7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
399
T /T c = 1.5. In this picture, the screened potential (Eq. (7.69)) can still give rise
to bound cc states provided their radius is smaller than r D . The pioneering study
of Matsui and Satz [41] concluded that screening in a QGP system would dissolve
the J//, or its c ¯
c precursor, at T ≥ 1.3 T c whereas the χ c and states would be
suppressed already directly above T c .
The corresponding energy density for J// suppression, employing
// c ≈ (T /T c )
4
≈ 2.9
(7.70)
(obtained with c ≈ 1 GeV/fm 3 from lattice QCD), would thus amount to about
2.9 GeV/fm 3 . This motivated an extensive experimental effort at the CERN SPS Pb
beam at
√
s = 17.3 GeV. We have seen in Sect. 7.2 that the Bjorken estimate [45]
of average transverse energy density reached in central Pb+Pb collisions [43, 44]
amounts to = (3.0 ± 0.6) GeV/fm 3 , with higher to be expected in the interior
fireball sections: encouraging conditions.
However, the above approach assumes the validity of a two-body potential
treatment at finite T , near a conjectured critical point of QCD. More recently the
quarkonium spectrum was calculated directly in finite temperature lattice QCD
[232], with the striking result that the J// dissociation temperature in a realistic
non-perturbative treatment of the QCD plasma state moves up to about T = 2 T c ,
whereas χ c and dissociation is expected [230] to occur at T = (1.1–1.2)T c .
In addition to high T breakup of c ¯
c or J//, we have to take account of the
so-called “normal suppression” of charmonium yields, observed in proton-nucleus
collisions [233]. This effect is due to a re-scattering dissociation of the primordially
produced, pre-hadronic cc system upon traversal of (cold) hadronic matter [234]. It
can be studied in p+A collisions where the data on J// production relative to pp
collisions can be described by the survival probability
S pA ≡
σ pA
Aσ pp
=
d
2 b
dz ρ A (b, z) exp
−(A − 1)
∞
z
dz
ρ A (b, z
)σ abs
(7.71)
where σ abs is the effective cross section for the “absorption” (break-up) of the cc in
cold nuclear matter, and ρ A is the transverse nuclear density profile. The data [233]
suggest σ abs = 4.2 mb. The generalization of Eq. (7.71) to the nucleus-nucleus
case [235] gives a good description of the J// suppression (relative to binary pp
scaling) in S+U and peripheral Pb+Pb collisions at top SPS energy [226]. It has thus
become customary to quantify the J// suppression in central A+A collisions by
relating the observed yield, not directly to the scaled pp yield (thus obtaining R AA ),
but to a hypothetical “normal absorption” yield baseline, established by Eq. (7.71).
All further absorption is called “anomalous suppression”.
Figure 7.54 shows the results gathered at
√
s = 17.3 GeV by the NA38–
NA50–NA60 di-muon spectrometer [236], for minimum bias S+U (
√
s = 20 GeV),
In+In and Pb+Pb. Up to N part ≈ 100 all yields gather at the “normal absorption”
399
T /T c = 1.5. In this picture, the screened potential (Eq. (7.69)) can still give rise
to bound cc states provided their radius is smaller than r D . The pioneering study
of Matsui and Satz [41] concluded that screening in a QGP system would dissolve
the J//, or its c ¯
c precursor, at T ≥ 1.3 T c whereas the χ c and states would be
suppressed already directly above T c .
The corresponding energy density for J// suppression, employing
// c ≈ (T /T c )
4
≈ 2.9
(7.70)
(obtained with c ≈ 1 GeV/fm 3 from lattice QCD), would thus amount to about
2.9 GeV/fm 3 . This motivated an extensive experimental effort at the CERN SPS Pb
beam at
√
s = 17.3 GeV. We have seen in Sect. 7.2 that the Bjorken estimate [45]
of average transverse energy density reached in central Pb+Pb collisions [43, 44]
amounts to = (3.0 ± 0.6) GeV/fm 3 , with higher to be expected in the interior
fireball sections: encouraging conditions.
However, the above approach assumes the validity of a two-body potential
treatment at finite T , near a conjectured critical point of QCD. More recently the
quarkonium spectrum was calculated directly in finite temperature lattice QCD
[232], with the striking result that the J// dissociation temperature in a realistic
non-perturbative treatment of the QCD plasma state moves up to about T = 2 T c ,
whereas χ c and dissociation is expected [230] to occur at T = (1.1–1.2)T c .
In addition to high T breakup of c ¯
c or J//, we have to take account of the
so-called “normal suppression” of charmonium yields, observed in proton-nucleus
collisions [233]. This effect is due to a re-scattering dissociation of the primordially
produced, pre-hadronic cc system upon traversal of (cold) hadronic matter [234]. It
can be studied in p+A collisions where the data on J// production relative to pp
collisions can be described by the survival probability
S pA ≡
σ pA
Aσ pp
=
d
2 b
dz ρ A (b, z) exp
−(A − 1)
∞
z
dz
ρ A (b, z
)σ abs
(7.71)
where σ abs is the effective cross section for the “absorption” (break-up) of the cc in
cold nuclear matter, and ρ A is the transverse nuclear density profile. The data [233]
suggest σ abs = 4.2 mb. The generalization of Eq. (7.71) to the nucleus-nucleus
case [235] gives a good description of the J// suppression (relative to binary pp
scaling) in S+U and peripheral Pb+Pb collisions at top SPS energy [226]. It has thus
become customary to quantify the J// suppression in central A+A collisions by
relating the observed yield, not directly to the scaled pp yield (thus obtaining R AA ),
but to a hypothetical “normal absorption” yield baseline, established by Eq. (7.71).
All further absorption is called “anomalous suppression”.
Figure 7.54 shows the results gathered at
√
s = 17.3 GeV by the NA38–
NA50–NA60 di-muon spectrometer [236], for minimum bias S+U (
√
s = 20 GeV),
In+In and Pb+Pb. Up to N part ≈ 100 all yields gather at the “normal absorption”