346
R. Stock
which implies that τ relax (RHIC) ≈ 0.25 τ relax (SPS) ≈ 0.5 fm/c if we employ the
estimate T (RHIC) = 2T (SPS). This crude estimate is, however, confirmed by the
parton transport model of Molar and Gyulassy [92].
Partonic equilibration at
√
s = 200 GeV should thus set in at a time scale
commensurate to the (slightly smaller) formation time scale, at which the to be
participant partons are resolved from the initial nucleon structure functions and
enter shower multiplication. Extrapolating to the conditions expected at LHC energy
(
√
s = 5.5 TeV for A+A collisions), where the initial parton density of the structure
functions in Fig. 7.14 is even higher (x ≈ 10 −3 at mid-rapidity), and so is the initial
energy density, we may expect conditions at which the resolved partons are almost
“born into equilibrium”.
Early dynamical local equilibrium at RHIC is required to understand the observations concerning elliptic flow, with which we shall deal, in detail, in Sect. 7.4. This
term refers to a collective anisotropic azimuthal emission pattern of bulk hadrons
in semi-peripheral collisions, a hydrodynamical phenomenon that originates from
the initial geometrical non-isotropy of the primordial interaction zone [93, 94]. A
detailed hydrodynamic model analysis of the corresponding elliptic flow signal
at RHIC [95] leads to the conclusion that local equilibrium (a prerequisite to the
hydrodynamic description) sets in at t 0 ≈ 0.6 fm/c. This conclusion agrees with the
estimate via Eq. (7.19) above, based on Bjorken energy density and corresponding
parton collisions frequency.
We note that the concept of a hydrodynamic evolution appears to be, almost
necessarily ingrained in the physics of a system born into (Hubble-type) expansion,
with a primordial correlation between coordinate and momentum space, and at
extreme initial parton density at which the partonic mean free path length λ is close
to the overall spatial resolution resulting from the saturation scale, i.e. λ ≈ 1/Q s .
The above considerations suggest that a quark-gluon plasma state should be
created early in the expansion dynamics at
√
s = 200 GeV, at about T = 300 MeV,
that expands hydrodynamically until hadronization is reached, at T ≈ 165–
170 MeV. Its manifestations will be considered in Sects. 7.3–7.6. At the lower SPS
energy, up to 17.3 GeV, we can conclude, with some caution, that a deconfined
hadronic matter system should exist at T ≈ 200 MeV, in the closer vicinity of
the hadronization transition. It may closely resemble the QGP state of lattice QCD,
near T c .
7.2.6 Bulk Hadron Transverse Spectra and Radial Expansion
Flow
In this chapter we analyze bulk hadron transverse momentum spectra obtained at
SPS and RHIC energy, confronting the data with predictions of the hydrodynamical
model of collective expansion matter flow that we have suggested in the previous
section, to arise, almost necessarily, from the primordial Hubble-type coupling
R. Stock
which implies that τ relax (RHIC) ≈ 0.25 τ relax (SPS) ≈ 0.5 fm/c if we employ the
estimate T (RHIC) = 2T (SPS). This crude estimate is, however, confirmed by the
parton transport model of Molar and Gyulassy [92].
Partonic equilibration at
√
s = 200 GeV should thus set in at a time scale
commensurate to the (slightly smaller) formation time scale, at which the to be
participant partons are resolved from the initial nucleon structure functions and
enter shower multiplication. Extrapolating to the conditions expected at LHC energy
(
√
s = 5.5 TeV for A+A collisions), where the initial parton density of the structure
functions in Fig. 7.14 is even higher (x ≈ 10 −3 at mid-rapidity), and so is the initial
energy density, we may expect conditions at which the resolved partons are almost
“born into equilibrium”.
Early dynamical local equilibrium at RHIC is required to understand the observations concerning elliptic flow, with which we shall deal, in detail, in Sect. 7.4. This
term refers to a collective anisotropic azimuthal emission pattern of bulk hadrons
in semi-peripheral collisions, a hydrodynamical phenomenon that originates from
the initial geometrical non-isotropy of the primordial interaction zone [93, 94]. A
detailed hydrodynamic model analysis of the corresponding elliptic flow signal
at RHIC [95] leads to the conclusion that local equilibrium (a prerequisite to the
hydrodynamic description) sets in at t 0 ≈ 0.6 fm/c. This conclusion agrees with the
estimate via Eq. (7.19) above, based on Bjorken energy density and corresponding
parton collisions frequency.
We note that the concept of a hydrodynamic evolution appears to be, almost
necessarily ingrained in the physics of a system born into (Hubble-type) expansion,
with a primordial correlation between coordinate and momentum space, and at
extreme initial parton density at which the partonic mean free path length λ is close
to the overall spatial resolution resulting from the saturation scale, i.e. λ ≈ 1/Q s .
The above considerations suggest that a quark-gluon plasma state should be
created early in the expansion dynamics at
√
s = 200 GeV, at about T = 300 MeV,
that expands hydrodynamically until hadronization is reached, at T ≈ 165–
170 MeV. Its manifestations will be considered in Sects. 7.3–7.6. At the lower SPS
energy, up to 17.3 GeV, we can conclude, with some caution, that a deconfined
hadronic matter system should exist at T ≈ 200 MeV, in the closer vicinity of
the hadronization transition. It may closely resemble the QGP state of lattice QCD,
near T c .
7.2.6 Bulk Hadron Transverse Spectra and Radial Expansion
Flow
In this chapter we analyze bulk hadron transverse momentum spectra obtained at
SPS and RHIC energy, confronting the data with predictions of the hydrodynamical
model of collective expansion matter flow that we have suggested in the previous
section, to arise, almost necessarily, from the primordial Hubble-type coupling