7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
385
7.5.2 Energy Loss in a QCD Medium
The attenuation model that we have hinted at consists of a gluon radiative energy
loss theory of the primordially produced leading, high p T parton as it traverses
a medium of color charges, by means of emission of gluon bremsstrahlung.
We expect that the resulting partonic specific energy loss, per unit pathlength
(i.e. its dE/dx) should reflect characteristic properties of the traversed medium,
most prominently the spatial density of color charges [176] but also the average
momentum transfer, per in-medium collision of the considered parton or, more
general, per unit pathlength at constant density. Most importantly, an aspect of
non-abelian QCD leads to a characteristic difference from the corresponding QED
situation: the radiated gluon is itself color-charged, and its emission probability is
influenced, again, by its subsequent interaction in the medium [186] which, in turn,
is proportional to medium color charge density and traversed pathlength L. Thus,
the traversed path-length L in-medium occurs, both in the probability to emit a
bremsstrahlung gluon, and in its subsequent rescattering trajectory, also of length
L, until the gluon finally decoheres. Quantum mechanical coherence thus leads to
the conclusion that non-abelian dE/dx is not proportional to pathlength L (as in
QED) but to L 2 [187].
This phenomenon occurs at intermediate values of the radiated gluon energy,
ω, in between the limits known as the Bethe-Heitler, and the factorization regimes
[186],
ω BH ≈ λ q
2
T ω ω fact ≈ L
2 q
2
T /λ ≤ E
(7.57)
where λ is the in-medium mean free path, q 2
T the (average) parton transverse
momentum square, created per collision, and E the total cm energy of the traveling
charge. In the BDMPSZ model [186–188] the properties of the medium are encoded
in the transport coefficient, defined as the average induced transverse momentum
squared per unit mean free path,
ˆ
q =
q
2
T
/λ.
(7.58)
The scale of the radiated gluon energy distribution ω dN/dω is set by the
characteristic gluon energy [186, 187]
ω c =
1
2
ˆ
q L
2 .
(7.59)
To see more explicitly how the various properties of the color charged medium enter
in ˆ
q we rewrite it as
ˆ
q = ρ
q
2
T dq
2
T
dσ
dq 2
T
≡ ρσ
q
2
T
= λ
−1
q
2
T
(7.60)
385
7.5.2 Energy Loss in a QCD Medium
The attenuation model that we have hinted at consists of a gluon radiative energy
loss theory of the primordially produced leading, high p T parton as it traverses
a medium of color charges, by means of emission of gluon bremsstrahlung.
We expect that the resulting partonic specific energy loss, per unit pathlength
(i.e. its dE/dx) should reflect characteristic properties of the traversed medium,
most prominently the spatial density of color charges [176] but also the average
momentum transfer, per in-medium collision of the considered parton or, more
general, per unit pathlength at constant density. Most importantly, an aspect of
non-abelian QCD leads to a characteristic difference from the corresponding QED
situation: the radiated gluon is itself color-charged, and its emission probability is
influenced, again, by its subsequent interaction in the medium [186] which, in turn,
is proportional to medium color charge density and traversed pathlength L. Thus,
the traversed path-length L in-medium occurs, both in the probability to emit a
bremsstrahlung gluon, and in its subsequent rescattering trajectory, also of length
L, until the gluon finally decoheres. Quantum mechanical coherence thus leads to
the conclusion that non-abelian dE/dx is not proportional to pathlength L (as in
QED) but to L 2 [187].
This phenomenon occurs at intermediate values of the radiated gluon energy,
ω, in between the limits known as the Bethe-Heitler, and the factorization regimes
[186],
ω BH ≈ λ q
2
T ω ω fact ≈ L
2 q
2
T /λ ≤ E
(7.57)
where λ is the in-medium mean free path, q 2
T the (average) parton transverse
momentum square, created per collision, and E the total cm energy of the traveling
charge. In the BDMPSZ model [186–188] the properties of the medium are encoded
in the transport coefficient, defined as the average induced transverse momentum
squared per unit mean free path,
ˆ
q =
q
2
T
/λ.
(7.58)
The scale of the radiated gluon energy distribution ω dN/dω is set by the
characteristic gluon energy [186, 187]
ω c =
1
2
ˆ
q L
2 .
(7.59)
To see more explicitly how the various properties of the color charged medium enter
in ˆ
q we rewrite it as
ˆ
q = ρ
q
2
T dq
2
T
dσ
dq 2
T
≡ ρσ
q
2
T
= λ
−1
q
2
T
(7.60)