7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
405
in which the photon luminosity of the emerging QGP matter phase is maximal.
The hydrodynamic model provides for the space-time evolution of the local photon
emission rate [223] which includes hard thermal loop diagrams to all orders, and
Landau-Migdal-Pomeranchuk (LPM) in-medium interference effects. Similar, in
outline, to previous models that combined algorithms of plasma photon radiation
luminosity with hydrodynamic expansion [250], the model [249] fits the data in
Fig. 7.57. It implies a picture in which the early stage of approach toward thermal
equilibrium at RHIC is governed by a symbolic, initial, effective “temperature”
of about 550 MeV which, after equilibration at t ≈ 0.6 fm/c, corresponds to
T ≈ 360 MeV in the primordial plasma [249]: close to the consensus about initial
T as derived from J// suppression, jet attenuation, elliptic flow and transverse
energy coupled with the 1-dimensional Bjorken expansion model.
However, we note that the employed theoretical framework, hard thermal loop
(HTL) QCD perturbation theory of a weakly coupled plasma state, as combined
with hydrodynamics, has a tendency to call for rather high initial T values. This
applies both to the above analysis [249] of RHIC data which is based on the thermal
field theory model of Arnold, Moore and Yaffe [223], and to previous analysis
[250] of the WA98 SPS data of Fig. 7.56. Direct photon production is even more
strongly biased toward the primordial, high T evolution than jet attenuation (that
may be proportional to T 3 [212]). Thus, by implication of the model [249] that
fits the low p T RHIC data of Fig. 7.57, the yield is highly sensitive to the (preequilibrium) formation period, 0.15 < t < 0.6 fm/c, where the HTL model might
not be fully applicable. This illustrates the present state of the art. The model(s)
based on perturbative QCD require extreme initial “temperatures” to produce the
high photon yield, indicated by the RHIC experiment. The strongly coupled nature
[213] of the non perturbative local equilibrium QGP state at RHIC, T ≈ 300 MeV,
may provide for an alternative approach to plasma photon production.
7.6.3 Low Mass Dilepton Spectra: Vector Mesons In-medium
We have dealt with dilepton spectra throughout the above discussion of J// and
direct photon production, as messenger processes sensitive to the energy density
prevailing (during and) at the end of the primordial equilibration phase. The third
tracer observable, low mass vector meson dilepton decay in-medium, samples—on
the contrary—the conditions and modalities of hadron deconfinement in the vicinity
of T = T c . SPS energy is ideally suited for such studies as the QGP fireball is
prepared near T c whereas, at RHIC, it races through the T c domain with developed
expansion flow. The major relevant data thus stem from the CERN SPS experiments
NA45 [251] and NA60 [136], which have analyzed e + e − and μ + μ − production at
invariant mass from 0.2 to 1.4 GeV.
Figure 7.58 shows NA45 data [251] for e + e − production in central Pb+Au
collisions at
√
s = 17.3 GeV. In searching for modifications of properties
and of π + π − annihilation via virtual intermediate decay to e + e − , in the high
405
in which the photon luminosity of the emerging QGP matter phase is maximal.
The hydrodynamic model provides for the space-time evolution of the local photon
emission rate [223] which includes hard thermal loop diagrams to all orders, and
Landau-Migdal-Pomeranchuk (LPM) in-medium interference effects. Similar, in
outline, to previous models that combined algorithms of plasma photon radiation
luminosity with hydrodynamic expansion [250], the model [249] fits the data in
Fig. 7.57. It implies a picture in which the early stage of approach toward thermal
equilibrium at RHIC is governed by a symbolic, initial, effective “temperature”
of about 550 MeV which, after equilibration at t ≈ 0.6 fm/c, corresponds to
T ≈ 360 MeV in the primordial plasma [249]: close to the consensus about initial
T as derived from J// suppression, jet attenuation, elliptic flow and transverse
energy coupled with the 1-dimensional Bjorken expansion model.
However, we note that the employed theoretical framework, hard thermal loop
(HTL) QCD perturbation theory of a weakly coupled plasma state, as combined
with hydrodynamics, has a tendency to call for rather high initial T values. This
applies both to the above analysis [249] of RHIC data which is based on the thermal
field theory model of Arnold, Moore and Yaffe [223], and to previous analysis
[250] of the WA98 SPS data of Fig. 7.56. Direct photon production is even more
strongly biased toward the primordial, high T evolution than jet attenuation (that
may be proportional to T 3 [212]). Thus, by implication of the model [249] that
fits the low p T RHIC data of Fig. 7.57, the yield is highly sensitive to the (preequilibrium) formation period, 0.15 < t < 0.6 fm/c, where the HTL model might
not be fully applicable. This illustrates the present state of the art. The model(s)
based on perturbative QCD require extreme initial “temperatures” to produce the
high photon yield, indicated by the RHIC experiment. The strongly coupled nature
[213] of the non perturbative local equilibrium QGP state at RHIC, T ≈ 300 MeV,
may provide for an alternative approach to plasma photon production.
7.6.3 Low Mass Dilepton Spectra: Vector Mesons In-medium
We have dealt with dilepton spectra throughout the above discussion of J// and
direct photon production, as messenger processes sensitive to the energy density
prevailing (during and) at the end of the primordial equilibration phase. The third
tracer observable, low mass vector meson dilepton decay in-medium, samples—on
the contrary—the conditions and modalities of hadron deconfinement in the vicinity
of T = T c . SPS energy is ideally suited for such studies as the QGP fireball is
prepared near T c whereas, at RHIC, it races through the T c domain with developed
expansion flow. The major relevant data thus stem from the CERN SPS experiments
NA45 [251] and NA60 [136], which have analyzed e + e − and μ + μ − production at
invariant mass from 0.2 to 1.4 GeV.
Figure 7.58 shows NA45 data [251] for e + e − production in central Pb+Au
collisions at
√
s = 17.3 GeV. In searching for modifications of properties
and of π + π − annihilation via virtual intermediate decay to e + e − , in the high