312
R. Stock
to occur between deconfined quarks and confined hadrons. At near-zero net
baryon density (corresponding to big bang conditions) non-perturbative LatticeQCD places this transition at an energy density of about 1 GeV/fm 3 , and at a
critical temperature, T crit ≈ 170 MeV [4–8] (see the article on Lattice QCD in
this Volume). The ultimate goal of the physics with ultrarelativistic heavy ions is
to locate this transition, elaborate its properties, and gain insight into the detailed
nature of the deconfined QGP phase that should exist above. What is meant by
the term “ultrarelativistic” is defined by the requirement that the reaction dynamics
reaches or exceeds the critical density ≈ 1 GeV/fm 3 . Required beam energies turn
out [8] to be
√
s ≥ 10 GeV, and various experimental programs have been carried
out or are being prepared at the CERN SPS (up to about 20 GeV), at the BNL RHIC
collider (up to 200 GeV) and finally reaching up to 5.5 TeV at the LHC of CERN.
QCD confinement-deconfinement is of course not limited to the domain that
is relevant to cosmological expansion dynamics, at very small excess of baryon
over anti-baryon number density and, thus, near zero baryo-chemical potential
μ B . In fact, modern QCD suggests [9–11] a detailed phase diagram of QCD
matter and its states, in the plane of T and baryo-chemical potential μ B . For a
map of the QCD matter phase diagram we are thus employing the terminology
of the grand canonical Gibbs ensemble that describes an extended volume V of
partonic or hadronic matter at temperature T . In it, total particle number is not
conserved at relativistic energy, due to particle production-annihilation processes
occurring at the microscopic level. However, the probability distributions (partition
functions) describing the relative particle species abundances have to respect the
presence of certain, to be conserved net quantum numbers (i), notably non-zero
net baryon number and zero net strangeness and charm. Their global conservation
is achieved by a thermodynamic trick, adding to the system Lagrangian a so-called
Lagrange multiplier term, for each of such quantum number conservation tasks. This
procedure enters a “chemical potential” μ i that modifies the partition function via
an extra term exp (−μ i /T ) occurring in the phase space integral (see Sect. 7.3 for
detail). It modifies the canonical “punishment factor” (exp (−E/T )), where E is the
total particle energy in vacuum, to arrive at an analogous grand canonical factor for
the extended medium, of exp (−E/T − μ i /T ). This concept is of prime importance
for a description of the state of matter created in heavy ion collisions, where
net-baryon number (valence quarks) carrying objects are considered—extended
“fireballs” of QCD matter. The same applies to the matter in the interior of neutron
stars. The corresponding conservation of net baryon number is introduced into the
grand canonical statistical model of QCD matter via the “baryo-chemical potential”
μ B .
We employ this terminology to draw a phase diagram of QCD matter in Fig. 7.1,
in the variables T and μ B . Note that μ B is high at low energies of collisions creating
a matter fireball. In a head-on collision of two mass 200 nuclei at
√
s = 15 GeV
the fireball contains about equal numbers of newly created quark-antiquark pairs
(of zero net baryon number), and of initial valence quarks. The accommodation of
the latter, into created hadronic species, thus requires a formidable redistribution
task of net baryon number, reflecting in a high value of μ B . Conversely, at LHC
R. Stock
to occur between deconfined quarks and confined hadrons. At near-zero net
baryon density (corresponding to big bang conditions) non-perturbative LatticeQCD places this transition at an energy density of about 1 GeV/fm 3 , and at a
critical temperature, T crit ≈ 170 MeV [4–8] (see the article on Lattice QCD in
this Volume). The ultimate goal of the physics with ultrarelativistic heavy ions is
to locate this transition, elaborate its properties, and gain insight into the detailed
nature of the deconfined QGP phase that should exist above. What is meant by
the term “ultrarelativistic” is defined by the requirement that the reaction dynamics
reaches or exceeds the critical density ≈ 1 GeV/fm 3 . Required beam energies turn
out [8] to be
√
s ≥ 10 GeV, and various experimental programs have been carried
out or are being prepared at the CERN SPS (up to about 20 GeV), at the BNL RHIC
collider (up to 200 GeV) and finally reaching up to 5.5 TeV at the LHC of CERN.
QCD confinement-deconfinement is of course not limited to the domain that
is relevant to cosmological expansion dynamics, at very small excess of baryon
over anti-baryon number density and, thus, near zero baryo-chemical potential
μ B . In fact, modern QCD suggests [9–11] a detailed phase diagram of QCD
matter and its states, in the plane of T and baryo-chemical potential μ B . For a
map of the QCD matter phase diagram we are thus employing the terminology
of the grand canonical Gibbs ensemble that describes an extended volume V of
partonic or hadronic matter at temperature T . In it, total particle number is not
conserved at relativistic energy, due to particle production-annihilation processes
occurring at the microscopic level. However, the probability distributions (partition
functions) describing the relative particle species abundances have to respect the
presence of certain, to be conserved net quantum numbers (i), notably non-zero
net baryon number and zero net strangeness and charm. Their global conservation
is achieved by a thermodynamic trick, adding to the system Lagrangian a so-called
Lagrange multiplier term, for each of such quantum number conservation tasks. This
procedure enters a “chemical potential” μ i that modifies the partition function via
an extra term exp (−μ i /T ) occurring in the phase space integral (see Sect. 7.3 for
detail). It modifies the canonical “punishment factor” (exp (−E/T )), where E is the
total particle energy in vacuum, to arrive at an analogous grand canonical factor for
the extended medium, of exp (−E/T − μ i /T ). This concept is of prime importance
for a description of the state of matter created in heavy ion collisions, where
net-baryon number (valence quarks) carrying objects are considered—extended
“fireballs” of QCD matter. The same applies to the matter in the interior of neutron
stars. The corresponding conservation of net baryon number is introduced into the
grand canonical statistical model of QCD matter via the “baryo-chemical potential”
μ B .
We employ this terminology to draw a phase diagram of QCD matter in Fig. 7.1,
in the variables T and μ B . Note that μ B is high at low energies of collisions creating
a matter fireball. In a head-on collision of two mass 200 nuclei at
√
s = 15 GeV
the fireball contains about equal numbers of newly created quark-antiquark pairs
(of zero net baryon number), and of initial valence quarks. The accommodation of
the latter, into created hadronic species, thus requires a formidable redistribution
task of net baryon number, reflecting in a high value of μ B . Conversely, at LHC