10 PHSD—A Microscopic Transport Approach for Strongly Interacting Systems
133
is, furthermore, calculated in leading order employing the DQPM propagators and
coupling.
When implementing the differential cross sections and parton masses into the
PHSD5.0 approach one has to specify the Lagrange parameters T and μ B in each
computational cell in space-time. This has been done by employing the DQPM
equation of state, which is practically identical to the lattice QCD equation of state,
and a diagonalization of the energy-momentum tensor from PHSD as described in
[37].
In Sect. 10.4 we then have calculated 5% central Au+Au (or Pb+Pb) collisions and
compared the results for hadronic rapidity distributions from the previous PHSD4.0
with the novel version PHSD5.0 (with and without the explicit dependence of the
partonic differential cross sections and parton masses on μ B ). No differences for
all the hadron bulk observables from the various PHSD versions have been found
at AGS and FAIR/NICA energies within linewidth which implies that there is no
sensitivity to the new partonic differential cross sections employed. Only in case of
the kaons and the antibaryons ¯
p and ¯
+ ¯
0 , a small difference between PHSD4.0
and PHSD5.0 could be seen at top SPS energy, however, no clear difference between
the PHSD5.0 calculations with partonic cross sections for μ B = 0 and actual μ B in
the local cells.
Our findings can be understood as follows: The fact that we find only small
traces of the μ B -dependence of partonic scattering dynamics in heavy-ion bulk
observables—although the differential cross sections and parton masses clearly
depend on μ B —means that one needs a sizable partonic density and large spacetime QGP volume to explore the dynamics in the QGP phase. These conditions are
only fulfilled at high bombarding energies (top SPS, RHIC energies) where, however, μ B is rather low. On the other hand, decreasing the bombarding energy to
FAIR/NICA energies and, thus, increasing μ B , leads to collisions that are dominated
by the hadronic phase where the extraction of information about the parton dynamics
will be rather complicated based on bulk observables. Further investigations of other
observables (such as flow coefficients v n of particles and antiparticles, fluctuations
and correlations) might contain more visible μ B −traces from the QGP phase.
Acknowledgements The authors acknowledge inspiring discussions with J. Aichelin, H. Berrehrah,
C. Ratti, E. Seifert, A. Palmese, and T. Steinert. This work was supported by the LOEWE center “HIC for FAIR”. Furthermore, P.M., L.O. and E.B. acknowledge support by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) through the grant CRC-TR 211
’Strong-interaction matter under extreme conditions’—Project number 315477589—TRR 211. O.S.
acknowledges support from HGS-HIRe for FAIR; L.O. and E.B. thank the COST Action THOR,
CA15213. The computational resources have been provided by the LOEWE-Center for Scientific
Computing.
133
is, furthermore, calculated in leading order employing the DQPM propagators and
coupling.
When implementing the differential cross sections and parton masses into the
PHSD5.0 approach one has to specify the Lagrange parameters T and μ B in each
computational cell in space-time. This has been done by employing the DQPM
equation of state, which is practically identical to the lattice QCD equation of state,
and a diagonalization of the energy-momentum tensor from PHSD as described in
[37].
In Sect. 10.4 we then have calculated 5% central Au+Au (or Pb+Pb) collisions and
compared the results for hadronic rapidity distributions from the previous PHSD4.0
with the novel version PHSD5.0 (with and without the explicit dependence of the
partonic differential cross sections and parton masses on μ B ). No differences for
all the hadron bulk observables from the various PHSD versions have been found
at AGS and FAIR/NICA energies within linewidth which implies that there is no
sensitivity to the new partonic differential cross sections employed. Only in case of
the kaons and the antibaryons ¯
p and ¯
+ ¯
0 , a small difference between PHSD4.0
and PHSD5.0 could be seen at top SPS energy, however, no clear difference between
the PHSD5.0 calculations with partonic cross sections for μ B = 0 and actual μ B in
the local cells.
Our findings can be understood as follows: The fact that we find only small
traces of the μ B -dependence of partonic scattering dynamics in heavy-ion bulk
observables—although the differential cross sections and parton masses clearly
depend on μ B —means that one needs a sizable partonic density and large spacetime QGP volume to explore the dynamics in the QGP phase. These conditions are
only fulfilled at high bombarding energies (top SPS, RHIC energies) where, however, μ B is rather low. On the other hand, decreasing the bombarding energy to
FAIR/NICA energies and, thus, increasing μ B , leads to collisions that are dominated
by the hadronic phase where the extraction of information about the parton dynamics
will be rather complicated based on bulk observables. Further investigations of other
observables (such as flow coefficients v n of particles and antiparticles, fluctuations
and correlations) might contain more visible μ B −traces from the QGP phase.
Acknowledgements The authors acknowledge inspiring discussions with J. Aichelin, H. Berrehrah,
C. Ratti, E. Seifert, A. Palmese, and T. Steinert. This work was supported by the LOEWE center “HIC for FAIR”. Furthermore, P.M., L.O. and E.B. acknowledge support by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) through the grant CRC-TR 211
’Strong-interaction matter under extreme conditions’—Project number 315477589—TRR 211. O.S.
acknowledges support from HGS-HIRe for FAIR; L.O. and E.B. thank the COST Action THOR,
CA15213. The computational resources have been provided by the LOEWE-Center for Scientific
Computing.