394
R. Stock
attenuation factor of about 0.2, the signal thus not being completely extinguished.
We infer R AA (L → 2R) ≈ 0.2.
In order to show how such data can be evaluated in a picture of in-medium leading parton attenuation (as finally reflected in leading hadron production observed
in the above di-hadron correlation data) we briefly consult the pQCD factorization
[210] prediction for the inclusive production of a high p T hadron at central rapidity,
in the nuclear collision A + B → h + x [196],
d 3 σ AB→hx
d 2 p T dy
= K NLO
abc
d r dx a dx b dz c F a/A (x a , Q
2 ,
r)
×F b/B (x b , Q
2 ,
b − −
r)
d 3 σ ab−c
d 2 p T (c) dy c
(x a , x b , Q
2 )
×
1
z 2
c
D h/c (z c , Q
2 )
(7.66)
where the parton (a, b) distribution functions F in nucleus A, B and the elementary
pQCD cross section for a +b → c+x have been already implied in Eq. (7.51). Their
spatial integral gets convoluted with the fragmentation function D that describes the
conversion of the leading parton c to a hadron carrying a fraction 0 < z c < 1 of its
transverse momentum. K is a factor introduced as a phenomenological correction
for “next to leading order” (NLO) QCD effects. Within the (further) approximation
that the leading parton c suffers medium induced gluon bremsstrahlung energy
loss but hadronizes outside the interaction volume (in vacuum), the in-medium
quenching leads, merely, to a re-scaling of the fragmentation function,
D
med
h/c =
d P (()
1
1 −
D
vac
h/c
z c
1 −
, Q
2
,
(7.67)
where the primary parton is implied to lose an energy fraction = c with
probability P (() [196]. Therefore the leading hadron is a fragment of a parton with
reduced energy (1 − c , and accordingly must carry a larger fraction of the parton
energy, z c /(1 − ). If no final state quenching is considered, P (() reduces to δ(().
The entire effect of medium attenuation on the leading parton is thus contained in
the shift of the fragmentation function.
An application of this formalism [196] is shown in Fig. 7.52. The in-medium
modification of the hadron-triggered fragmentation function (see Eq. (7.67)) is
evaluated for central Au+Au collisions at
√
s = 200 GeV. In adaptation to the
modalities of RHIC di-hadron correlation data, the opposite side fragmentation
function (for observation of trigger-related hadrons with p T > 2 GeV/c) is studied
in dependence of the trigger selected p T window. Its attenuation is quantified by the
ratio D (with quenching) to D (without quenching), as a function of the fraction
z T , of opposite side hadron p T to trigger hadron p T . Referring to the observational
conditions implied in Fig. 7.50 (left) p
trig
T ≈ 4–6 GeV/c and opposite side p T >
R. Stock
attenuation factor of about 0.2, the signal thus not being completely extinguished.
We infer R AA (L → 2R) ≈ 0.2.
In order to show how such data can be evaluated in a picture of in-medium leading parton attenuation (as finally reflected in leading hadron production observed
in the above di-hadron correlation data) we briefly consult the pQCD factorization
[210] prediction for the inclusive production of a high p T hadron at central rapidity,
in the nuclear collision A + B → h + x [196],
d 3 σ AB→hx
d 2 p T dy
= K NLO
abc
d r dx a dx b dz c F a/A (x a , Q
2 ,
r)
×F b/B (x b , Q
2 ,
b − −
r)
d 3 σ ab−c
d 2 p T (c) dy c
(x a , x b , Q
2 )
×
1
z 2
c
D h/c (z c , Q
2 )
(7.66)
where the parton (a, b) distribution functions F in nucleus A, B and the elementary
pQCD cross section for a +b → c+x have been already implied in Eq. (7.51). Their
spatial integral gets convoluted with the fragmentation function D that describes the
conversion of the leading parton c to a hadron carrying a fraction 0 < z c < 1 of its
transverse momentum. K is a factor introduced as a phenomenological correction
for “next to leading order” (NLO) QCD effects. Within the (further) approximation
that the leading parton c suffers medium induced gluon bremsstrahlung energy
loss but hadronizes outside the interaction volume (in vacuum), the in-medium
quenching leads, merely, to a re-scaling of the fragmentation function,
D
med
h/c =
d P (()
1
1 −
D
vac
h/c
z c
1 −
, Q
2
,
(7.67)
where the primary parton is implied to lose an energy fraction = c with
probability P (() [196]. Therefore the leading hadron is a fragment of a parton with
reduced energy (1 − c , and accordingly must carry a larger fraction of the parton
energy, z c /(1 − ). If no final state quenching is considered, P (() reduces to δ(().
The entire effect of medium attenuation on the leading parton is thus contained in
the shift of the fragmentation function.
An application of this formalism [196] is shown in Fig. 7.52. The in-medium
modification of the hadron-triggered fragmentation function (see Eq. (7.67)) is
evaluated for central Au+Au collisions at
√
s = 200 GeV. In adaptation to the
modalities of RHIC di-hadron correlation data, the opposite side fragmentation
function (for observation of trigger-related hadrons with p T > 2 GeV/c) is studied
in dependence of the trigger selected p T window. Its attenuation is quantified by the
ratio D (with quenching) to D (without quenching), as a function of the fraction
z T , of opposite side hadron p T to trigger hadron p T . Referring to the observational
conditions implied in Fig. 7.50 (left) p
trig
T ≈ 4–6 GeV/c and opposite side p T >