10 PHSD—A Microscopic Transport Approach for Strongly Interacting Systems
125
conservation (cf. [34]). In contrast to the familiar coalescence models this hadronization scheme solves the problem of simultaneously fulfilling all conservation laws and
the constraint of entropy production. For further details we refer the reader to [29,
34].
10.2.2 Initial Conditions
The initial conditions for the parton/hadron dynamical system have to be specified
additionally. In order to describe relativistic heavy-ion reactions we start with two
nuclei in their semi-classical groundstate, boosted toward each other with a velocity β
(in z-direction), fixed by the bombarding energy. The initial phase-space distributions
of the projectile and target nuclei are determined in the local Thomas-Fermi limit
as in the HSD transport approach [12] or the UrQMD model [13]. We recall that
at relativistic energies the initial interactions of two nucleons are well described
by the excitation of two color neutral strings which decay in time to the known
hadrons (mesons, baryons, antibaryons) [10]. Initial hard processes—i.e., the shortrange high-momentum transfer reactions that can be well described by perturbative
QCD—are treated in PHSD (as in HSD) via PYTHIA. The novel element in PHSD
(relative to HSD) is the string melting concept as also used in the A Multi-Phase
Transport (AMPT) model [28] in a similar context. However, in PHSD the strings
(or possibly formed hadrons) are only allowed to melt if the local energy density
(x) (in the local rest frame) is above the transition energy density c which in the
DQPM is c ≈ 0.5 GeV/fm
3 . The mesonic strings then decay to quark-antiquark
pairs according to an intrinsic quark momentum distribution,
F(q) ∼ exp(−2b
2 q
2
) ,
(10.6)
in the meson rest frame (cf. (10.2) for the inverse process). The parton final fourmomenta are selected randomly according to the momentum distribution (10.6) (with
b= 0.66 fm), and the parton-energy distribution is fixed by the DQPM at given energy
density s ) in the local cell with scalar parton density ρ s . The flavor content of the
q ¯
q pair is fully determined by the flavor content of the initial string. By construction
the “string melting” to massive partons conserves energy and momentum as well as
the flavor content. In contrast to [28] the partons are of finite mass— in line with
their local spectral function—and obtain a random color c = (1, 2, 3) or (r, b, g)
in addition. Of course, the color appointment is color neutral, i.e., when selecting
a color c for the quark randomly the color for the antiquark is fixed by −c. The
baryonic strings melt analogously into a quark and a diquark while the diquark,
furthermore, decays to two quarks. Dressed gluons are generated by the fusion of
nearest neighbor q + ¯
q pairs (q + ¯
q → g) that are flavor neutral until the ratio of
gluons to quarks reaches the value N g /(N q + N ¯
q ) given by the DQPM for the energy
density of the local cell. This recombination is performed for all cells in space during
the passage time of the target and projectile (before the calculation continues with the
125
conservation (cf. [34]). In contrast to the familiar coalescence models this hadronization scheme solves the problem of simultaneously fulfilling all conservation laws and
the constraint of entropy production. For further details we refer the reader to [29,
34].
10.2.2 Initial Conditions
The initial conditions for the parton/hadron dynamical system have to be specified
additionally. In order to describe relativistic heavy-ion reactions we start with two
nuclei in their semi-classical groundstate, boosted toward each other with a velocity β
(in z-direction), fixed by the bombarding energy. The initial phase-space distributions
of the projectile and target nuclei are determined in the local Thomas-Fermi limit
as in the HSD transport approach [12] or the UrQMD model [13]. We recall that
at relativistic energies the initial interactions of two nucleons are well described
by the excitation of two color neutral strings which decay in time to the known
hadrons (mesons, baryons, antibaryons) [10]. Initial hard processes—i.e., the shortrange high-momentum transfer reactions that can be well described by perturbative
QCD—are treated in PHSD (as in HSD) via PYTHIA. The novel element in PHSD
(relative to HSD) is the string melting concept as also used in the A Multi-Phase
Transport (AMPT) model [28] in a similar context. However, in PHSD the strings
(or possibly formed hadrons) are only allowed to melt if the local energy density
(x) (in the local rest frame) is above the transition energy density c which in the
DQPM is c ≈ 0.5 GeV/fm
3 . The mesonic strings then decay to quark-antiquark
pairs according to an intrinsic quark momentum distribution,
F(q) ∼ exp(−2b
2 q
2
) ,
(10.6)
in the meson rest frame (cf. (10.2) for the inverse process). The parton final fourmomenta are selected randomly according to the momentum distribution (10.6) (with
b= 0.66 fm), and the parton-energy distribution is fixed by the DQPM at given energy
density s ) in the local cell with scalar parton density ρ s . The flavor content of the
q ¯
q pair is fully determined by the flavor content of the initial string. By construction
the “string melting” to massive partons conserves energy and momentum as well as
the flavor content. In contrast to [28] the partons are of finite mass— in line with
their local spectral function—and obtain a random color c = (1, 2, 3) or (r, b, g)
in addition. Of course, the color appointment is color neutral, i.e., when selecting
a color c for the quark randomly the color for the antiquark is fixed by −c. The
baryonic strings melt analogously into a quark and a diquark while the diquark,
furthermore, decays to two quarks. Dressed gluons are generated by the fusion of
nearest neighbor q + ¯
q pairs (q + ¯
q → g) that are flavor neutral until the ratio of
gluons to quarks reaches the value N g /(N q + N ¯
q ) given by the DQPM for the energy
density of the local cell. This recombination is performed for all cells in space during
the passage time of the target and projectile (before the calculation continues with the