1. Triple-gluon and Triple-quark Elastic Scatterings and Early Thermalization Xiao-Ming Xu Shanghai University X.-M. Xu, Y. Sun, A.-Q. Chen, L. Zheng, Nucl. Phys. 744(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 R A =6.4 fm, Y=5, t ini =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 v 2 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. At three angles relative to the incoming beam direction: ……. θ=0 o – – –θ=45 o — - — θ=90 o — Juttner distribution

23. At three angles relative to the incoming beam direction: ··· θ=0 o – – – θ=45 o – · – θ=90 o — Juttner distribution

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 are important at RHIC energies and yield the effect of rapid thermalization. (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