dependent part

13. Analytic Results by HTL Gluon Propagator

14. Numerical Evaluation T : the temperature for QGP
s : the Mandelstam variable

15. HTL versus Static Potential Model
Both under small angle approximation
versus
versus

16. HTL versus Static Potential Model

17. Further Things to Consider
Including the collective longitudinal momentum distribution
Including the real thermal momentum distribution
The numerical evaluation is still on !

18. 谢谢大家！ Summary A huge orbital angular momentum exists
in non-central A+A collision at high energy.
Quarks (or anti-quarks) are polarized along the direction of the initial orbital angular momentum due to spin-orbital coupling in QCD.
We should calculate the polarization with HTL gluon propagator instead of static potential model .
Quark’s polarization can lead to many consequences!
谢谢大家！