428
R. Stock
For reference of such data, e.g. statistical species equilibrium (Sect. 7.3), dilepton
studies of light vector meson “melting” at the phase boundary (Sect. 7.6.3), and
hadronic event-by-event fluctuations (Sects. 7.7.2 and 7.7.3), to theoretical QCD
predictions, a recent progress of lattice QCD [8–10] is of foremost importance.
The technical limitation of lattice QCD to the singular case of vanishing chemical
potential, μ B = 0 (which arises from the Fermion determinant in the lattice
formulation of the grand canonical partition function), has been overcome recently.
Three different approaches have been outlined, the respective inherent approximation schemes touching upon the limits of both the mathematical and conceptual
framework of lattice theory, and of present day computation power even with multiteraflop machines. First results comprise the prediction of the parton-hadron phase
boundary line, which interpolates between the well studied limits of the crossoverregion at μ B → 0, T ≥ T c and the high net baryon density, low T region for
which a first order character of the phase transition has been predicted by chiral
QCD models [15]. We have illustrated this line in Fig. 7.1, and we have shown in
Sect. 7.3 that hadronic freeze-out occurs at, or near this line at
√
s ≥ 17.3 GeV
(top SPS energy). The coexistence line includes an intermediate (T, μ B ) domain
featuring a critical point of QCD at which the first order line at higher μ B terminates,
in a critical domain of (T, μ B ) in which the transition is of second order. One
thus expects the nature of the confining hadronization transition—an open QCD
question—to change from a crossover to a second order, and onward to a first
order characteristics in a relatively small interval of μ B that is accessible to nuclear
collision dynamics at the relatively modest
√
s of about 5 to 15 GeV. This domain
has as of yet only received a first experimental glance, but the top AGS and low SPS
energy experiments exhibit phenomena that can be connected to the occurrence of a
critical point and/or a first order phase transition, notably the “SPS plateau” in m T
the non-monotonous K + /π + excitation function, and the eventwise fluctuations of
this ratio (Sects. 7.2.6, 7.3, 7.7.2 and 7.7.3). A renewed effort is underway at RHIC,
at the CERN SPS and at the future GSI FAIR facility to study hadronization, inmedium meson modification induced by the onset of QCD chiral restoration, as
well as critical fluctuations and flow, in the low
√
s domain.
7.9 Postscript
Reinhard Stock
7.9.1 Progress of the Field
Returning, after a decade, to the topic of “Relativistic Nucleus-Nucleus Collisions
and the QCD Phase Diagram”, one is struck by the impressive progress that has
transported many of the crucial themes, and physics observables, from initial,
R. Stock
For reference of such data, e.g. statistical species equilibrium (Sect. 7.3), dilepton
studies of light vector meson “melting” at the phase boundary (Sect. 7.6.3), and
hadronic event-by-event fluctuations (Sects. 7.7.2 and 7.7.3), to theoretical QCD
predictions, a recent progress of lattice QCD [8–10] is of foremost importance.
The technical limitation of lattice QCD to the singular case of vanishing chemical
potential, μ B = 0 (which arises from the Fermion determinant in the lattice
formulation of the grand canonical partition function), has been overcome recently.
Three different approaches have been outlined, the respective inherent approximation schemes touching upon the limits of both the mathematical and conceptual
framework of lattice theory, and of present day computation power even with multiteraflop machines. First results comprise the prediction of the parton-hadron phase
boundary line, which interpolates between the well studied limits of the crossoverregion at μ B → 0, T ≥ T c and the high net baryon density, low T region for
which a first order character of the phase transition has been predicted by chiral
QCD models [15]. We have illustrated this line in Fig. 7.1, and we have shown in
Sect. 7.3 that hadronic freeze-out occurs at, or near this line at
√
s ≥ 17.3 GeV
(top SPS energy). The coexistence line includes an intermediate (T, μ B ) domain
featuring a critical point of QCD at which the first order line at higher μ B terminates,
in a critical domain of (T, μ B ) in which the transition is of second order. One
thus expects the nature of the confining hadronization transition—an open QCD
question—to change from a crossover to a second order, and onward to a first
order characteristics in a relatively small interval of μ B that is accessible to nuclear
collision dynamics at the relatively modest
√
s of about 5 to 15 GeV. This domain
has as of yet only received a first experimental glance, but the top AGS and low SPS
energy experiments exhibit phenomena that can be connected to the occurrence of a
critical point and/or a first order phase transition, notably the “SPS plateau” in m T
the non-monotonous K + /π + excitation function, and the eventwise fluctuations of
this ratio (Sects. 7.2.6, 7.3, 7.7.2 and 7.7.3). A renewed effort is underway at RHIC,
at the CERN SPS and at the future GSI FAIR facility to study hadronization, inmedium meson modification induced by the onset of QCD chiral restoration, as
well as critical fluctuations and flow, in the low
√
s domain.
7.9 Postscript
Reinhard Stock
7.9.1 Progress of the Field
Returning, after a decade, to the topic of “Relativistic Nucleus-Nucleus Collisions
and the QCD Phase Diagram”, one is struck by the impressive progress that has
transported many of the crucial themes, and physics observables, from initial,