86
G. Altarelli and S. Forte
depend on the number of quark flavours n f and on their masses. For example,
for n f = 2 or 2 + 1 (i.e. two light u and d quarks and one heavier s quark),
T C ∼ 175 MeV and C ) ∼ 0.5 − 1.0 GeV/fm 3 . For realistic values of the masses
m s and m u,d the phase transition appears to be a second order one, while it becomes
first order for very small or very large m u,d,s . The hadronic phase and the deconfined
phase are separated by a crossover line at small densities and by a critical line at
high densities. Determining the exact location of the critical point in T and μ B is
an important challenge for theory which is also important for the interpretation of
heavy ion collision experiments. At high densities the colour superconducting phase
is also present with bosonic diquarks acting as Cooper pairs.
A large investment is being done in experiments of heavy ion collisions with
the aim of finding some evidence of the quark gluon plasma phase. Many exciting
results have been found at the CERN SPS in the past years and more recently at
RHIC. The status of the experimental search for the quark-gluon plasma will be
reviewed in Chap. 7.
The linearly rising term in the potential makes it energetically impossible to
separate a q − ¯
q pair. If the pair is created at one space-time point, for example
in e + e − annihilation, and then the quark and the antiquark start moving away from
each other in the center of mass frame, it soon becomes energetically favourable
to create additional pairs, smoothly distributed in rapidity between the two leading
charges, which neutralise colour and allow the final state to be reorganised into two
jets of colourless hadrons, that communicate in the central region by a number of
“wee” hadrons with small energy. It is just like the familiar example of the broken
magnet: if you try to isolate a magnetic pole by stretching a dipole, the magnet
breaks down and two new poles appear at the breaking point.
Confinement is essential to explain why nuclear forces have very short range
while massless gluon exchange would be long range. Nucleons are colour singlets
and they cannot exchange colour octet gluons but only colourless states. The lightest
colour singlet hadronic particles are pions. So the range of nuclear forces is fixed by
the pion mass r m −1
π 10 −13 cm : V ≈ exp(−m π r)/r.
Why SU (N C = 3) colour ? The selection of SU (3) as colour gauge group is
unique in view of a number of constraints. (a) The group must admit complex
representations because it must be able to distinguish a quark from an antiquark.
In fact there are meson states made up of q ¯
q but not analogous qq bound states.
Among simple groups this restricts the choice to SU (N) with N ≥ 3, SO(4N + 2)
with N ≥ 2 (taking into account that SO(6) has the same algebra as SU (4)) and
E(6). (b) The group must admit a completely antisymmetric colour singlet baryon
made up of 3 quarks: qqq. In fact, from the study of hadron spectroscopy we
know that the low lying baryons, completing an octet and a decuplet of (flavour)
SU (3) (the approximate symmetry that rotate the three light quarks u, d and s), are
made up of three quarks and are colour singlets. The qqq wave function must be
completely antisymmetric in colour in order to agree with Fermi statistics. Indeed
if we consider, for example, a N ∗++ with spin z-component +3/2, this is made
up of (u ⇑ u ⇑ u ⇑) in an s-state. Thus its wave function is totally symmetric in
space, spin and flavour so that complete antisymmetry in colour is required by Fermi
G. Altarelli and S. Forte
depend on the number of quark flavours n f and on their masses. For example,
for n f = 2 or 2 + 1 (i.e. two light u and d quarks and one heavier s quark),
T C ∼ 175 MeV and C ) ∼ 0.5 − 1.0 GeV/fm 3 . For realistic values of the masses
m s and m u,d the phase transition appears to be a second order one, while it becomes
first order for very small or very large m u,d,s . The hadronic phase and the deconfined
phase are separated by a crossover line at small densities and by a critical line at
high densities. Determining the exact location of the critical point in T and μ B is
an important challenge for theory which is also important for the interpretation of
heavy ion collision experiments. At high densities the colour superconducting phase
is also present with bosonic diquarks acting as Cooper pairs.
A large investment is being done in experiments of heavy ion collisions with
the aim of finding some evidence of the quark gluon plasma phase. Many exciting
results have been found at the CERN SPS in the past years and more recently at
RHIC. The status of the experimental search for the quark-gluon plasma will be
reviewed in Chap. 7.
The linearly rising term in the potential makes it energetically impossible to
separate a q − ¯
q pair. If the pair is created at one space-time point, for example
in e + e − annihilation, and then the quark and the antiquark start moving away from
each other in the center of mass frame, it soon becomes energetically favourable
to create additional pairs, smoothly distributed in rapidity between the two leading
charges, which neutralise colour and allow the final state to be reorganised into two
jets of colourless hadrons, that communicate in the central region by a number of
“wee” hadrons with small energy. It is just like the familiar example of the broken
magnet: if you try to isolate a magnetic pole by stretching a dipole, the magnet
breaks down and two new poles appear at the breaking point.
Confinement is essential to explain why nuclear forces have very short range
while massless gluon exchange would be long range. Nucleons are colour singlets
and they cannot exchange colour octet gluons but only colourless states. The lightest
colour singlet hadronic particles are pions. So the range of nuclear forces is fixed by
the pion mass r m −1
π 10 −13 cm : V ≈ exp(−m π r)/r.
Why SU (N C = 3) colour ? The selection of SU (3) as colour gauge group is
unique in view of a number of constraints. (a) The group must admit complex
representations because it must be able to distinguish a quark from an antiquark.
In fact there are meson states made up of q ¯
q but not analogous qq bound states.
Among simple groups this restricts the choice to SU (N) with N ≥ 3, SO(4N + 2)
with N ≥ 2 (taking into account that SO(6) has the same algebra as SU (4)) and
E(6). (b) The group must admit a completely antisymmetric colour singlet baryon
made up of 3 quarks: qqq. In fact, from the study of hadron spectroscopy we
know that the low lying baryons, completing an octet and a decuplet of (flavour)
SU (3) (the approximate symmetry that rotate the three light quarks u, d and s), are
made up of three quarks and are colour singlets. The qqq wave function must be
completely antisymmetric in colour in order to agree with Fermi statistics. Indeed
if we consider, for example, a N ∗++ with spin z-component +3/2, this is made
up of (u ⇑ u ⇑ u ⇑) in an s-state. Thus its wave function is totally symmetric in
space, spin and flavour so that complete antisymmetry in colour is required by Fermi