Previous studies have indicated that the near-side peak of high-$p_T$
triggered correlations can be decomposed into two parts, the \textit{Jet} and
the \textit{Ridge}. We present data on the yield per trigger of the
\textit{Jet} and the \textit{Ridge} from $d+Au$, $Cu+Cu$ and $Au+Au$ collisions
at $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV and compare data on the \textit{Jet}
to PYTHIA 8.1 simulations for $p+p$. PYTHIA describes the \textit{Jet}
component up to a scaling factor, meaning that PYTHIA can provide a better
understanding of the \textit{Ridge} by giving insight into the effects of the
kinematic cuts. We present collision energy and system dependence of the
\textit{Ridge} yield, which should help distinguish models for the production
mechanism of the \textit{Ridge}.Comment: 4 pages, 6 figures, proceedings for Hot Quarks in Estes Park,
  Colorad

B.B. Back

B.I. Abelev

C. Nattrass

C.Y. Wong

Christine Nattrass

J. Adams

J. Bielcikova

J. Putschke

K.H. Ackermann

M. Bombara

N. Armesto

R. Hwa

S. Voloshin

English

arXiv

Springer - Publisher Connector

Energy and system dependence of high-p T triggered two-particle near-side correlations

Crossref

Energy and system dependence of high-p
                     
                T
               triggered two-particle near-side correlations

Eur. Phys. J. C (2009) 62: 265–269
DOI 10.1140/epjc/s10052-009-1037-8
Regular Article - Experimental Physics
Energy and system dependence of high-pT triggered two-particle
near-side correlations
Christine Nattrassa
for the STAR Collaboration
WNSL, Yale University, 272 Whitney Ave., New Haven, CT 06520, USA
Received: 30 September 2008 / Revised: 17 March 2009 / Published online: 5 May 2009
© Springer-Verlag / Società Italiana di Fisica 2009
Abstract Previous studies have indicated that the near-side
peak of high-pT triggered correlations can be decomposed
into two parts, the Jet and the Ridge. We present data on
the yield per trigger of the Jet and the Ridge from d + Au,
Cu + Cu and Au + Au collisions at √sNN = 62.4 GeV and
200 GeV and compare data on the Jet to PYTHIA 8.1 sim-
ulations for p + p. PYTHIA describes the Jet component
up to a scaling factor, meaning that PYTHIA can provide a
better understanding of the Ridge by giving insight into the
effects of the kinematic cuts. We present collision energy
and system dependence of the Ridge yield, which should
help distinguish models for the production mechanism of
the Ridge.
PACS 25.75.-q · 21.65.Qr · 24.85.+p · 25.75.Bh
1 Introduction
Previous studies demonstrated that there are two structures
in the near-side peak in high-pT triggered correlations in
Au + Au collisions at √sNN = 200 GeV. The Jet similar to
what is observed in d + Au, narrow in both azimuth (φ)
and pseudorapidity (η), and is similar to that expected
from vacuum fragmentation. In contrast, the Ridge is narrow
in azimuth but broad in pseudorapidity and has properties
similar to the bulk [1, 2]. These studies test whether these
conclusions hold for other collision systems and energies by
comparing data from Au + Au and Cu + Cu collisions at√
sNN = 62.4 GeV and √sNN = 200 GeV.
Several mechanisms have been proposed for the produc-
tion of the Ridge [3–7] but there have been few calculations
which can be directly compared to data. This is in part be-
cause there are many factors which must be considered when
a e-mail: nattrass@rhig.physics.yale.edu
calculating the experimentally measured quantities. Because
trends expected with changing collision energy and in nu-
clei collided should be easier to calculate theoretically, the
results presented here should provide a good test of models
for the production of the Jet and Ridge.
2 Method
Data from the STAR detector from year 3 d + Au collisions
as
√
sNN = 200 GeV, year 4 Au + Au collisions at √sNN =
62.4 GeV and √sNN = 200 GeV, and year 5 Cu + Cu col-
lisions at √sNN = 62.4 GeV and √sNN = 200 GeV were
used for the comparison of collision systems and energies.
Details of the STAR detector can be found in [8]. The pri-
mary detector used for these analyses was the STAR Time
Projection Chamber (TPC.)
A high transverse momentum (pT ) particle is selected
and the distribution of other particles in the event rela-
tive to that trigger particle in azimuth (φ) and pseudo-
rapidity (η) d2N
dφdη
was determined. The pT of the
trigger and associated particles was restricted in order to
reduce the soft background; unless otherwise mentioned
1.5 GeV/c < passociatedT < p
trigger
T and 3.0 < p
trigger
T <
6.0 GeV/c. d2N
dφdη
is normalized by the number of trig-
ger particles. This was corrected for the single particle effi-
ciency and for detector acceptance, which is dependent on
the collision system and energy, pT , η, φ, and colli-
sion multiplicity. Except for studies of Npart dependence,
the Cu + Cu data at both energies are for 0–60% centrality,
Au + Au data at √sNN = 62.4 GeV are for 0–80% central-
ity, and Au + Au data at √sNN = 200 GeV are for 0–10%
centrality. d + Au data are minimum bias.
The yield measured is the number of particles associated
with the trigger particle within the limits on passociatedT and
p
trigger
T . The Ridge was previously observed to be roughly
266 Eur. Phys. J. C (2009) 62: 265–269
independent of η within the acceptance of the STAR
TPC [2]. To extract the yield it is assumed that the Ridge
is independent of η. Previous studies have demonstrated
that the Jet component extends to |η| = 0.75 in the pT
range studied here and that limited detector acceptance lim-
its studies to |η| < 1.75 [1, 2, 9]. To determine the Jet yield
YJet , the projection of the distribution of particles d2Ndφdη
is taken in two different ranges in pseudorapidity:
dYRidge
dφ
= 1/Ntrigger
∫ −0.75
−1.75
d2N
dφdη
dη
+ 1/Ntrigger
∫ 1.75
0.75
d2N
dφdη
dη
dYJet+Ridge
dφ
= 1/Ntrigger
∫ 0.75
−0.75
d2N
dφdη
dη
where the former contains only the Ridge and the latter con-
tains both the Jet and the Ridge. The jet-like yield on the
near-side is the integral over −1 < φ < 1:
YJet =
∫ 1
−1
(
dYJet+Ridge
dφ
− 0.75
1
dYRidge
dφ
)
dφ.
The factor in front of the second term is the ratio of the
η width in the region containing the Jet and the Ridge
to the width of the region containing only the Ridge. With
this method for subtracting the Ridge contribution to YJet,
the systematic errors due to v2 cancel out assuming that v2
is roughly independent of η, a reasonable assumption in
the mid-rapidity range |η| < 1 based on the available data
[11, 12]. It is also assumed that the Ridge is independent
of η.
To determine YRidge the integration is done over the entire
η region to minimize the effects of statistical fluctuations
in the determination of the background:
YRidge = 1/Ntrigger
∫ 1.75
−1.75
∫ 1
−1
d2N
dφdη
dφdη − YJet.
The integration over η is done by bin counting. The
integration over φ is done by fitting a Gaussian to the near-
side. This partially compensates for a detector effect which
causes lost tracks at φ ≈ 0 and η ≈ 0; this effect is less
than 10% in the pT range studied here [10].
The combinatorial background is correlated in azimuth
due to particles correlated indirectly with each other in az-
imuth due to their correlation with the reaction plane. This
random background is given by
dYbkgd
dφ
= B(1 + 2〈vtrigger2 〉〈vassociated2 〉 cos(2φ))
where v2 is the second order harmonic in a Fourier expan-
sion of the momentum anisotropy relative to the reaction
plane, and must be subtracted in order to study the compo-
nent associated with the jet. Systematic errors come from the
errors on B, 〈vtrigger2 〉 and 〈vassociated2 〉. It is assumed that v2 is
the same for events with a trigger particle as for events with-
out a trigger particle and that v2 is roughly independent of
η. For each data set v2(pT ) was fit in centrality bins to de-
termine 〈vtrigger2 〉 and 〈vassociated2 〉. Details of the v2 subtrac-
tion for Au + Au collisions at √sNN = 200 GeV are given
in [1] and for Cu+Cu collisions at √sNN = 200 GeV in [9].
For Cu + Cu collisions at √sNN = 62.4 GeV, the v2 using
the reaction plane as determined from tracks in the Forward
Time Projection Chamber was used as the nominal value
and the lower bound was determined from a multiplicity-
dependent approximation as described for √sNN = 200 GeV
in [9]. For Au + Au collisions at √sNN = 62.4 GeV, v2 and
its systematic errors were taken from [13]. B is fixed using
the ZYAM method [14].
PYTHIA 8.1 was used to simulate p + p collisions for
comparisons to YJet. A trigger particle was selected and the
distribution of particles in azimuth was calculated, as in the
experimental measurements. The yield was determined as
the number of charged hadrons in the range −1 < φ < 1.
For comparisons to data identical limits on passociatedT and
p
trigger
T were applied. The minimum pˆT is the parameter
in PYTHIA for the transverse momentum in the hard sub-
process [15]. A minimum value of pˆT = 0.1 GeV/c was
used and 108 events were simulated to ensure that the mini-
mum pˆT did not affect the yield and that the statistical error
was negligible. It was not necessary to study the distribu-
tion of particles in pseudorapidity since there is no Ridge in
PYTHIA.
3 Results
3.1 The jet
Figure 1 compares the dependence of YJet on ptriggerT for all
systems and energies to the yield from PYTHIA 8.1 scaled
by 2/3. An overall scaling factor of 2/3 was applied to the
PYTHIA yields to match the data. The need for the scaling
factor implies that PYTHIA assumes that too many particles
are produced in hard processes, however, kinematic effects
should still be reflected accurately in PYTHIA. The scaled
PYTHIA yield describes the shape of the ptriggerT depen-
dence well, with a few deviations at lower ptriggerT . PYTHIA
describes the energy dependence of YJet well, indicating that
the energy dependence can be explained as a pQCD ef-
fect. If YJet is dominated by pQCD effects, deviations from
PYTHIA at lower pT would be expected. No system depen-
dence is observed in the data, as would be expected for an
effect dominated by pQCD.
Eur. Phys. J. C (2009) 62: 265–269 267
The dependence of YJet on passociatedT is shown in Fig. 2.
As in Fig. 1, the scaled PYTHIA yield describes the shape
of the data well and there is no system dependence. The
inverse slope parameters from exponential fits to the data
and to PYTHIA shown in Table 1 likewise support indepen-
Table 1 Inverse slope parameter k (MeV/c) of passociatedT for fits of
data in Fig. 2. The inverse slope parameter from a fit to π− as a function
of pT in Au+Au from [16] above 1.0 GeV/c is k = 280.9±0.4 MeV/c
for √sNN = 62.4 GeV and is k = 330.9 ± 0.3 MeV/c for √sNN =
200 GeV. Statistical errors only
√
sNN = 62.4 GeV √sNN = 200 GeV
h-h h-h
Au + Au Jet 317 ± 26 478 ± 8
Cu + Cu Jet 355 ± 21 445 ± 20
d + Au Jet 469 ± 8
PYTHIA 424 ± 5 473 ± 3
Fig. 1 (Color online) ptriggerT dependence of the YJet for Cu + Cu and
Au + Au at √sNN = 62.4 GeV and d + Au, Cu + Cu, and Au + Au at√
sNN = 200 GeV compared to the yield from PYTHIA scaled by 2/3
Fig. 2 (Color online) passociatedT dependence of YJet for Cu + Cu and
Au + Au at √sNN = 62.4 GeV and d + Au, Cu + Cu, and Au + Au at√
sNN = 200 GeV compared to the yield from PYTHIA scaled by 2/3.
The inverse slope parameters from fits of an exponential to the data and
to PYTHIA are given in Table 1
dence on collision system. Slight deviations from the scaled
PYTHIA yield at lower passociatedT in Fig. 2 for collisions at√
sNN = 62.4 GeV are reflected in the inverse slope parame-
ter, which is higher than that of the data.
The Npart dependence of YJet is shown in Fig. 3 and com-
pared to the scaled PYTHIA yield. In contrast to measure-
ments at higher pT , which show no Npart dependence, a
small increase with Npart is observed. This may be caused
by either slight modifications of the Jet which increase with
system size or some of the Ridge being misidentified as part
of the Jet. If the Ridge were not completely independent of
η, some of the particles in the Ridge could be associated
with the Jet. Since the Ridge has roughly four times as many
particles than the Jet in central Au + Au, this would give
a smaller relative error to the Ridge than the Jet. However,
the Jet has also been observed to be considerably broader in
η in A + A collisions than in p + p and d + Au collisions
[2, 10], which would imply modifications of the Jet in A+A
collisions. At this point models for Jet and Ridge production
cannot distinguish these mechanisms.
That PYTHIA describes the ptriggerT and p
associated
T de-
pendence of YJet fairly well implies that PYTHIA can be
Fig. 3 (Color online) Npart dependence of the YJet for Cu + Cu and
Au + Au at √sNN = 62.4 GeV and d + Au, Cu + Cu, and Au + Au at√
sNN = 200 GeV compared to the yield from PYTHIA
Fig. 4 (Color online) (a) distribution of trigger particles zT and (b) pˆT
distribution in PYTHIA at √sNN = 62.4 GeV from PYTHIA 8.1 for
1.5 GeV/c < passociatedT < p
trigger
T and 3.0 < p
trigger
T < 6.0 GeV/c at√
sNN = 62.4 GeV and √sNN = 200 GeV
268 Eur. Phys. J. C (2009) 62: 265–269
used to approximate the momentum fraction carried by the
leading hadron, zT . Figure 4 shows the pˆT distribution and
the distribution of trigger particles in zT = ptriggerT /pˆT pre-
dicted by PYTHIA for √sNN = 62.4 GeV and √sNN =
200 GeV. Figure 4(a) shows that for the same ptriggerT and
passociatedT , the mean zT is higher in
√
sNN = 62.4 GeV
and therefore the mean jet energy is lower. Figure 4(b)
shows that this is caused by the steeper spectrum at √sNN =
62.4 GeV. The lower YJet in collisions at
√
sNN = 62.4 GeV
results from the higher mean zT and is dominantly a kine-
matic effect.
3.2 The ridge
The dependence of YRidge on Npart is given in Fig. 5. In col-
lisions at both √sNN = 62.4 GeV and √sNN = 200 GeV
YRidge increases with Npart. As seen in Fig. 3, the yield at√
sNN = 62.4 GeV is considerably smaller than at √sNN =
200 GeV. Figure 6 shows the ratio YRidge/YJet and shows
that this ratio does not depend on √sNN . PYTHIA simula-
tions demonstrated that the data at √sNN = 62.4 GeV likely
Fig. 5 (Color online) YRidge dependence on Npart for √sNN =
62.4 GeV and √sNN = 200 GeV
Fig. 6 (Color online) YRidge/YJet dependence on Npart for √sNN =
62.4 GeV and √sNN = 200 GeV
correspond to a lower jet energy, so this implies that YRidge
decreases with energy just like YJet.
Few models have attempted to make quantitative predic-
tions for YRidge. An exception is the momentum kick model,
which is consistent with data on the energy dependence of
YRidge [17]. The collision energy dependence of YRidge is po-
tentially a sensitive test of models because the dominant
factor in collision energy dependence should be different
for various classes of models. Models which involve par-
ton energy loss due to interaction with the medium such as
the momentum kick model should have a smaller Ridge at
lower energy, as observed in the data, because the initial
parton energy was lower. The radial flow+trigger bias model
should predict a dependence of YRidge on the amount of ra-
dial flow in the system. An analysis similar to [18] could
yield predictions for the collision system and energy de-
pendence. Plasma instability models [7] should depend on
whether plasma instabilities are more or less likely in small
systems and at lower energies. When more detailed calcu-
lations are available, it is likely that the data could exclude
some production mechanisms.
4 Conclusions
The data from d + Au, Cu + Cu, and Au + Au and √sNN =
62.4 GeV and √sNN = 200 GeV demonstrate that the Jet
shows no system dependence. In addition, the collision en-
ergy dependence of YJet is described well by PYTHIA even
at fairly low pT and the ptriggerT and p
associated
T dependencies
agree with PYTHIA up to a scaling factor, with a few devi-
ations at lower pT . This implies that the dominant produc-
tion mechanism of the Jet is fragmentation. Deviations from
PYTHIA may imply modifications of the Jet in A + A col-
lisions. It also implies that PYTHIA or other models can be
used to determine the effect of the kinematic cuts on ptriggerT
on the zT and jet energy distribution, which could be very
useful for the theoretical interpretation of the Ridge.
YRidge is smaller at lower collision energies and increases
with system size independent of collision system. There is
no dependence on the collision system. Data on the collision
energy and system dependence could provide a robust test
of models, and comparisons of YJet to PYTHIA imply that
the effects of the kinematic cuts on the distribution of jet
energies can be inferred from PYTHIA.
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Energy and system dependence of high-
                      triggered two-particle near-side correlations

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