269 research outputs found
Shear Viscosity of a Gluon Plasma in Perturbative QCD
We calculate the shear viscosity to entropy density ratio of a gluon plasma in kinetic theory including the gg->gg and ggggg
processes. Due to the suppressed contribution to in the gg->gg forward
scattering, it is known that the gluon bremsstrahlung ggggg process also
contributes at the same order in perturbative QCD. Using
the Gunion-Bertsch formula for the ggggg matrix element which is valid for
the limit of soft bremsstrahlung, we find that the result is sensitive to
whether the same limit is taken for the phase space. Using the exact phase
space, the ggggg contribution becomes more important to than gg->gg
for . Therefore, at , , between 2.7 obtained by Arnold, Moore and Yaffe (AMY) and 0.5
obtained by Xu and Greiner. If the soft bremsstrahlung limit is imposed on the
phase space such that the recoil effect from the bremsstrahlung gluon is
neglected, then the correction from the ggggg process is about 10-30% of the
total which is close to AMY's prediction. This shows that the soft
bremsstrahlung approximation is not as good as previously expected.Comment: RevTex 4, 14 pages, 3 figures; The results for the soft
bremsstrahlung limit for the phase space are added. The difference between
AMY and XG approach is addressed with more clarificatio
How Perfect a Gluon Plasma Can Be in Perturbative QCD?
The shear viscosity to entropy density ratio, \eta /s, characterizes how
perfect a fluid is. We calculate the leading order \eta /s of a gluon plasma in
perturbation using the kinetic theory. The leading order contribution only
involves the elastic gg -> gg (22) process and the inelastic ggggg (23)
process. The Hard-Thermal-Loop (HTL) treatment is used for the 22 matrix
element, while the exact matrix element in vacuum is supplemented by the gluon
Debye mass insertion for the 23 process. Also, the asymptotic mass is used for
the external gluons in the kinetic theory. The errors from not implementing HTL
and the Landau-Pomeranchuk-Migdal effect in the 23 process, and from the
uncalculated higher order corrections, are estimated. Our result for \eta /s
lies between that of Arnold, Moore and Yaffe (AMY) and Xu and Greiner (XG). Our
result shows that although the finite angle contributions are important at
intermediate \alpha_s (\alpha_s \sim 0.01-0.1), the 22 process is still more
important than 23 when \alpha_s < 0.1. This is in qualitative agreement with
AMY's result. We find no indication that the proposed perfect fluid limit \eta
/s \simeq 1/(4\pi) can be achieved by perturbative QCD alone.Comment: ReVTex 4, 11 pages, 5 figures. A coding error in the exact matrix
element for the 23 process is corrected. Results in Fig. 2,3 and Table I are
re-calculated, and relevant discussions are adjusted. Part of the conclusion
is change
Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD: Comparison of Different Treatments for the gg<->ggg Process
The leading order contribution to the shear and bulk viscosities, \eta and
\zeta, of a gluon plasma in perturbative QCD includes the gg -> gg (22)
process, gg ggg (23) process and multiple scattering processes known as the
Landau-Pomeranchuk-Migdal (LPM) effect. Complete leading order computations for
\eta and \zeta were obtained by Arnold, Moore and Yaffe (AMY) and Arnold, Dogan
and Moore (ADM), respectively, with the inelastic processes computed by an
effective g gg gluon splitting. We study how complementary calculations
with 22 and 23 processes and a simple treatment to model the LPM effect compare
with the results of AMY and ADM. We find that our results agree with theirs
within errors. By studying the contribution of the 23 process to \eta, we find
that the minimum angle \theta among the final state gluons in the fluid local
rest frame has a distribution that is peaked at \theta \sim \sqrt{\alpha_{s}},
analogous to the near collinear splitting asserted by AMY and ADM. However, the
average of \theta is much bigger than its peak value, as its distribution is
skewed with a long tail. The same \theta behavior is also seen if the 23 matrix
element is taken to the soft gluon bremsstrahlung limit in the center-of-mass
(CM) frame. This suggests that the soft gluon bremsstrahlung in the CM frame
still has some near collinear behavior in the fluid local rest frame. We also
generalize our result to a general SU(N_c) pure gauge theory and summarize the
current viscosity computations in QCD.Comment: ReVTex 4, 18 pages, 7 figures, accepted version in Phys. Rev.
Bulk Viscosity of a Gas of Massless Pions
In the hadronic phase, the dominant configuration of QCD with two flavors of
massless quarks is a gas of massless pions. We calculate the bulk viscosity
(zeta) using the Boltzmann equation with the kinetic theory generalized to
incorporate the trace anomaly. We find that the dimensionless ratio zeta/s, s
being the entropy density, is monotonic increasing below T=120 MeV, where
chiral perturbation theory is applicable. This, combined with previous results,
shows that zeta/s reaches its maximum near the phase transition temperature Tc,
while eta/s, eta being the shear viscosity, reaches its minimum near Tc in QCD
with massless quarks.Comment: 12 pages, 1 figure; the version to appear in PR
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