7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
437
the suppression theme is now turning over to the bottonomium production at the
LHC [326], visible there because of the much lower thermal bottom quark density.
7.9.5 Hadronization and the QCD Phase Diagram
This chapter will have two main topics, first the analysis of hadron production
multiplicities with the Statistical Hadronization Model (SHM) that incorporates the
canonical or grandcanonical partition functions of a hadron-resonance gas (HRG)
model. This will be an update on Sect. 7.3. Second, however, we turn to new
developments of lattice QCD theory, extension to finite baryochemical potential and
determination of the hadronization parameters T vs. μ B from, first, a determination
of the overlap between Lattice QCD and the HRG model [327], to reveal the
“hadronization point” and, second, from fitting new data concerning fluctuation of
conserved charges to higher order Lattice susceptibilities [328]. Some remarks are
also necessary with regard to the Lattice conclusion that the parton to hadron phase
transition is “merely” a cross-over at small μ B , top RHIC and LHC energy.
We have shown in Sect. 7.3.4 that, ideally, the Statistical Hadronization
Model(SHM) freeze-out curve should reveal the QCD parton-hadron phase
transformation line in the (T, μ B ) plane, i.e. the most prominent feature of the QCD
phase diagram. This follows from the assumption that inelastic reactions (except
resonance decays) among hadrons cease directly at the instant of hadronization:
chemical hadron freeze-out determines the hadronization “point” corresponding to
the chosen A+A collision energy. Add, for correctness: as long as freeze-out occurs
from the QCD hadronization transition, i.e. from a QGP. About freeze-out from hot,
dense hadronic matter in expansion, we do not yet know the final interpretation
of the hadronic multiplicities. Now, the above ideal picture, absence of final state
effects from the afterburning phase, may require certain corrections. It has been
shown [329] that, on the one hand, the bulk hadrons from a relativistic A + A
collision (i.e. pions and kaons that carry about 95% of the total cm energy output
at LHC energy) do indeed pass the afterburner stage essentially unchanged. At the
relatively low SPS energies, this applies also to protons and Lambdas. Whereas
the antibaryon yields get reduced, away from chemical equilibrium, by annihilation
processes that occur throughout the hadron/resonance expansion phase. At top
RHIC and LHC energies, baryons and antibaryons are similarly affected, with the
exception of the Omega hyperons which suffer little annihilation. These afterburner
effects were quantified [330] by the microscopic transport model UrQMD [312]
which is employed in many of the current multi-stage “hybrid” models [313, 316]
for the afterburner stage. The thus obtained modification factors for each species
were applied to the grand canonical partition functions of the SHM [330]. We
show the results in Fig. 7.78, which gives (T , μ B ) points for AGS, SPS and LHC
energies. The overall result of the annihilation corrections is seen to be an upward
shift of the hadronization curve(see also [331]), above the curve resulting from
the uncorrected SHM procedure which agrees with other SHM work [332]. The
437
the suppression theme is now turning over to the bottonomium production at the
LHC [326], visible there because of the much lower thermal bottom quark density.
7.9.5 Hadronization and the QCD Phase Diagram
This chapter will have two main topics, first the analysis of hadron production
multiplicities with the Statistical Hadronization Model (SHM) that incorporates the
canonical or grandcanonical partition functions of a hadron-resonance gas (HRG)
model. This will be an update on Sect. 7.3. Second, however, we turn to new
developments of lattice QCD theory, extension to finite baryochemical potential and
determination of the hadronization parameters T vs. μ B from, first, a determination
of the overlap between Lattice QCD and the HRG model [327], to reveal the
“hadronization point” and, second, from fitting new data concerning fluctuation of
conserved charges to higher order Lattice susceptibilities [328]. Some remarks are
also necessary with regard to the Lattice conclusion that the parton to hadron phase
transition is “merely” a cross-over at small μ B , top RHIC and LHC energy.
We have shown in Sect. 7.3.4 that, ideally, the Statistical Hadronization
Model(SHM) freeze-out curve should reveal the QCD parton-hadron phase
transformation line in the (T, μ B ) plane, i.e. the most prominent feature of the QCD
phase diagram. This follows from the assumption that inelastic reactions (except
resonance decays) among hadrons cease directly at the instant of hadronization:
chemical hadron freeze-out determines the hadronization “point” corresponding to
the chosen A+A collision energy. Add, for correctness: as long as freeze-out occurs
from the QCD hadronization transition, i.e. from a QGP. About freeze-out from hot,
dense hadronic matter in expansion, we do not yet know the final interpretation
of the hadronic multiplicities. Now, the above ideal picture, absence of final state
effects from the afterburning phase, may require certain corrections. It has been
shown [329] that, on the one hand, the bulk hadrons from a relativistic A + A
collision (i.e. pions and kaons that carry about 95% of the total cm energy output
at LHC energy) do indeed pass the afterburner stage essentially unchanged. At the
relatively low SPS energies, this applies also to protons and Lambdas. Whereas
the antibaryon yields get reduced, away from chemical equilibrium, by annihilation
processes that occur throughout the hadron/resonance expansion phase. At top
RHIC and LHC energies, baryons and antibaryons are similarly affected, with the
exception of the Omega hyperons which suffer little annihilation. These afterburner
effects were quantified [330] by the microscopic transport model UrQMD [312]
which is employed in many of the current multi-stage “hybrid” models [313, 316]
for the afterburner stage. The thus obtained modification factors for each species
were applied to the grand canonical partition functions of the SHM [330]. We
show the results in Fig. 7.78, which gives (T , μ B ) points for AGS, SPS and LHC
energies. The overall result of the annihilation corrections is seen to be an upward
shift of the hadronization curve(see also [331]), above the curve resulting from
the uncorrected SHM procedure which agrees with other SHM work [332]. The