Transcript Early Thermalization at RHIC Xiao

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
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, fourgluon 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
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.
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
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
…….
θ=0o
– – –θ=45o
— -—
θ=90o
··· θ=0o
– – – θ=45o
–·–
θ=90o
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 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.
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