378
R. Stock
Considering first attempts to derive a quantitative estimate of the dimensionless
ratio of (shear) viscosity to entropy, we note that η/s is a good way to characterize
the intrinsic ability of a substance to relax toward equilibrium [167]. It can be
estimated from the expression [94]
η/s ≈ T λ f c s
(7.49)
where T is the temperature, λ f the mean free path, and c s is the sound speed derived
from the partonic matter EOS. A fit by the perfect fluid “Buda-Lund” model [168]
to the scaled v 2 data shown in Fig. 7.40 yields T = 165 ± 3 MeV; c s is estimated
as 0.35 ± 0.05 [94, 162], and λ f ≈ 0.30 fm taken from a parton cascade calculation
including 2 ↔ 3 scattering [169]. The overall result is [94]
η/s = 0.09 ± 0.02
(7.50)
in agreement with former estimates of Teaney and Gavin [170]. This value is very
small and, in fact, close to the universal lower bound of η/s = 1/4π recently derived
field theoretically [171].
Elliptic flow measurements thus confirm that the quark-gluon matter produced
as
√
s → 200 GeV is to a good approximation in local thermal equilibrium up to
about 3–4 fm/c. In addition, the final hadron mass dependence of the flow pattern
is consistent with a universal scaling appropriate for a nearly non-viscous hydrodynamic flow of partons, and the observed v 2 signal reflects a primordial equation of
state that is consistent with first numerical QCD computations [153, 154, 165] of
a strongly coupled quark-gluon plasma (sQGP) state. First estimates of its proper
shear viscosity to entropy ratio, η/s, are emerging from systematic analysis of the
elliptic flow signal. At lower
√
s precursor elliptic flow phenomena are observed,
as well, but are more difficult to analyze as the crucial, new feature offered by top
RHIC energies is missing here: a clear cut separation in time, between primordial
formation of local partonic equilibrium conditions, and hadronization. At RHIC
(and at future LHC) energy elliptic flow systematics thus captures the emerging
quark-gluon state of QCD at energy densities in the vicinity of = 6–15 GeV/fm 3 ,
at temperature T ≈ 300 MeV, and μ B → 0, describing it as a strongly coupled, low
viscosity liquid medium.
7.5 In-medium Attenuation of High p T Hadronand Jet
Production
In the preceding sections we have followed the dynamical evolution of bulk matter
in A+A collisions (at p T ≤ 2 GeV which covers about 95% of the hadronic output),
from initial formation time of partonic matter which reflects in charged particle
R. Stock
Considering first attempts to derive a quantitative estimate of the dimensionless
ratio of (shear) viscosity to entropy, we note that η/s is a good way to characterize
the intrinsic ability of a substance to relax toward equilibrium [167]. It can be
estimated from the expression [94]
η/s ≈ T λ f c s
(7.49)
where T is the temperature, λ f the mean free path, and c s is the sound speed derived
from the partonic matter EOS. A fit by the perfect fluid “Buda-Lund” model [168]
to the scaled v 2 data shown in Fig. 7.40 yields T = 165 ± 3 MeV; c s is estimated
as 0.35 ± 0.05 [94, 162], and λ f ≈ 0.30 fm taken from a parton cascade calculation
including 2 ↔ 3 scattering [169]. The overall result is [94]
η/s = 0.09 ± 0.02
(7.50)
in agreement with former estimates of Teaney and Gavin [170]. This value is very
small and, in fact, close to the universal lower bound of η/s = 1/4π recently derived
field theoretically [171].
Elliptic flow measurements thus confirm that the quark-gluon matter produced
as
√
s → 200 GeV is to a good approximation in local thermal equilibrium up to
about 3–4 fm/c. In addition, the final hadron mass dependence of the flow pattern
is consistent with a universal scaling appropriate for a nearly non-viscous hydrodynamic flow of partons, and the observed v 2 signal reflects a primordial equation of
state that is consistent with first numerical QCD computations [153, 154, 165] of
a strongly coupled quark-gluon plasma (sQGP) state. First estimates of its proper
shear viscosity to entropy ratio, η/s, are emerging from systematic analysis of the
elliptic flow signal. At lower
√
s precursor elliptic flow phenomena are observed,
as well, but are more difficult to analyze as the crucial, new feature offered by top
RHIC energies is missing here: a clear cut separation in time, between primordial
formation of local partonic equilibrium conditions, and hadronization. At RHIC
(and at future LHC) energy elliptic flow systematics thus captures the emerging
quark-gluon state of QCD at energy densities in the vicinity of = 6–15 GeV/fm 3 ,
at temperature T ≈ 300 MeV, and μ B → 0, describing it as a strongly coupled, low
viscosity liquid medium.
7.5 In-medium Attenuation of High p T Hadronand Jet
Production
In the preceding sections we have followed the dynamical evolution of bulk matter
in A+A collisions (at p T ≤ 2 GeV which covers about 95% of the hadronic output),
from initial formation time of partonic matter which reflects in charged particle