10 PHSD—A Microscopic Transport Approach for Strongly Interacting Systems
121
for p+p and A+A collisions has provided very similar results for hadron spectra and
flows up to
√
s N N = 17.3 GeV [14]. Furthermore, a relativistic extension of the QMD
model—based on the NJL Lagrangian—has been proposed in [15] but not followed
up further except for a comparative study in [16].
By Legendre transformations the Hamiltonian density could be easily evaluated
in the RBUU models and the nuclear EoS in thermal (or chemical) equilibrium,
accordingly. However, it was soon noticed that with increasing temperature T and
baryon density ρ B (or baryon chemical potential μ B ) the energy density was likely
to exceed some critical energy density (∼1 GeV/fm
3 ) as indicated by early lattice
QCD (lQCD) calculations which also showed that with increasing T a restoration
of chiral symmetry should happen as seen from the temperature dependence of the
scalar quark condensate < ¯
qq > (T ). Furthermore, the interaction rates of strongly
interacting hadrons reached a couple of hundred MeV at high baryon density ρ B
and temperature T such that the on-shell quasiparticle limit—applied in the standard models— became questionable. Furthermore, the spectral evolution especially
of vector mesons in a hot and dense environment became of primary interest since
the electromagnetic decay of vector mesons into dilepton pairs could be measured
experimentally and was considered as a primary probe for the restoration of chiral
symmetry in these media. To this end the relativistic transport approach was extended
to off-shell dynamics on the basis of the Kadanoff–Baym dynamics in the turn of the
Millenium [17–19] and it became possible to calculate the in-medium spectroscopy
of vector mesons in heavy-ion collisions [20]. On the other hand, experimental observations at the Relativistic Heavy Ion Collider (RHIC) indicated that a new medium
(Quark-Gluon Plasma (QGP)) was created in ultra-relativistic Au+Au collisions that
is interacting more strongly than hadronic matter. Moreover, in line with theoretical
studies in [21–23] the QCD medium showed phenomena of an almost perfect liquid
of partons [24, 25] as extracted from the strong radial expansion and the scaling of
elliptic flow v 2 ( p T ) of mesons and baryons with the number of constituent quarks
and antiquarks [24].
The question about the properties of this (non perturbative) QGP liquid became
of primary interest as well as dynamical concepts describing the formation of
color neutral hadrons from colored partons (hadronization). A fundamental issue
for hadronization is the conservation of 4-momentum as well as the entropy problem
because by fusion/coalescence of massless (or low constituent mass) partons to color
neutral bound states of low invariant mass (e.g., pions) the number of degrees of freedom and thus the total entropy is reduced in the hadronization process [26–28]. This
problem—a violation of the second law of thermodynamics as well as the conservation of four-momentum and flavor currents—has been addressed in [29] on the basis
of the Dynamical QuasiParticle Model (DQPM) employing covariant transition rates
for the fusion of massive quarks and antiquarks to color neutral hadronic resonances
or strings. The DQPM is an effective field-theoretical model based on covariant
propagators for quarks/antiquarks and gluons that have a finite width in their spectral functions (imaginary parts of the propagators). The determination/extraction of
complex self energies for the partonic degrees of freedom has been performed in
[30, 31] by fitting lattice QCD (lQCD) data within the DQPM and thus extracting
121
for p+p and A+A collisions has provided very similar results for hadron spectra and
flows up to
√
s N N = 17.3 GeV [14]. Furthermore, a relativistic extension of the QMD
model—based on the NJL Lagrangian—has been proposed in [15] but not followed
up further except for a comparative study in [16].
By Legendre transformations the Hamiltonian density could be easily evaluated
in the RBUU models and the nuclear EoS in thermal (or chemical) equilibrium,
accordingly. However, it was soon noticed that with increasing temperature T and
baryon density ρ B (or baryon chemical potential μ B ) the energy density was likely
to exceed some critical energy density (∼1 GeV/fm
3 ) as indicated by early lattice
QCD (lQCD) calculations which also showed that with increasing T a restoration
of chiral symmetry should happen as seen from the temperature dependence of the
scalar quark condensate < ¯
qq > (T ). Furthermore, the interaction rates of strongly
interacting hadrons reached a couple of hundred MeV at high baryon density ρ B
and temperature T such that the on-shell quasiparticle limit—applied in the standard models— became questionable. Furthermore, the spectral evolution especially
of vector mesons in a hot and dense environment became of primary interest since
the electromagnetic decay of vector mesons into dilepton pairs could be measured
experimentally and was considered as a primary probe for the restoration of chiral
symmetry in these media. To this end the relativistic transport approach was extended
to off-shell dynamics on the basis of the Kadanoff–Baym dynamics in the turn of the
Millenium [17–19] and it became possible to calculate the in-medium spectroscopy
of vector mesons in heavy-ion collisions [20]. On the other hand, experimental observations at the Relativistic Heavy Ion Collider (RHIC) indicated that a new medium
(Quark-Gluon Plasma (QGP)) was created in ultra-relativistic Au+Au collisions that
is interacting more strongly than hadronic matter. Moreover, in line with theoretical
studies in [21–23] the QCD medium showed phenomena of an almost perfect liquid
of partons [24, 25] as extracted from the strong radial expansion and the scaling of
elliptic flow v 2 ( p T ) of mesons and baryons with the number of constituent quarks
and antiquarks [24].
The question about the properties of this (non perturbative) QGP liquid became
of primary interest as well as dynamical concepts describing the formation of
color neutral hadrons from colored partons (hadronization). A fundamental issue
for hadronization is the conservation of 4-momentum as well as the entropy problem
because by fusion/coalescence of massless (or low constituent mass) partons to color
neutral bound states of low invariant mass (e.g., pions) the number of degrees of freedom and thus the total entropy is reduced in the hadronization process [26–28]. This
problem—a violation of the second law of thermodynamics as well as the conservation of four-momentum and flavor currents—has been addressed in [29] on the basis
of the Dynamical QuasiParticle Model (DQPM) employing covariant transition rates
for the fusion of massive quarks and antiquarks to color neutral hadronic resonances
or strings. The DQPM is an effective field-theoretical model based on covariant
propagators for quarks/antiquarks and gluons that have a finite width in their spectral functions (imaginary parts of the propagators). The determination/extraction of
complex self energies for the partonic degrees of freedom has been performed in
[30, 31] by fitting lattice QCD (lQCD) data within the DQPM and thus extracting