1. 三胶子以及三夸克弹性散射 与早期热平衡化 Xiao-Ming Xu, Y. Sun, A.-Q. Chen, L. Zheng,
Nucl. Phys. A744(2004)347

2. Gluon number density at τ=0.2fm/c:
~ 38 fm-3 at RHIC
~ 140 fm-3 at LHC
At very high gluon number density, three-gluon scatterings, four-gluon scatterings, five-gluon scatterings etc. are important.
This can be shown by Monte Carlo simulations of initial gluon distribution
RA=6.4 fm, Y=5, tini=0.2 fm/c

3. If the closest distance of two gluons is less than a given interaction range, a scattering of the two gluons occurs.
If three gluons are within a sphere which center is at the center of mass of the three gluons and which radius equals the given interaction range, a scattering of the three gluons occurs.

4. Ratio of three-gluon to two-gluon secondary scattering numbers versus the interaction range

5. Effect of triple-gluon elastic scatterings:
Early thermalization of gluon matter initially produced in central Au-Au collisions.
Early thermalization: a thermal state is achieved within a time of less than 1 fm/c from the moment when quark-gluon matter is initially created in a Au-Au collision.

6. Early Thermalization Evidences:
(1) Hydrodynamic calculations for the elliptic flow coefficient v2 have shown that matter created in Au-Au collisions thermalizes within a time of less than 1 fm/c. During thermalization energy density is well above the critical value for QCD phase transition .
(2) Jet quenching
(3) Two-jet correlation

7. Physics:
triple-gluon elastic scatterings lead to early thermalization.
Thermalization by two-body elastic scatterings is conventional:
a kilogram of cold water + a kilogram of hot water
→ two kilograms of warm water
In the mixing process, the elastic scatterings between water
molecules establish a new temperature.
Thermalization by three-body elastic scatterings is new.

8. STAR Collaboration, Phys. Rev. Lett. 86(2001)402; 90(2003)032301

11. Scatterings of three gluons

22. ……. θ=0o – – –θ=45o — - — θ=90o

23. ··· θ=0o – – – θ=45o – · – θ=90o

25. Triple-quark elastic scatterings

26. Boltzmann-type transport equation for up-quark distribution function

27. Thermalization time of initial quark matter is 1.8 fm/c.

28. Conclusions
(1)The three-gluon scattering processes give a variation of the gluon distribution function considerably larger than the two-gluon scattering processes. The triple-gluon elastic scatterings dominate the evolution of gluon matter while the number density is high.
(2)The triple-gluon scatterings cause gluon matter to thermalize rapidly at high density.
(3)The triple-quark scatterings give a variation of quark distribution function comparable to the one that resulted from the quark-quark scatterings.
(4)Quark matter itself cannot thermalizes rapidly at RHIC energies.

29. thank you