7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
387
length L traversed:
=
ω
dN
dω
dω ∝ α s C R ˆ
q L
2 .
(7.61)
This relation [193] represents the eikonal approximation limit of extended medium
and high leading parton initial energy E > ω c (Eq. (7.59)). The average energy loss
is thus proportional to the appropriate strong coupling constant α s , to the Casimir
factor corresponding to the leading parton (with value 4/3 for quarks, and 3 for
gluons), as well as to ˆ
q and L 2 .
In order to verify the non-abelian nature of radiative parton energy loss in a
partonic QCD medium it would, of course, be most convincing if a direct, explicit
L 2 dependence of could be demonstrated. Such a demonstration is lacking
thus far, chiefly because of the obvious difficulty of simultaneously knowing the
primordial parton energy E, the transport coefficient ˆ
q and—in finite nuclear collision geometry—its variation along the actual traversed path L as the surrounding
medium expands with propagation time. Moreover, the partonic medium induced
energy loss E of the primordial parton is not directly observable. Even if we
assume that high p T partons evolve into the observed hadrons only after leaving the
fireball medium [176], their ensuing “fragmentation” to hadrons (which is known
from p + p jet physics) results in several hadrons usually comprising a “leading”
hadron which transports a major fraction z ≡
E h /E p
of the fragmenting parton
energy E p , which, in turn, equals E p (primordial)—E, with E sampled from
a probability distribution with mean according to Eq. (7.61). The observed
leading hadron energy or transverse momentum is thus subject to sampling, both,
z from the fragmentation function, and E from in-medium energy loss. Finally,
inclusive high p T leading hadron observation in A+A collisions involves an average
over all potential initial parton production points, within the primordially produced
density profile. A specific distribution of in medium path lengths f (L) arises, for
each such production point, which, moreover, depends on a model of space-time
fireball expansion. The final inclusive yield thus requires a further, weighted volume
average over f (L) per production point. Thus, typical of an inclusive mode of
observation, the “ideal” relationship of Eq. (7.61), between radiative in-medium
energy loss E and traversed path length L gets shrouded by double averages,
independently occurring at either side of the equation [176, 179, 189, 194–196]. A
detailed L 2 law verification cannot be expected from inclusive central collision data
alone (see next section).
However, the unmistakably clear signal of a strong, in-medium high p T parton
quenching effect, gathered at RHIC by R AA measurement for a multitude of
hadronic species (Figs. 7.20, 7.41, 7.42, 7.43, 7.45, and 7.47), in Au+Au collisions
at
√
s = 200 GeV, has resulted in first estimates of the transport coefficient ˆ
q,
the medium—specific quantity entering Eq. (7.61), in addition to the geometry—
specific path length L. In fact, the transport coefficient can, to some extent, be
analyzed independently, owing to the fact that ˆ
q ∝ from Eq. (7.60). The density
falls down rapidly during expansion, but it is initially rather well constrained
387
length L traversed:
=
ω
dN
dω
dω ∝ α s C R ˆ
q L
2 .
(7.61)
This relation [193] represents the eikonal approximation limit of extended medium
and high leading parton initial energy E > ω c (Eq. (7.59)). The average energy loss
is thus proportional to the appropriate strong coupling constant α s , to the Casimir
factor corresponding to the leading parton (with value 4/3 for quarks, and 3 for
gluons), as well as to ˆ
q and L 2 .
In order to verify the non-abelian nature of radiative parton energy loss in a
partonic QCD medium it would, of course, be most convincing if a direct, explicit
L 2 dependence of could be demonstrated. Such a demonstration is lacking
thus far, chiefly because of the obvious difficulty of simultaneously knowing the
primordial parton energy E, the transport coefficient ˆ
q and—in finite nuclear collision geometry—its variation along the actual traversed path L as the surrounding
medium expands with propagation time. Moreover, the partonic medium induced
energy loss E of the primordial parton is not directly observable. Even if we
assume that high p T partons evolve into the observed hadrons only after leaving the
fireball medium [176], their ensuing “fragmentation” to hadrons (which is known
from p + p jet physics) results in several hadrons usually comprising a “leading”
hadron which transports a major fraction z ≡
E h /E p
of the fragmenting parton
energy E p , which, in turn, equals E p (primordial)—E, with E sampled from
a probability distribution with mean according to Eq. (7.61). The observed
leading hadron energy or transverse momentum is thus subject to sampling, both,
z from the fragmentation function, and E from in-medium energy loss. Finally,
inclusive high p T leading hadron observation in A+A collisions involves an average
over all potential initial parton production points, within the primordially produced
density profile. A specific distribution of in medium path lengths f (L) arises, for
each such production point, which, moreover, depends on a model of space-time
fireball expansion. The final inclusive yield thus requires a further, weighted volume
average over f (L) per production point. Thus, typical of an inclusive mode of
observation, the “ideal” relationship of Eq. (7.61), between radiative in-medium
energy loss E and traversed path length L gets shrouded by double averages,
independently occurring at either side of the equation [176, 179, 189, 194–196]. A
detailed L 2 law verification cannot be expected from inclusive central collision data
alone (see next section).
However, the unmistakably clear signal of a strong, in-medium high p T parton
quenching effect, gathered at RHIC by R AA measurement for a multitude of
hadronic species (Figs. 7.20, 7.41, 7.42, 7.43, 7.45, and 7.47), in Au+Au collisions
at
√
s = 200 GeV, has resulted in first estimates of the transport coefficient ˆ
q,
the medium—specific quantity entering Eq. (7.61), in addition to the geometry—
specific path length L. In fact, the transport coefficient can, to some extent, be
analyzed independently, owing to the fact that ˆ
q ∝ from Eq. (7.60). The density
falls down rapidly during expansion, but it is initially rather well constrained