360
R. Stock
multiplicity equation (7.36) and the contributions arising from the unresolved decay
of heavier hadrons and resonances:
N
observed
i
= N
primary
i
+
j
Br(j → i) N j .
(7.37)
After having exposed the formal gear of grand canonical ensemble analysis we
note that Eq. (7.36) permits a simple, first orientation concerning the relation of T
to μ B in A+A collisions by considering, e.g., the antiproton to proton production
ratio. From Eq. (7.36) we infer the simple expression
N(p)/N(p) = exp(−2μ B /T ).
(7.38)
Taking the mid-rapidity value 0.8 for p/p (from Fig. 7.26) at top RHIC energy,
and assuming that hadronization occurs directly at the QCD phase boundary, and
hence T ≈ T c ≈ 165 MeV, we get μ B 18 MeV from Eq. (7.38), in close
agreement with the result, μ B = 20 MeV, obtained [108] from the full SHM
analysis. Equation (7.38) illustrates the role played by μ B in the grand canonical
ensemble. It logarithmically depends on the ratio of newly created quark-antiquark
pairs (the latter represented by the ¯
p yield), to the total number of quarks including
the net baryon number-carrying valence quarks (represented by the p yield).
The most outstanding property of the hadronic multiplicities observed in central
A+A collisions is the enhancement of all strange hadron species, by factors ranging
from about 2 to 20, as compared to the corresponding production rates in elementary
hadron-hadron (and e + e − annihilation) reactions at the same
√
s. I.e. the nuclear
collision modifies the relative strangeness output by a “nuclear modification factor”,
R AA
s
= N AA
s /0.5 N part · N
pp
s , which depends on
√
s and N part and features a
hierarchy with regard to the strangeness number s = 1, 2, 3 of the considered
species, R AA
s=1 < R AA
s=2 < R AA
s=3 . These properties are illustrated in Figs. 7.28
and 7.29. The former shows the ratio of total K + to positive pion multiplicities
in central Au+Au/Pb+Pb collisions, from lower AGS to top RHIC energies, in
comparison to corresponding ratios from minimum bias p+p collisions [100]. We
have chosen this ratio, instead of
K +
/N part , because it reflects, rather directly, the
“Wroblewski ratio” of produced strange to non-strange quarks [107], contained in
the produced hadrons,
λ s ≡
2(s + s)
+ d + u +
d
≈
0.2 inpp
0.45 inAA.
(7.39)
The low value of λ s in pp (and all other elementary) collisions reflects a quark population far away from u, d, s flavor equilibrium, indicating strangeness suppression
[109].
The so-called strangeness enhancement property of A+A collisions (obvious
from Figs. 7.28 and 7.29) is, thus, seen as the removal of strangeness suppression;
R. Stock
multiplicity equation (7.36) and the contributions arising from the unresolved decay
of heavier hadrons and resonances:
N
observed
i
= N
primary
i
+
j
Br(j → i) N j .
(7.37)
After having exposed the formal gear of grand canonical ensemble analysis we
note that Eq. (7.36) permits a simple, first orientation concerning the relation of T
to μ B in A+A collisions by considering, e.g., the antiproton to proton production
ratio. From Eq. (7.36) we infer the simple expression
N(p)/N(p) = exp(−2μ B /T ).
(7.38)
Taking the mid-rapidity value 0.8 for p/p (from Fig. 7.26) at top RHIC energy,
and assuming that hadronization occurs directly at the QCD phase boundary, and
hence T ≈ T c ≈ 165 MeV, we get μ B 18 MeV from Eq. (7.38), in close
agreement with the result, μ B = 20 MeV, obtained [108] from the full SHM
analysis. Equation (7.38) illustrates the role played by μ B in the grand canonical
ensemble. It logarithmically depends on the ratio of newly created quark-antiquark
pairs (the latter represented by the ¯
p yield), to the total number of quarks including
the net baryon number-carrying valence quarks (represented by the p yield).
The most outstanding property of the hadronic multiplicities observed in central
A+A collisions is the enhancement of all strange hadron species, by factors ranging
from about 2 to 20, as compared to the corresponding production rates in elementary
hadron-hadron (and e + e − annihilation) reactions at the same
√
s. I.e. the nuclear
collision modifies the relative strangeness output by a “nuclear modification factor”,
R AA
s
= N AA
s /0.5 N part · N
pp
s , which depends on
√
s and N part and features a
hierarchy with regard to the strangeness number s = 1, 2, 3 of the considered
species, R AA
s=1 < R AA
s=2 < R AA
s=3 . These properties are illustrated in Figs. 7.28
and 7.29. The former shows the ratio of total K + to positive pion multiplicities
in central Au+Au/Pb+Pb collisions, from lower AGS to top RHIC energies, in
comparison to corresponding ratios from minimum bias p+p collisions [100]. We
have chosen this ratio, instead of
K +
/N part , because it reflects, rather directly, the
“Wroblewski ratio” of produced strange to non-strange quarks [107], contained in
the produced hadrons,
λ s ≡
2(s + s)
+ d + u +
d
≈
0.2 inpp
0.45 inAA.
(7.39)
The low value of λ s in pp (and all other elementary) collisions reflects a quark population far away from u, d, s flavor equilibrium, indicating strangeness suppression
[109].
The so-called strangeness enhancement property of A+A collisions (obvious
from Figs. 7.28 and 7.29) is, thus, seen as the removal of strangeness suppression;