380
R. Stock
From Eqs. (7.51) and (7.52) it is clear that the primordial high Q 2 inclusive
parton cross section in a minimum bias A+B reaction scales as A · B times the
corresponding (N+N or) p+p cross section. Furthermore, as each leading parton
ends up in an observed high p T hadron h, we thus write the invariant hard hadron
cross section as
E dσ AB→h /d
3 p = A · B · E dσ pp→h /d
3 p.
(7.53)
Since nucleus-nucleus experiments usually measure invariant yields N h for a given
centrality bin, corresponding to an average impact parameter b, one writes instead:
E dN AB→h (b)/d
3 p = T AB (b) E dσ pp→h /d
3 p,
(7.54)
where T AB (b) is the Glauber geometrical overlap function of nuclei A, B at impact
parameter b, which accounts for the average number of participant parton collisions
at given impact geometry [174], N coll (b). One can thus quantify the attenuating
medium effects, as experienced by the primordially produced tracer parton on its
way toward hadronization, by the so-called nuclear modification factor for hard
collisions (analogous to Eq. (7.6), that refers to soft, bulk hadron production):
R AB (p T , y, b) =
d 2 N AB /dy dp T
T AB (b) d 2 σ pp /dy dp T
.
(7.55)
Obviously, this concept of assessing the in-medium modification of hadron production at high p T requires corresponding p+p collision data, as a reference basis. Such
data have been, in fact, gathered at top RHIC, and top SPS energies,
√
s = 200 and
17.3 GeV, respectively. Alternatively, in situations where the relevant reference data
are not known, one considers the production ratio of hadronic species h, observed
in central relative to peripheral collisions:
R CP (p T , y) =
d 2 N h (b 1 )/dy dp T
d 2 N h (b 2 )/dy dp T
×
T AB (b 2 )
T AB (b 1 )
(7.56)
where b 1 b 2 are the average impact parameters corresponding to the employed
trigger criteria for “central” and “peripheral” A+A collisions, respectively. This ratio
recasts, to a certain extent, the in-medium attenuation analysis, offered by R AB ,
insofar as peripheral collisions approach the limiting conditions, of a few single
nucleon-nucleon collisions occurring in the dilute surface sections of the nuclear
density profiles, i.e. essentially in vacuum.
Employing the above analysis schemes, the RHIC experiments have, in fact,
demonstrated a dramatic in-medium suppression of the high p T yield, for virtually
all hadronic species. Figure 7.41 shows R AA for neutral pions produced in min.
bias Cu+Cu and Au+Au collisions at
√
s = 200 GeV where PHENIX extended the
p T range up to 18 GeV/c [175]; the nuclear modification factor refers to the range
R. Stock
From Eqs. (7.51) and (7.52) it is clear that the primordial high Q 2 inclusive
parton cross section in a minimum bias A+B reaction scales as A · B times the
corresponding (N+N or) p+p cross section. Furthermore, as each leading parton
ends up in an observed high p T hadron h, we thus write the invariant hard hadron
cross section as
E dσ AB→h /d
3 p = A · B · E dσ pp→h /d
3 p.
(7.53)
Since nucleus-nucleus experiments usually measure invariant yields N h for a given
centrality bin, corresponding to an average impact parameter b, one writes instead:
E dN AB→h (b)/d
3 p = T AB (b) E dσ pp→h /d
3 p,
(7.54)
where T AB (b) is the Glauber geometrical overlap function of nuclei A, B at impact
parameter b, which accounts for the average number of participant parton collisions
at given impact geometry [174], N coll (b). One can thus quantify the attenuating
medium effects, as experienced by the primordially produced tracer parton on its
way toward hadronization, by the so-called nuclear modification factor for hard
collisions (analogous to Eq. (7.6), that refers to soft, bulk hadron production):
R AB (p T , y, b) =
d 2 N AB /dy dp T
T AB (b) d 2 σ pp /dy dp T
.
(7.55)
Obviously, this concept of assessing the in-medium modification of hadron production at high p T requires corresponding p+p collision data, as a reference basis. Such
data have been, in fact, gathered at top RHIC, and top SPS energies,
√
s = 200 and
17.3 GeV, respectively. Alternatively, in situations where the relevant reference data
are not known, one considers the production ratio of hadronic species h, observed
in central relative to peripheral collisions:
R CP (p T , y) =
d 2 N h (b 1 )/dy dp T
d 2 N h (b 2 )/dy dp T
×
T AB (b 2 )
T AB (b 1 )
(7.56)
where b 1 b 2 are the average impact parameters corresponding to the employed
trigger criteria for “central” and “peripheral” A+A collisions, respectively. This ratio
recasts, to a certain extent, the in-medium attenuation analysis, offered by R AB ,
insofar as peripheral collisions approach the limiting conditions, of a few single
nucleon-nucleon collisions occurring in the dilute surface sections of the nuclear
density profiles, i.e. essentially in vacuum.
Employing the above analysis schemes, the RHIC experiments have, in fact,
demonstrated a dramatic in-medium suppression of the high p T yield, for virtually
all hadronic species. Figure 7.41 shows R AA for neutral pions produced in min.
bias Cu+Cu and Au+Au collisions at
√
s = 200 GeV where PHENIX extended the
p T range up to 18 GeV/c [175]; the nuclear modification factor refers to the range