7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
427
applied to elliptic flow v 2 [94, 170]. As a consequence, ˆ
q cannot grow beyond a
certain upper bound that should be established at LHC energy.
These considerations are an example of the recent intense theoretical search for
alternative methods of real-time strong coupling calculations, complementary to
lattice QCD. In this regime, lattice QCD has to date been the prime non-perturbative
calculational tool. However, understanding collective flow, jet quenching and
primordial photon radiation requires real time dynamics, on which lattice QCD
information is at present both scarce and indirect. Complementary methods for
real-time strong coupling calculations at high temperature are therefore being
explored. For a class of non-abelian thermal gauge field theories, the conjecture
of a correspondence between anti-de Sitter space-time theory and conformal field
theory (the so-called AdS/CFT conjecture) has been shown [301] to present such
an alternative. It maps nonperturbative problems at strong coupling onto calculable
problems of classical gravity in a five-dimensional anti-de Sitter (ADS 5 ) black hole
space-time theory [302]. In fact, this formalism has been recently applied [212] in a
calculation of the transport coefficient ˆ
q that governs in-medium jet attenuation,
resulting in an effective, expansion time averaged ˆ
q eff = 5 GeV 2 /fm at T =
300 MeV corresponding to top RHIC energy, rather close to the experimental
estimates (c.f. Figs. 7.41 and 7.48).
Thus, it does not seem to be too far-fetched to imagine [301] that the quarkgluon plasma of QCD, as explored at RHIC, and soon at the LHC (and theoretically
in lattice QCD), and the thermal plasma of certain supersymmetric conformal gauge
field theories (for example N = 4 “Super-Yang-Mills” (SYM) theory as employed
in [212, 301]) share certain fundamental common properties.
The focus on early time in the dynamical evolution of matter in nucleus-nucleus
collisions is specific to RHIC energy as the initial interpenetration period of two
Lorentz contracted mass 200 nuclei amounts to 0.15 fm/c only. The subsequent
evolution is thus reflected in a multitude of observables. It is, at first, described as
a one-dimensional Hubble expansion [61], setting the stage for the emergence of
the medium specific quantities addressed above (gluon saturation, direct photon
production, hydrodynamic elliptic flow, jet quenching and J// suppression).
These observables tend to settle toward their eventually observed patterns at
t ≤ 1.0–1.5 fm/c, owing to the fact that they are most prominently determined
under primordial conditions of high temperature and density. For example, photon
production reflects T 4 , and the transport coefficient ˆ
q falls with T 3 [212].
On the contrary, at the energy of former studies at the CERN SPS, 6 ≤
√
s ≤
20 GeV, such early times stay essentially unresolved as the initial interpenetration
takes upward of 1.5 fm/c. A fireball system in local (or global) equilibrium
thus develops toward t = 3 fm/c, at T about 220 MeV, closer to the onset of
hadronization [85, 86]. Also the baryo-chemical potential is much higher than in
RHIC collisions, 250 ≤ μ B ≤ 450 MeV. However, we thus gain insight into
the QCD physics of the hadronization, and high μ B domain of the phase diagram
sketched in Fig. 7.1, in the vicinity of the conjectured parton-hadron coexistence
line of QCD.
427
applied to elliptic flow v 2 [94, 170]. As a consequence, ˆ
q cannot grow beyond a
certain upper bound that should be established at LHC energy.
These considerations are an example of the recent intense theoretical search for
alternative methods of real-time strong coupling calculations, complementary to
lattice QCD. In this regime, lattice QCD has to date been the prime non-perturbative
calculational tool. However, understanding collective flow, jet quenching and
primordial photon radiation requires real time dynamics, on which lattice QCD
information is at present both scarce and indirect. Complementary methods for
real-time strong coupling calculations at high temperature are therefore being
explored. For a class of non-abelian thermal gauge field theories, the conjecture
of a correspondence between anti-de Sitter space-time theory and conformal field
theory (the so-called AdS/CFT conjecture) has been shown [301] to present such
an alternative. It maps nonperturbative problems at strong coupling onto calculable
problems of classical gravity in a five-dimensional anti-de Sitter (ADS 5 ) black hole
space-time theory [302]. In fact, this formalism has been recently applied [212] in a
calculation of the transport coefficient ˆ
q that governs in-medium jet attenuation,
resulting in an effective, expansion time averaged ˆ
q eff = 5 GeV 2 /fm at T =
300 MeV corresponding to top RHIC energy, rather close to the experimental
estimates (c.f. Figs. 7.41 and 7.48).
Thus, it does not seem to be too far-fetched to imagine [301] that the quarkgluon plasma of QCD, as explored at RHIC, and soon at the LHC (and theoretically
in lattice QCD), and the thermal plasma of certain supersymmetric conformal gauge
field theories (for example N = 4 “Super-Yang-Mills” (SYM) theory as employed
in [212, 301]) share certain fundamental common properties.
The focus on early time in the dynamical evolution of matter in nucleus-nucleus
collisions is specific to RHIC energy as the initial interpenetration period of two
Lorentz contracted mass 200 nuclei amounts to 0.15 fm/c only. The subsequent
evolution is thus reflected in a multitude of observables. It is, at first, described as
a one-dimensional Hubble expansion [61], setting the stage for the emergence of
the medium specific quantities addressed above (gluon saturation, direct photon
production, hydrodynamic elliptic flow, jet quenching and J// suppression).
These observables tend to settle toward their eventually observed patterns at
t ≤ 1.0–1.5 fm/c, owing to the fact that they are most prominently determined
under primordial conditions of high temperature and density. For example, photon
production reflects T 4 , and the transport coefficient ˆ
q falls with T 3 [212].
On the contrary, at the energy of former studies at the CERN SPS, 6 ≤
√
s ≤
20 GeV, such early times stay essentially unresolved as the initial interpenetration
takes upward of 1.5 fm/c. A fireball system in local (or global) equilibrium
thus develops toward t = 3 fm/c, at T about 220 MeV, closer to the onset of
hadronization [85, 86]. Also the baryo-chemical potential is much higher than in
RHIC collisions, 250 ≤ μ B ≤ 450 MeV. However, we thus gain insight into
the QCD physics of the hadronization, and high μ B domain of the phase diagram
sketched in Fig. 7.1, in the vicinity of the conjectured parton-hadron coexistence
line of QCD.