GLOBAL POLARIZATION OF QUARKS IN NON-CENTRAL A+A COLLISIONS

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Presentation transcript:

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, 102301 (2005); Gao Jian-hua and Liang Zuo-tang , in preparation

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

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

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

Local Orbital Angular Momentum

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

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

Analytic Results in Static Potential Model z x y Integrated over the half plane above y-axis

“Small Angle Approximation” Not Enough at RHIC Averaged quark polarization Liang Zuo-tang and Wang Xin-Nian, Phys. Rev. Lett. 94, 102301 (2005) Estimate of polarization at RHIC Need to go beyond small angle approximation! What differences beyond static potential model?

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

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:

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

Analytic Results by HTL Gluon Propagator

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

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

HTL versus Static Potential Model

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

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！