408
R. Stock
widening with collision centrality [136]. The best theoretical representation of the
excess yield again results (like in Fig. 7.58, right panel) from the broadening model
[133, 135, 255] where the spectral function is smeared due to various coupling
mechanisms within the medium via the vector dominance model, prior to hadronic
freeze-out. In the VDM couples, both, to pion pair annihilation, and to excited
baryon states like the N ∗ (1520), via their Nππ decay branches.
The above data still imply serious conceptual questions. It is unclear to exactly
which stage of the dynamical evolution (in the vicinity of T = T c ) the excess
dilepton yield should correspond. As the observations appear to be coupled to inmedium meson “metabolism” we need to identify a period of temporal extension
above the (in vacuo) half life (of 1.3 fm/c), safely 2 fm/c. This period should
be located in the vicinity of hadro-chemical freeze-out. From top SPS to RHIC
energy, hadro-chemical freeze-out should closely coincide with hadron formation,
i.e. it should occur near the parton-hadron coexistence line, at T = T c . The
microscopic parton cascade model of reference [85] implements the Webber [121]
phenomenological, non-perturbative QCD hadronization model (recall Sect. 7.3.3)
which proposes pre-hadronization clusters of color neutralization (Fig. 7.31) as the
central hadronization step. In it, so one might speculate, the transition from pQCD to
non perturbative QCD creates the chiral condensates qq, spontaneously breaking
chiral symmetry [256] (see below), and creating hadronic mass. The overall process,
from pQCD color neutralization to on-shell hadrons, takes about 2.5 fm/c [85, 86]
at top SPS energy. This could, thus, be the period of excess dilepton yield creation.
However, the relation of the models employed above [133–135, 255, 256] to this
primordial spontaneous creation of chiral condensates is still essentially unknown
[256].
Thus, at present, the 1990s paradigm of a direct observation of the chiral phase
transition in QCD has been lost. The Brown-Rho model [134] predicted the mass
to drop to zero at T = T c , occurring as a certain power of the ratio qq
med / qq
vac
of the chiral condensate in medium and in vacuum which approaches zero at
the chiral phase transition temperature, then expected to coincidence with the
deconfinement temperature. This “dropping mass” model is ruled out by the data
in Fig. 7.58 and 7.59. This is, perhaps, a further manifestation of the fact that the
deconfined QGP state at T ≥ T c is not a simple pQCD gas of quarks and gluons
[213]. In fact, lattice calculations [232, 257] find indications of surviving light qq
pair correlations in the vector channel at T ≥ T c . Thus the two most prominent
symmetries of the QCD Lagrangian, non abelian gauge invariance (related to
confinement) and chiral invariance (related to mass) might exhibit different critical
patterns at T = T c and low baryo-chemical potential. This conjecture is best
illustrated by the observation that the broad, structureless NA60 excess dilepton
spectrum of Fig. 7.59 (after cocktail subtraction) is equally well reproduced by a
T ≈ 160–170 MeV calculation in hadronic (equilibrium) matter [133, 253, 254],
and by a thermal QGP fireball of qq annihilation at this average temperature [252],
as illustrated here by the model curve labeled “Kaempfer” in Fig. 7.58 (right panel).
This observation has invited the concept of parton-hadron duality near T c [258],
which might be provocatively translated as “the QCD chiral transition properties
R. Stock
widening with collision centrality [136]. The best theoretical representation of the
excess yield again results (like in Fig. 7.58, right panel) from the broadening model
[133, 135, 255] where the spectral function is smeared due to various coupling
mechanisms within the medium via the vector dominance model, prior to hadronic
freeze-out. In the VDM couples, both, to pion pair annihilation, and to excited
baryon states like the N ∗ (1520), via their Nππ decay branches.
The above data still imply serious conceptual questions. It is unclear to exactly
which stage of the dynamical evolution (in the vicinity of T = T c ) the excess
dilepton yield should correspond. As the observations appear to be coupled to inmedium meson “metabolism” we need to identify a period of temporal extension
above the (in vacuo) half life (of 1.3 fm/c), safely 2 fm/c. This period should
be located in the vicinity of hadro-chemical freeze-out. From top SPS to RHIC
energy, hadro-chemical freeze-out should closely coincide with hadron formation,
i.e. it should occur near the parton-hadron coexistence line, at T = T c . The
microscopic parton cascade model of reference [85] implements the Webber [121]
phenomenological, non-perturbative QCD hadronization model (recall Sect. 7.3.3)
which proposes pre-hadronization clusters of color neutralization (Fig. 7.31) as the
central hadronization step. In it, so one might speculate, the transition from pQCD to
non perturbative QCD creates the chiral condensates qq, spontaneously breaking
chiral symmetry [256] (see below), and creating hadronic mass. The overall process,
from pQCD color neutralization to on-shell hadrons, takes about 2.5 fm/c [85, 86]
at top SPS energy. This could, thus, be the period of excess dilepton yield creation.
However, the relation of the models employed above [133–135, 255, 256] to this
primordial spontaneous creation of chiral condensates is still essentially unknown
[256].
Thus, at present, the 1990s paradigm of a direct observation of the chiral phase
transition in QCD has been lost. The Brown-Rho model [134] predicted the mass
to drop to zero at T = T c , occurring as a certain power of the ratio qq
med / qq
vac
of the chiral condensate in medium and in vacuum which approaches zero at
the chiral phase transition temperature, then expected to coincidence with the
deconfinement temperature. This “dropping mass” model is ruled out by the data
in Fig. 7.58 and 7.59. This is, perhaps, a further manifestation of the fact that the
deconfined QGP state at T ≥ T c is not a simple pQCD gas of quarks and gluons
[213]. In fact, lattice calculations [232, 257] find indications of surviving light qq
pair correlations in the vector channel at T ≥ T c . Thus the two most prominent
symmetries of the QCD Lagrangian, non abelian gauge invariance (related to
confinement) and chiral invariance (related to mass) might exhibit different critical
patterns at T = T c and low baryo-chemical potential. This conjecture is best
illustrated by the observation that the broad, structureless NA60 excess dilepton
spectrum of Fig. 7.59 (after cocktail subtraction) is equally well reproduced by a
T ≈ 160–170 MeV calculation in hadronic (equilibrium) matter [133, 253, 254],
and by a thermal QGP fireball of qq annihilation at this average temperature [252],
as illustrated here by the model curve labeled “Kaempfer” in Fig. 7.58 (right panel).
This observation has invited the concept of parton-hadron duality near T c [258],
which might be provocatively translated as “the QCD chiral transition properties