426
R. Stock
Overall we thus obtain entries in the QCD phase diagram of Fig. 7.1. RHIC
creates a parton plasma at about T = 300 MeV and μ B = 20 MeV. It turns out
to behave like an ideal fluid and features an extremely short mean free path λ, thus
inviting a description by relativistic hydrodynamics. The small shear viscosity η (or
the small viscosity to entropy ratio η/s) are highlighted by the striking observation
that even the fluctuations of primordial parton density in individual, single events,
are preserved in the single event variation of elliptic flow [267, 268]. Moreover, the
observed scaling of elliptic flow with hadron valence quark number [94]—and thus
not with hadronic mass as in radial flow [103]—confirms the implied origin of the
elliptic flow signal from the partonic phase.
At the LHC the phase of early QCD plasma formation is expected to shift to yet
higher energy density, in the vicinity of T = 600 MeV and μ B = 5 MeV. One is thus
getting nearer to the domain of QCD asymptotic freedom, and might expect a falloff
of the partonic cross section which is extremely high at RHIC [61], as reflected by
the small η/s and λ values.
The observed features of the QCD plasma produced at RHIC energy have
invited the terminology of a “strongly coupled” quark-gluon plasma (sQGP [165]).
Further evidence for the strongly coupled, non perturbative nature of the primordial
partonic state stems from the various observed, strong in-medium attenuation effects
on initially produced high p T partons. In Au+Au collisions at
√
s = 200 GeV
this high medium opacity leads to a universal quenching of the high p T hadron
yield [175] including, most remarkably, heavy charm quark propagation to D
mesons [175, 178]. We have shown in Sect. 7.5 that the interior of the collisional
fireball at midrapidity is almost “black” at t < 1 fm/c. This is also reflected in a
strong suppression of the back-to-back correlation of hadrons from primordially
produced di-jets [207, 208], and in a similarly strong suppression of the J//
yield [237] which we have shown in Sect. 7.6 to be ascribed to an in-medium
dissolution of the primordially produced c ¯
c pairs [41] at T about 300 MeV.
The underlying high medium opacity can be formally expressed [188, 193, 195]
by an effective parton transport coefficient ˆ
q (Eqs. (7.58) and (7.62)) which
quantifies the medium induced transverse momentum squared per unit mean free
path λ. The value of ˆ
q derived from analysis of the various attenuation phenomena
turns out to be almost an order of magnitude higher than what was expected from
former, perturbative QCD based models [196]. Analogously, η/s has turned out
to be much smaller than the previous perturbative QCD expectation [92]. The two
quantities may be related [300] via the heuristic expression
η
s
≈ 3.75 C
T 3
ˆ
q
(7.93)
with C a to be determined constant; C = 1/3 from [300]. This relation shows that a
larger value of ˆ
q implies a small value for the ratio η/s. The latter has a lower bound
by the general quantum gauge field theory limit η/s ≥ (4π) −1 [171], a value not too
far from the estimate η/s = 0.09 ± 0.02 derived from relativistic hydrodynamics
R. Stock
Overall we thus obtain entries in the QCD phase diagram of Fig. 7.1. RHIC
creates a parton plasma at about T = 300 MeV and μ B = 20 MeV. It turns out
to behave like an ideal fluid and features an extremely short mean free path λ, thus
inviting a description by relativistic hydrodynamics. The small shear viscosity η (or
the small viscosity to entropy ratio η/s) are highlighted by the striking observation
that even the fluctuations of primordial parton density in individual, single events,
are preserved in the single event variation of elliptic flow [267, 268]. Moreover, the
observed scaling of elliptic flow with hadron valence quark number [94]—and thus
not with hadronic mass as in radial flow [103]—confirms the implied origin of the
elliptic flow signal from the partonic phase.
At the LHC the phase of early QCD plasma formation is expected to shift to yet
higher energy density, in the vicinity of T = 600 MeV and μ B = 5 MeV. One is thus
getting nearer to the domain of QCD asymptotic freedom, and might expect a falloff
of the partonic cross section which is extremely high at RHIC [61], as reflected by
the small η/s and λ values.
The observed features of the QCD plasma produced at RHIC energy have
invited the terminology of a “strongly coupled” quark-gluon plasma (sQGP [165]).
Further evidence for the strongly coupled, non perturbative nature of the primordial
partonic state stems from the various observed, strong in-medium attenuation effects
on initially produced high p T partons. In Au+Au collisions at
√
s = 200 GeV
this high medium opacity leads to a universal quenching of the high p T hadron
yield [175] including, most remarkably, heavy charm quark propagation to D
mesons [175, 178]. We have shown in Sect. 7.5 that the interior of the collisional
fireball at midrapidity is almost “black” at t < 1 fm/c. This is also reflected in a
strong suppression of the back-to-back correlation of hadrons from primordially
produced di-jets [207, 208], and in a similarly strong suppression of the J//
yield [237] which we have shown in Sect. 7.6 to be ascribed to an in-medium
dissolution of the primordially produced c ¯
c pairs [41] at T about 300 MeV.
The underlying high medium opacity can be formally expressed [188, 193, 195]
by an effective parton transport coefficient ˆ
q (Eqs. (7.58) and (7.62)) which
quantifies the medium induced transverse momentum squared per unit mean free
path λ. The value of ˆ
q derived from analysis of the various attenuation phenomena
turns out to be almost an order of magnitude higher than what was expected from
former, perturbative QCD based models [196]. Analogously, η/s has turned out
to be much smaller than the previous perturbative QCD expectation [92]. The two
quantities may be related [300] via the heuristic expression
η
s
≈ 3.75 C
T 3
ˆ
q
(7.93)
with C a to be determined constant; C = 1/3 from [300]. This relation shows that a
larger value of ˆ
q implies a small value for the ratio η/s. The latter has a lower bound
by the general quantum gauge field theory limit η/s ≥ (4π) −1 [171], a value not too
far from the estimate η/s = 0.09 ± 0.02 derived from relativistic hydrodynamics