7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
391
which summarizes the contributions arising from the different shower partons i.
Here, C i are the weight coefficients of the particular process, and D part(i)→h are the
individual fragmentation functions (FFs) for turning parton i into hadron h. Similar
to the parton distribution functions (PDFs) in Eq. (7.51), derived from deep inelastic
electron-parton scattering (DIS) and shown in Fig. 7.14, the FFs are semi-empirical
non-perturbative QCD functions that have an intuitive probabilistic interpretation.
They quantify the probability that the primordial parton produced at short distance
1/Q fragments into i shower partons, forming a jet that includes the hadron h [205,
206].
At Fermilab energy,
√
s = 1.8 TeV, the jet spectrum reaches up to E T ≈
400 GeV, and a typical 100 GeV jet comprises about 10 hadrons which can
be identified above background by jet-cone reconstruction algorithms [205]. This
allows for a complete determination of the corresponding fragmentation function,
and for a rather accurate reconstruction of the p T and E T of the primordial parton
that initiated the jet. Similar conditions will prevail in jet spectroscopy of Pb+Pb
collisions at LHC energy,
√
s = 5.5 TeV.
However, at RHIC energy a typical jet at 15 ≤ E T ≤ 25 GeV features a
fragmentation function comprised of a few hadrons with E T in the 2–15 GeV range.
Considering the high background, arising in the lower fraction of this energy domain
from concurrent, unrelated high p T hadron production processes, a complete jetcone analysis cannot succeed. The RHIC experiments thus confront back-to-back
di-jet production with an analysis of the azimuthal correlation between high p T
hadrons. Defining the observational geometry by selecting a high p T “trigger”
hadron observed at azimuthal emission angle ϕ trig , the associated production of
high p T hadrons is inspected as a function of = ϕ ass − ϕ trig . If the trigger
has caught a leading jet hadron one expects the hadrons of the balancing back-toback jet to occur at the side opposite to the trigger, ≈ π. The trigger condition
thus imposes the definition of a “near-side” and an “away side” azimuthal domain.
Furthermore, the relatively narrow rapidity acceptance of the STAR and PHENIX
experiments (centered at y = 0) selects di-jets with axis perpendicular to the beam
direction.
Originating from a uniform distribution of primordial back-to-back di-parton
production vertices, throughout the primordial reaction volume, the trigger selected
di-jet partons thus experience an (anti-)correlated average path length L to arrive
at the surface while experiencing medium-specific attenuation, with
L trig
≈ 2R −
L away
, R being the transverse medium radius. No such geometric constraint exists
in the study of inclusive high p T hadron production. We thus expect information
different from the inclusive R AA (p T ) signal. The geometrical selectivity can be
even further constrained by fixing the direction of the impact parameter (i.e. the
reaction plane) in semi-central collisions (recall Sect. 7.4), and observing the di-jet
correlation signal in dependence of the di-jet axis orientation relative to the reaction
plane.
The very first di-hadron correlation measurements confirmed the existence of
strong in-medium attenuation. Figure 7.50 shows the azimuthal yield distributions,
per trigger hadron, as observed by STAR at
√
s = 200 GeV [207]. The left panel
391
which summarizes the contributions arising from the different shower partons i.
Here, C i are the weight coefficients of the particular process, and D part(i)→h are the
individual fragmentation functions (FFs) for turning parton i into hadron h. Similar
to the parton distribution functions (PDFs) in Eq. (7.51), derived from deep inelastic
electron-parton scattering (DIS) and shown in Fig. 7.14, the FFs are semi-empirical
non-perturbative QCD functions that have an intuitive probabilistic interpretation.
They quantify the probability that the primordial parton produced at short distance
1/Q fragments into i shower partons, forming a jet that includes the hadron h [205,
206].
At Fermilab energy,
√
s = 1.8 TeV, the jet spectrum reaches up to E T ≈
400 GeV, and a typical 100 GeV jet comprises about 10 hadrons which can
be identified above background by jet-cone reconstruction algorithms [205]. This
allows for a complete determination of the corresponding fragmentation function,
and for a rather accurate reconstruction of the p T and E T of the primordial parton
that initiated the jet. Similar conditions will prevail in jet spectroscopy of Pb+Pb
collisions at LHC energy,
√
s = 5.5 TeV.
However, at RHIC energy a typical jet at 15 ≤ E T ≤ 25 GeV features a
fragmentation function comprised of a few hadrons with E T in the 2–15 GeV range.
Considering the high background, arising in the lower fraction of this energy domain
from concurrent, unrelated high p T hadron production processes, a complete jetcone analysis cannot succeed. The RHIC experiments thus confront back-to-back
di-jet production with an analysis of the azimuthal correlation between high p T
hadrons. Defining the observational geometry by selecting a high p T “trigger”
hadron observed at azimuthal emission angle ϕ trig , the associated production of
high p T hadrons is inspected as a function of = ϕ ass − ϕ trig . If the trigger
has caught a leading jet hadron one expects the hadrons of the balancing back-toback jet to occur at the side opposite to the trigger, ≈ π. The trigger condition
thus imposes the definition of a “near-side” and an “away side” azimuthal domain.
Furthermore, the relatively narrow rapidity acceptance of the STAR and PHENIX
experiments (centered at y = 0) selects di-jets with axis perpendicular to the beam
direction.
Originating from a uniform distribution of primordial back-to-back di-parton
production vertices, throughout the primordial reaction volume, the trigger selected
di-jet partons thus experience an (anti-)correlated average path length L to arrive
at the surface while experiencing medium-specific attenuation, with
L trig
≈ 2R −
L away
, R being the transverse medium radius. No such geometric constraint exists
in the study of inclusive high p T hadron production. We thus expect information
different from the inclusive R AA (p T ) signal. The geometrical selectivity can be
even further constrained by fixing the direction of the impact parameter (i.e. the
reaction plane) in semi-central collisions (recall Sect. 7.4), and observing the di-jet
correlation signal in dependence of the di-jet axis orientation relative to the reaction
plane.
The very first di-hadron correlation measurements confirmed the existence of
strong in-medium attenuation. Figure 7.50 shows the azimuthal yield distributions,
per trigger hadron, as observed by STAR at
√
s = 200 GeV [207]. The left panel