Are There Mach Cones in Heavy Ion Collisions? Three-Particle
  Correlations from STAR
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QM2006PosterProceedings˙V4
International Journal of Modern Physics E
c© World Scientific Publishing Company
ARE THERE MACH CONES IN HEAVY ION COLLISIONS?
THREE-PARTICLE CORRELATIONS FROM STAR
JASON GLYNDWR ULERY FOR THE STAR COLLABORATION
Department of Physics, Purdue University, 525 Northwestern Avenue
West Lafayette, Indiana 47907, USA
ulery@physics.purdue.edu
Received (received date)
Revised (revised date)
We present results from STAR on 3-particle azimuthal correlations for a 3 < pT < 4
GeV/c trigger particle with two softer 1 < pT < 2 GeV/c particles. Results are shown
for pp, d+Au and high statistics Au+Au collisions at
sNN = 200GeV . We observe
a 3-particle correlation in central Au+Au collisions which may indicate the presence of
conical emission. In addition, the dependence of the observed signal angular position on
the pT of the associated particles can be used to distinguish conical flow from simple
QCD-Čerenkov radiation. An important aspect of the analysis is the subtraction of
combinatorial backgrounds. Systematic uncertainties due to this subtraction and the
flow harmonics v2 and v4 are investigated in detail.
1. Introduction
Heavy ion collisions create a medium that may be the quark gluon plasma (QGP).
This medium can be studied through jets and jet-correlations. Jets make a good
probe because their properties can be calculated in the vacuum with perturba-
tive quantum chromodynamics (pQCD). Two-particle jet-like azimuthal correla-
tions have shown the away-side shape in central Au+Au collisions to be broadened
with respect to pp and peripheral Au+Au collisions or even double humped 1,2
(see Fig. 1a). The away-side structure is consistent with many different physics
mechanisms including: large angle gluon radiation 3,4, jets deflected by radial flow
or preferential selection of particles due to path-length dependent energy loss, hy-
drodynamic conical flow generated by Mach-cone shock waves 5,6, and Čerenkov
radiation 7,8. Three-particle correlations can be used to differentiate conical flow
and Čerenkov radiation, which have the characteristic of conical emission, from
other mechanisms. In addition, the associated particle pT dependence of the coni-
cal emission angle can be used to differentiate between hydrodynamic conical flow
and simple Čerenkov radiation.
http://arxiv.org/abs/0704.0224v1
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2 Jason Glyndwr Ulery For the STAR Collaboration
2. Analysis Procedure
The 3-particle correlation analysis method is rigorously described in 9. The results
reported here are for charged trigger particles of 3 < pT < 4 GeV/c and two
charged associated particles of 1 < pT < 2 GeV/c (except where otherwise noted).
The data were all taken in the STAR time projection chamber for pp, d+Au and
Au+Au collisions at
sNN=200 GeV/c.
Figure 1b shows the raw 3-particle azimuthal distribution in ∆φaT = φa − φT
and ∆φbT = φb − φT where φT , φa, and φb are the azimuthal angles of the trigger
particle and the two associated particles respectively. Combinatorial backgrounds
must be removed to obtain the genuine 3-particle correlation signal. The analysis is
performed by treating the events as composed of two components, particles that are
jet-like correlated with the trigger particle and background particles. One source of
background, the hard-soft background, results when one of the associated particles
has a jet-like correlation with the trigger particle and the other is uncorrelated,
except for the correlation due to flow. The background is constructed from the 2-
particle jet-like correlation, Ĵ2, folded with the normalized 2-particle background,
, Fig. 1a. The 2-particle background is constructed by mixing events with the
flow modulation added in pairwise from the average v2 values from the measure-
ments based on the reaction plane and 4-particle cumulant methods 1. For the v4
contribution we use the parameterization v4 = 1.15v
from the data10. The back-
ground is normalized (with scale factor α) to the signal within 0.8 < |∆φ| < 1.2
(zero yield at 1 radian or ZYA1). We shall refer to the hard-soft background as
Ĵ2 ⊗ αBinc2 .
φ-φ=φ∆
-1 0 1 2 3 4 5
-1 0 1 2 3 4 5
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
(a) (b) (c) (d)
Fig. 1. (color online) (a) Raw 2-particle correlation (points), background from mixed events with
flow modulation added-in (solid) and scaled by ZYA1 (dashed), and background subtracted 2-
particle correlation (insert). (b) Raw 3-particle correlation, (c) soft-soft background, βα2Binc
and (d) hard-soft background + trigger flow, Ĵ2⊗αBinc2 + βα2B
inc,TF
. See text for detail. Plots
are from ZDC-triggered 0-12% Au+Au collisions at
sNN=200 GeV/c.
Another source of background, the soft-soft background, results from correla-
tions between the two associated particles which are independent of the trigger
particle. This background is obtained from mixed events, where the trigger particle
and the associated particles are from different events in the same centrality win-
dow. We shall refer to the soft-soft background as Binc
. Since the two associated
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QM2006PosterProceedings˙V4
ARE THERE MACH CONES IN HEAVY ION COLLISIONS? THREE-PARTICLE CORRELATIONS FROM STAR 3
particles are from the same event, this background contains all of the correlations
between the two associated particles that are independent of the trigger particle,
including correlations from minijets, other jets in the event, and flow.
The flow between the two associated particles that is independent of the trigger
particle was accounted for in the soft-soft term, but particles are also correlated with
the trigger particle via flow. The trigger flow is added in triplet-wise from mixed
events, where the trigger and associated particles are all from different events in
the same centrality window. The v2 and v4 values are obtained the same way as for
the 2-particle background. The number of triplets is determined from the inclusive
events. We shall refer to the backgrounds from trigger flow as B
inc,TF
. The total
background is then, Ĵ2 ⊗ αBinc2 + βα2(Binc3 + B
inc,TF
). Both Binc
and B
inc,tf
are scaled by βα2. The normalization α2 corrects for the multiplicity bias from
requiring a trigger particle. The factor β accounts for the effect of non-poission
multiplicity distributions and is obtained such that the number of associated pairs
in the background subtracted jet-like three-particle correlation signal equals the
square of the number of associated particles in the background subtracted jet-like
two-particle correlation signal. Figure 1c and d show βα2Binc
and Ĵ2 ⊗ αBinc2 +
inc,TF
, respectively.
3. Results
-1 0 1 2 3 4 5-1
-0.02
-1 0 1 2 3 4 5-1
-0.02
-1 0 1 2 3 4 5-1
-0.05
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
STAR Preliminary
Fig. 2. (color online) Background subtracted 3-particle correlations for pp (top left), d+Au (top
middle), and Au+Au 50-80% (top right), 30-50% (bottom left), 10-30% (bottom center), and ZDC
triggered 0-12% (bottom right) collisions at
sNN=200 GeV/c.
Figure 2 shows background subtracted 3-particle jet-like correlation signals. The
pp and d+Au results are similar. Peaks are clearly visible for the near-side, (0,0), the
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4 Jason Glyndwr Ulery For the STAR Collaboration
away-side, (π,π) and the two cases of one particle on the near-side and the other on
the away-side, (0,π) and (π,0). The away-side peak displays diagonal elongation that
is consistent with kT broadening. The perpherial Au+Au results show additional
on-diagonal elongation of the away-side peak which may be due to contribution
from deflected jets. The additional on-diagonal broadening persists into the more
central Au+Au collisions. In addition, the more central Au+Au collisions display
an off-diagonal structure, at about π± 1.45 radians, that is consistent with conical
emission. The structure increases in magnitude with centrality and is prominent in
the high statistics top 12% central data provided by the on-line ZDC trigger.
partN
0 1 2 3 4 5 6
0.5 Near
1.45)±πDeflected (
1.45)±πCone (
STAR Preliminary
partN
0 1 2 3 4 5 6
1.00)±πDeflected-Cone (
1.30)±πDeflected-Cone (
1.45)±πDeflected-Cone (
STAR Preliminary
Fig. 3. (color online) (left) Average signals in 0.7 × 0.7 boxes at (0,0) (triangle), (π,π) (star),
(π± 1.45,π± 1.45) (square), and (π± 1.45,π∓ 1.45) (circle). (right) Differences in average signals,
between (π ± 1.45,π ± 1.45) and (π ± 1.45,π ∓ 1.45) (triangle), between (π ± 1.3,π ± 1.3) and
(π± 1.3,π∓ 1.3) (square), and between (π± 1.0,π± 1.0) and (π± 1.0,π∓ 1.0) (circle). Solid error
bars are statistical and shaded are systematic. Npart is the number of participants. The ZDC
0-12% points (open symbols) are shifted to the left for clarity.
Figure 3 (left) shows the centrality dependence of the average signal strengths
in different regions. The off-diagonal signals (circle) increase with centrality and
significantly deviate from zero in central Au+Au collisions. The locations of the
off-diagonal signals were determined from a double Gaussian fit to a strip projected
to the off-diagonal, Fig. 4, and were found to be 1.45 radians from π. The differ-
ences between on-diagonal signals, where both conical emission and deflected jets
may contribute, and off-diagonal signals, where only conical emission contributes is
shown in figure 3 (right). Since conical emission signals are expected to be of equal
magnitude on-diagonal as off-diagonal, the difference may indicate the contribution
from deflected jets. The difference decreases with distance from (π,π).
The Mach cone emission angle is expected to be independent of the associated
particle momentum 6, while the Čerenkov radiation model in Ref. 7 predicts an
emission angle that is sharply decreasing with increasing associated particle mo-
mentum. Figure 5 (left) shows the dependence the off-diagonal peak angle on asso-
ciated particle pT . The angle is consistent with constant as a function of associated
particle pT .
Figure 5 (right) shows the centrality dependence the off-diagonal peak angle.
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ARE THERE MACH CONES IN HEAVY ION COLLISIONS? THREE-PARTICLE CORRELATIONS FROM STAR 5
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-0.2
STAR Preliminary
Fig. 4. (color online) Away-side projections of a strip of width 0.7 radians for (left) d+Au and
(right) 0-12% ZDC Triggered Au+Au. Off-diagonal projection (solid) is (∆φ1 − ∆φ)/2 and on-
diagonal projection (open) is (∆φ1 +∆φ)/2− π. Shaded bands are systematic errors.
 Assoc (GeV/c)
0 0.5 1 1.5 2 2.5
0.02±Au+Au 0-12 1.41
0.02±Au+Au 0-50 1.45
Statistical
Systematic
STAR Preliminary
partN(
3 3.5 4 4.5 5 5.5 6
Au+Au 0-12% (shifted)
Au+Au 30-50%, 10-30% and 0-10%
0.03±1.46
STAR Preliminary
Fig. 5. (color online) Emission angles from double Gaussian fits. (left) Angle as a function of
associated particle pT for Au+Au 0-12% ZDC triggered data (filled) and Au+Au 0-50% from
minimum bias data (open). (right) Angle as a function of centrality for Au+Au 0-12% ZDC
triggered data (circle) and Au+Au 30-50%, 10-30% and 0-10% from minimum bias data (square).
The 0-12% point has been shifted for clarity. Corresponding off-diagonal peak values from fits to
a constant are indicated in the legends. The dashed line is at π/2. Solid error bars are statistical
and shaded are systematic.
The angle is consistent with remaining constant as a function of centrality for mid-
central and central Au+Au collisions. The solid line at 1.46 on the plot is from a
fit to a constant.
4. Systematics
The major sources of systematic error are the elliptic flow measurement and the
normalization. The default v2 used is the average those measured by the reaction
plane and 4-particle cumulant methods. We use the reaction plane and 4-particle
cumulant v2 as the upper and lower bounds to estimate the systematic uncertainty
of the v2 subtraction. Figure 6a and b show the background subtracted 3-particle
correlation for reaction plane and 4-particle v2 respectively. The signal is robust with
respect to this variation. The hard-soft background and trigger flow backgrounds
individually vary a great deal with the change in elliptic flow but the variations
cancel to first order in the sum.
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6 Jason Glyndwr Ulery For the STAR Collaboration
To study the effect of the normalization the size of the normalization window
was doubled to 0.6 < |∆φ| < 1.4. The signal is robust with respect to this change
in normalization. Other sources of systematic error include the effect on the trigger
particle flow from requiring a correlated particle (20% on trigger particle v2), un-
certainty in the v4 parameterization, and multiplicity bias effects on the soft-soft
background. The systematic errors shown in figures include all sources mentioned.
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
(a) (b) (c)
Fig. 6. (color online) 0-12% Au+Au ZDC triggerd data for different systematic checks: (a) reaction
plane v2, (b) 4-particle cumulant v2, and (c) normalization region for α of 0.6 < |∆φ| < 1.4
5. Conclusion
Three-particle azimuthal correlations have been studied for trigger particles of 3 <
pT < 4 GeV/c and associated particles of 1 < pT < 2 GeV/c in pp, d+Au, and
Au+Au collisions at
sNN=200 GeV/c by STAR. This analysis treats events as the
sum of two components, particles that are jet-like correlated with the trigger and
background particles. On-diagonal broadening has been observed in pp and d+Au
consistent with kT broadening. Additional on-diagonal broadening has been seen in
Au+Au collisions possibly due to deflected jets. Off-diagonal peaks consistent with
conical emission are present in central Au+Au collisions. To discriminate between
Mach cone emission and simple Čerenkov gluon radiation, a study of the associated
particle pT dependence was performed. No strong pT dependence of the angles on
associated particle pT is observed. This result is consistent with Mach cone emission.
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http://arxiv.org/abs/nucl-ex/0609016
	Introduction
	Analysis Procedure
	Results
	Systematics
	Conclusion
