388
R. Stock
by the conditions of one-dimensional Bjorken expansion that we have described
in Sects. 7.2 and 7.4. The major contribution to partonic E arises in the early
expansion phase (via a high ˆ
q), in close analogy to the formation of the elliptic flow
signal. These two signals are, thus, closely correlated: the primordial hydrodynamic
expansion phase of bulk matter evolution sets the stage for the attenuation, during
this stage of QCD matter, of primordially produced “tracer” partons, traversing the
bulk matter medium as test particles.
The bias in partonic E to the primordial expansion period is borne out in an
expression [193, 195] which replaces the ˆ
q coefficient, appropriate to an infinitely
extended static medium considered in the original BDMPSZ model, by an effective,
expansion time averaged
ˆ
q eff =
2
L 2
L
t 0
dt (t − t 0 ) ˆ
q (t)
(7.62)
to be employed in the realistic case of an expanding fireball source. Due to the
rapid fall-off of , in ˆ
q =
q 2
T
from Eq. (7.60), the integral depends, far more
strongly, on ˆ
q (t ≈ t 0 ) than on total path length L. Furthermore, inserting ˆ
q eff into
the BDMPSZ formula [193, 195] for the transverse momentum downward shift,
occurring in leading parton or hadron p T spectra (of power law form p
−ν
T , see
Fig. 7.20)
p T ≈ −α s
π ˆ
qL 2 p T /ν,
(7.63)
we see that the first order proportionality to L 2 is removed. The downward p T shift
is thus, primarily, a consequence of ˆ
q eff which, in turn, is biased to reflect the “ideal”
transport coefficient ˆ
q at early evolution time. Within this terminology, the p T
shift (see Eq. (7.63)) determines the experimentally measured ratio R AA (p T ) which
quantifies the effective transport coefficient ˆ
q eff for the p T domain considered. It
can be related, as a cross check, to the initial gluon rapidity density if the collision
region expands according to Bjorken scaling [187, 197]:
ˆ
q = α s
2
L
R
−2
A
dN g
dy
.
(7.64)
A typical result of application of the model described above [195] is shown in
Fig. 7.48. Analogous to Fig. 7.41, R AA for neutral pions and charged hadrons is
averaged over the range 4.5 ≤ p T ≤ 10 GeV/c, and shown as a function of
centrality (assessed by N part ) in minimum bias Au+Au collision at
√
s = 200 GeV
[190, 191, 198]. A path-averaged ˆ
q eff of 14 GeV 2 /fm is inferred from the fit, in close
agreement to the value found in [195].
A more recent study [199] of the PHENIX R AA data for π 0 in central Au+Au
collisions (Fig. 7.42) is shown in Fig. 7.49. The analysis is carried out in the framework of the WHDG model [200], which replaces the (effective) transport coefficient
ˆ
q (employed in the BDMPSZ model [186–188], and turned into the data analysis
R. Stock
by the conditions of one-dimensional Bjorken expansion that we have described
in Sects. 7.2 and 7.4. The major contribution to partonic E arises in the early
expansion phase (via a high ˆ
q), in close analogy to the formation of the elliptic flow
signal. These two signals are, thus, closely correlated: the primordial hydrodynamic
expansion phase of bulk matter evolution sets the stage for the attenuation, during
this stage of QCD matter, of primordially produced “tracer” partons, traversing the
bulk matter medium as test particles.
The bias in partonic E to the primordial expansion period is borne out in an
expression [193, 195] which replaces the ˆ
q coefficient, appropriate to an infinitely
extended static medium considered in the original BDMPSZ model, by an effective,
expansion time averaged
ˆ
q eff =
2
L 2
L
t 0
dt (t − t 0 ) ˆ
q (t)
(7.62)
to be employed in the realistic case of an expanding fireball source. Due to the
rapid fall-off of , in ˆ
q =
q 2
T
from Eq. (7.60), the integral depends, far more
strongly, on ˆ
q (t ≈ t 0 ) than on total path length L. Furthermore, inserting ˆ
q eff into
the BDMPSZ formula [193, 195] for the transverse momentum downward shift,
occurring in leading parton or hadron p T spectra (of power law form p
−ν
T , see
Fig. 7.20)
p T ≈ −α s
π ˆ
qL 2 p T /ν,
(7.63)
we see that the first order proportionality to L 2 is removed. The downward p T shift
is thus, primarily, a consequence of ˆ
q eff which, in turn, is biased to reflect the “ideal”
transport coefficient ˆ
q at early evolution time. Within this terminology, the p T
shift (see Eq. (7.63)) determines the experimentally measured ratio R AA (p T ) which
quantifies the effective transport coefficient ˆ
q eff for the p T domain considered. It
can be related, as a cross check, to the initial gluon rapidity density if the collision
region expands according to Bjorken scaling [187, 197]:
ˆ
q = α s
2
L
R
−2
A
dN g
dy
.
(7.64)
A typical result of application of the model described above [195] is shown in
Fig. 7.48. Analogous to Fig. 7.41, R AA for neutral pions and charged hadrons is
averaged over the range 4.5 ≤ p T ≤ 10 GeV/c, and shown as a function of
centrality (assessed by N part ) in minimum bias Au+Au collision at
√
s = 200 GeV
[190, 191, 198]. A path-averaged ˆ
q eff of 14 GeV 2 /fm is inferred from the fit, in close
agreement to the value found in [195].
A more recent study [199] of the PHENIX R AA data for π 0 in central Au+Au
collisions (Fig. 7.42) is shown in Fig. 7.49. The analysis is carried out in the framework of the WHDG model [200], which replaces the (effective) transport coefficient
ˆ
q (employed in the BDMPSZ model [186–188], and turned into the data analysis