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

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

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.

Ratio of three-gluon to two-gluon secondary scattering numbers versus the

interaction range

Effect of triple-gluon elastic scatterings: Early thermalization of gluon matter initially produced in c

entral 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.

Early Thermalization

Evidences:(1) Hydrodynamic calculations for the elliptic flow coefficien

t 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

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.

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

Scatterings of three gluons

At three angles relative to the incoming beam direction:

……. θ=0o – – –θ=45o — - — θ=90o — Juttner distribution

At three angles relative to the incoming beam direction: ··· θ=0o – – – θ=45o – · – θ=90o

— Juttner distribution

Triple-quark elastic scatterings

Boltzmann-type transport equation for up-quark distribution function

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

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 distri

bution function comparable to the one that resulted from the quark-quark scatterings.

(4)Quark matter itself cannot thermalizes rapidly at RHIC energies.

thank you