Triple-gluon and Triple-quark Elastic Scatterings and Early Thermalization
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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
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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
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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.
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Ratio of three-gluon to two-gluon secondary scattering numbers versus the
interaction range
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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.
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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
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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.
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STAR Collaboration, Phys. Rev. Lett. 86(2001)402; 90(2003)032301
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Scatterings of three gluons
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At three angles relative to the incoming beam direction:
……. θ=0o – – –θ=45o — - — θ=90o — Juttner distribution
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At three angles relative to the incoming beam direction: ··· θ=0o – – – θ=45o – · – θ=90o
— Juttner distribution
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Triple-quark elastic scatterings
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Boltzmann-type transport equation for up-quark distribution function
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Thermalization time of initial quark matter is 1.8 fm/c.
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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.
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thank you