November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
International Journal of Modern Physics E
c© World Scientific Publishing Company
THREE PARTICLE CORRELATIONS FROM STAR
Jason Glyndwr Ulery
Department of Physics, Purdue University, 525 Northwestern Avenue
West Lafayette, IN 47907, USA
ulery@physics.purdue.edu
Received (received date)
Revised (revised date)
Two-particle correlations have shown modification to the away-side shape in central
Au+Au collisions relative to pp, d+Au and peripheral Au+Au collisions. Different sce-
narios can explain this modification including: large angle gluon radiation, jets deflected
by transverse flow, path length dependent energy loss, Cerenkov gluon radiation of fast
moving particles, and conical flow generated by hydrodynamic Mach-cone shock-waves.
Three-particle correlations have the power to distinguish the scenarios with conical
emission, conical flow and Cerenkov radiation, from other scenarios. In addition, the
dependence of the observed shapes on the pT of the associated particles can be used to
distinguish conical emission from a sonic boom (Mach-cone) and from QCD-Čerenkov
radiation. We present results from STAR on 3-particle azimuthal correlations for a high
pT trigger particle with two softer particles. Results are shown for pp, d+Au and high
statistics Au+Au collisions at
sNN=200 GeV. An important aspect of the analysis is
the subtraction of combinatorial backgrounds. Systematic uncertainties due to this sub-
traction and the flow harmonics v2 and v4 are investigated in detail. The implications
of the results for the presence or absence of conical flow from Mach-cones are discussed.
1. Introduction
Though relativistic heavy ion collisions a medium is created that may be the quark
gluon plasma (QGP). We can study this medium though the use of jets and jet-
like correlations. Jets make good probes because their properties in vacuum can be
calculated with perturbative quantum chromodynamics (pQCD). Previous results
on two-particle azimuthal jet-like correlations have revealed a broadened away-side
shape in central Au+Au collisions relative to pp, d+Au and peripheral Au+Au
collisions, or even double humped 1,2,3,4. The away-side shape is consistent with
many different physics mechanisms including: large angle gluon radiation 5,6, jets
deflected by radial flow or preferential selection of particles due to path-length
dependent energy loss, hydrodynamic conical flow generated by Mach-cone shock
waves 7,8, and Čerenkov gluon radiation 9,10. 3-particle correlations can be used to
differentiate mechanisms with conical emission, Mach-cone and Ĉerenkov radiation,
from the other mechanisms. Additionally, the dependence of the conical emission
angle on associated particle pT can be used to differentiate between Mach-cone and
http://arxiv.org/abs/0704.0220v1
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
2 Jason Glyndwr Ulery For the STAR Collaboration
QCD-Čerenkov radiation.
2. Analysis Procedure
The 3-particle correlation analysis method has been rigorously described in refer-
ence 11. Results are reported here for trigger particles of 3 < pT < 4 Gev/c and
associated particles of 1 < pT < 2 GeV/c, except where otherwise noted. Results
are from pp, d+Au, and Au+Au collisions at
sNN = 200 GeV/c. All particles are
charged particles measuremented in the STAR time projection chamber (TPC).
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.
Results are from ZDC-triggered 0-12% Au+Au collisions at
sNN=200 GeV/c.
Figure 1a shows the 2-particle azimuthal distribution (J2), its background (B
and the background subtracted 2-particle correlations (Ĵ2). The background is con-
structed from mixed events where the trigger particle and the associated particles
are from different events within the same centrality window. The flow modulation
is added in pairwise using the average v2 values from the measurements based on
the reaction plane and 4-particle cumulant methods 1 and the v4 contribution uses
the parameterization v4 = 1.15v
from the data12. The background is normalized
(with scale factor α) to the signal within 0.8 < |∆φ| < 1.2 (zero yield at 1 radian
or ZYA1).
Figure 1b shows the 3-particle azimuthal distribution (J3) in ∆φaT = φa −
φTrigger and ∆φbT = φb −φT where φT , φa, and φb are the azimuthal angles of the
trigger particle and the two associated particles respectively. Combinatorial back-
grounds must be removed to extract the genuine jet-like 3-particle signal. Events are
treated 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 is jet-like correlated
with the trigger particle and the other uncorrelated, other than the correlation
due to flow. It is constructed from the 2-particle jet-like correlations, Ĵ2 folded
with the normalized 2-particle background, αBinc
. We shall refer to the hard-soft
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
Three-Particle Correlations from STAR 3
background as Ĵ2 ⊗ αBinc2 .
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 mixing the trigger particle with a dif-
ferent event of the same centrality. We shall refer to this background as Binc
. Since
the two associated particle are from the same event all correlations between them
that are independent of the trigger are preserved. This may include contribution
from minijets, other jets in the event and flow. The soft-soft background is shown
in figure 1c.
Although the flow correlations between the two associated particles is accounted
for by the soft-soft term, those between the associated particles and the trigger par-
ticle are not. Those correlations are added in triplet-wise from mixed events where
the trigger and the associated particles are all from different events in the same
centrality window. The v2 and v4 values are obtained from the same measurements
as used in the 2-particle background. The total number of triplets is determined
from the soft-soft. We shall refer to this background as B
inc,TF
The total background is then, Ĵ2 ⊗ αBinc2 + βα2(Binc3 + B
inc,TF
). Binc
inc,tf
are scaled by βα2. The normalization factor α is determined from 2-particle
correlations and deviates from unity due to the combined effects of trigger bias and
centrality definition. If the events are poisson then α2 is the correct multiplicity
scaling in 3-particle correlations. The normalization factor β corrects for the effect
of non-poisson multiplicity distributions and is obtained such that the number
of triplets in the background subtracted jet-like three-particles correlation equals
the square of the number of pairs in the background subtracted jet-like 2-particle
correlation. Figure 1d shows Ĵ2 ⊗ αBinc2 + βα2B
inc,TF
3. Results
Figure 2 shows background subtracted 3-particle jet-like correlation signals for dif-
ferent collisions and centralities. The pp and d+Au results are similar with peaks
clearly visible for the near-side, (0,0), 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 on-diagonal elongation which is consistent with kT broadening.
Additional on-diagonal elongation is present in the Au+Au results, possibly due
to deflected jets or large angle gluon radiation. The more central Au+Au colli-
sions display an off-diagonal structure, at about π± 1.45 radians, that is consistent
with conical emission. This structure increases in magnitude with centrality and is
prominent in the high statistics top 12% data provided by the online zero degree
calorimeter (ZDC) trigger.
Figure 3 shows away-side projections of on-diagonal strips to (∆φaT+∆φbT )/2−
π and off-diagonal strips to (∆φaT − ∆φbT )/2. In d+Au collisions only a strong
central peak is present for both on-diagonal and off-diagonal projections. The on-
diagonal projection is broader than the off-diagonal projection, likely due to kT
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
4 Jason Glyndwr Ulery For the STAR Collaboration
-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 jet-like 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.
-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. 3. (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 (∆φaT − ∆φbT )/2 and
on-diagonal projection (open) is (∆φaT +∆φbT )/2 − π. Shaded bands are systematic errors.
broadening. In central Au+Au collisions strong peaks are seen in the off-diagonal
projection, as expected for conical emission. The on-diagonal projection is similar
to the off-diagonal but with additional contribution between the peaks likely due to
deflected jets and/or large angle gluon radiation. The fitted angle of the side peaks
in the off-diagonal projection is about 1.45 radians.
Figure 4 shows the centrality dependence of the average signal strengths in
different regions. The right panel shows the away-side signal, average singal centered
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Three-Particle Correlations from STAR 5
0 1 2 3 4 5 6
-0.05
0 1 2 3 4 5 6
-0.05
0 1 2 3 4 5 6
-0.05
Deflected + Cone
partN(
Fig. 4. (color online) Average signals in 0.7 × 0.7 boxes at (0,0), left, (π ± 1.45,π ∓ 1.45), center,
and (π ± 1.45,π ± 1.45). 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.
at (π,π). It increases with centrality in pp, d+Au and perpherial Au+Au and then
seems to level off for mid-central and central Au+Au collisions. The middle panel
shows the average signal where we only expect conical emission, at (π ± 1.45,π ∓
1.45). It increases with centrality and significantly deviates from zero in central
Au+Au collisions. The right panel shows the average signal were conical emissions
deflected jets, and large angle gluon radiation could all contribute, at π ± 1.45,π±
1.45). This signal is similar to what we see where we only expect conical emission.
Figure 5 shows the difference between on-diagonal signals, where conical emis-
sion, deflected jets, and large angle gluon radiation could contribute, and off-
diagonal signals, where only conical emission contributes. Since conical emission
signals are expected to be of equal magnitude on-diagonal and off-diagonal, the
difference may indicate the contribution from deflected jets and large angle gluon
radiation. The centrality dependence is shown for three different angles. The differ-
ence decreases with distance from (π,π).
If we have Mach-cone emission, the emission angle is expected to be indepen-
dent of the associated particle momentum; however, the Čerenkov radiation model
in Ref. 10 predicts an emission angle that is sharply decreasing with associated
particle momentum. For this reason we shall look at the associated particle pT
dependence of our signal. Figure 6 shows the background subtracted 3-particle cor-
relations for different associated pT bins. The angle is determined from fitting the
off-diagonal projection, (∆φaT − ∆φbT )/2, to a central Gaussian and two symet-
ric side Gaussians. The strength of the off-diagonal signal decrease with increasing
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
6 Jason Glyndwr Ulery For the STAR Collaboration
partN
0 1 2 3 4 5 6
1.00)±πDeflected (
1.30)±πDeflected (
1.45)±πDeflected (
STAR Preliminary
Fig. 5. (color online) 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.
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
-0.15
-0.05
-1 0 1 2 3 4 5-1
-0.05
-1 0 1 2 3 4 5-1
-0.02
(a) (b) (c) (d)
Fig. 6. (color online) Background subtracted jet-like 3-particle correlations for 0.75 < p
< 1.0
GeV/c (left), 1.0 < p
< 1.5 GeV/c (left center), 1.5 < p
< 2.0 GeV/c (right center), and
2.0 < p
< 3.0 GeV/c (right). Trigger particle pT is 3 < p
< 4 GeV/c. Results are from ZDC
triggered top 12% central Au+Au collisons at
sNN=200 GeV.
pT and is almost gone in the highest pT bin. This is not surprising since we need
two away-side particles each with a pT that is a significant fraction of the trigger
particle pT . Figure 7 (left) shows the dependence of the angle of the off-diagonal
peaks on associated particle pT . The angle is consistent with remaining constant as
a function of associated particle pT .
Figure 7 (right) shows the centrality dependence of the angle of the off-diagonal
peaks obtained from fits to the projections as done for the pT dependence. The
angle is consistent with remaining constant from mid-central to central Au+Au
collisions. If we have Mach-cone emission this likely implies the speed of sound in
the medium does not greatly vary from mid-central to central Au+Au collisions.
The solid line at 1.46 on the plot is from a fit to a constant.
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
Three-Particle Correlations from STAR 7
 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. 7. (color online) Emission angles from double Gaussian fits. (left) Angle as a function of
associated particle pT for Au+Au 0-12% ZDC triggered (filled) and Au+Au 0-50% from minimum
bias (open). Numbers on the plot are results from a fit to a constant for the data points with the
fit errors displayed. (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. The number is from a fit to a constant for the points, shown with
the solid line. The dashed line is at π/2. Solid error bars are statistical and shaded are systematic.
4. Systematics
The major sources of systematic error are from the elliptic flow measurements
and the background normalization. Our default v2 is the average of measurements
from the reaction plane and 4-particle cumulant methods. The systematic uncer-
tainty due to the v2 has been determined by varying it between the reaction plane
and 4-particle cumulant results. Figure 8a and b show the background subtracted
3-particle correlation for the reaction plane and 4-particle v2, respectively. Even
though the hard-soft background and trigger flow backgrounds individually vary a
great deal with the change in elliptic flow, the variations cancel out to first order.
Therefore the signal, as seen in Fig. 8 is robust with respect to the variation in
elliptic flow.
-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. 8. (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
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
8 Jason Glyndwr Ulery For the STAR Collaboration
To study the effect of the background normalization the size of the normalization
window used to determine α was doubled to 0.6 < |∆φ| < 1.4. The signal is robust
with this change in normalization. Figure 8 shows the background subtracted 3-
particle correlation using this larger normalization window.
Other sources of systematic error include the effect on the trigger particle flow
from requiring a correlated particle (a 20% change on trigger particle v2 is applied),
uncertainity in the v4 parameterization, and multiplicity bias effects on the soft-
soft background. The systematic errors shown in Figures 3, 4, 5, and 7 reflect the
quadratic sum of all the systematic uncertainties mentioned.
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
collisions that is consistent with kT broadening. Additional on-diagonal broadening
has been observed in heavy ion collisions that may be due to contributions from
deflected jets and/or large angle gluon radiation. Off-diagonal peaks have been
detected in central Au+Au collisions that are consistent with conical emission.
A study of the angle as a function of associated particle pT was performed to
discriminate between hydrodynamic conical flow and Čerenkov gluon radiation. No
strong dependence on associated particle pT was beheld. This result is consistent
with Mach-cone emission.
References
1. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 95, 152301 (2005).
2. S.S. Adler et al. (PHENIX Collaboration), Phys. Rev. Lett. 97, 052301 (2006).
3. J. Ulery et al. (STAR Collaboration), Nuc. Phys. A774, 581-584 (2006).
4. M. Horner et al. (STAR Collaboration), QM2006 Talk Proceedings to appear in Jour.
Phys. G.
5. I. Vitev, Phys. Lett. B 630, 78 (2005).
6. A.D. Polosa and C.A. Salgado, hep-ph/0607295.
7. H. Stoecker, Nucl. Phys. A750, 121 (2005).
8. J. Casalderrey-Solana, E. Shuryak and D. Teaney, J. Phys. Conf. Ser. 27, 23 (2005).
9. I.M. Dremin, Nucl. Phys. A767 233 (2006).
10. V. Koch, A. Majumder and X.-N. Wang, Phys. Rev. Lett. 96, 172302 (2006).
11. J. Ulery and F. Wang, nucl-ex/0609016.
12. J. Adams et al. (STAR Collaboration), Phys. Rev. C 72, 014904 (2004).
http://arxiv.org/abs/hep-ph/0607295
http://arxiv.org/abs/nucl-ex/0609016
	Introduction
	Analysis Procedure
	Results
	Systematics
	Conclusion

  Two-particle correlations have shown modification to the away-side shape in
central Au+Au collisions relative to $pp$, d+Au and peripheral Au+Au
collisions. Different scenarios can explain this modification including: large
angle gluon radiation, jets deflected by transverse flow, path length dependent
energy loss, Cerenkov gluon radiation of fast moving particles, and conical
flow generated by hydrodynamic Mach-cone shock-waves. Three-particle
correlations have the power to distinguish the scenarios with conical emission,
conical flow and Cerenkov radiation, from other scenarios. In addition, the
dependence of the observed shapes on the $p_T$ of the associated particles can
be used to distinguish conical emission from a sonic boom (Mach-cone) and from
QCD-Cerenkov radiation. We present results from STAR on 3-particle azimuthal
correlations for a high $p_T$ trigger particle with two softer particles.
Results are shown for $pp$, d+Au and high statistics Au+Au collisions at
$\sqrt{s_{NN}}$=200 GeV. 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. The implications
of the results for the presence or absence of conical flow from Mach-cones are
discussed.

Introduction
Though relativistic heavy ion collisions a medium is created that may be the quark
gluon plasma (QGP). We can study this medium though the use of jets and jet-
like correlations. Jets make good probes because their properties in vacuum can be
calculated with perturbative quantum chromodynamics (pQCD). Previous results
on two-particle azimuthal jet-like correlations have revealed a broadened away-side
shape in central Au+Au collisions relative to pp, d+Au and peripheral Au+Au
collisions, or even double humped 1,2,3,4. The away-side shape is consistent with
many different physics mechanisms including: large angle gluon radiation 5,6, jets
deflected by radial flow or preferential selection of particles due to path-length
dependent energy loss, hydrodynamic conical flow generated by Mach-cone shock
waves 7,8, and Čerenkov gluon radiation 9,10. 3-particle correlations can be used to
differentiate mechanisms with conical emission, Mach-cone and Ĉerenkov radiation,
from the other mechanisms. Additionally, the dependence of the conical emission
angle on associated particle pT can be used to differentiate between Mach-cone and
http://arxiv.org/abs/0704.0220v1
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
2 Jason Glyndwr Ulery For the STAR Collaboration
QCD-Čerenkov radiation.
2. Analysis Procedure
The 3-particle correlation analysis method has been rigorously described in refer-
ence 11. Results are reported here for trigger particles of 3 < pT < 4 Gev/c and
associated particles of 1 < pT < 2 GeV/c, except where otherwise noted. Results
are from pp, d+Au, and Au+Au collisions at
sNN = 200 GeV/c. All particles are
charged particles measuremented in the STAR time projection chamber (TPC).
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.
Results are from ZDC-triggered 0-12% Au+Au collisions at
sNN=200 GeV/c.
Figure 1a shows the 2-particle azimuthal distribution (J2), its background (B
and the background subtracted 2-particle correlations (Ĵ2). The background is con-
structed from mixed events where the trigger particle and the associated particles
are from different events within the same centrality window. The flow modulation
is added in pairwise using the average v2 values from the measurements based on
the reaction plane and 4-particle cumulant methods 1 and the v4 contribution uses
the parameterization v4 = 1.15v
from the data12. The background is normalized
(with scale factor α) to the signal within 0.8 < |∆φ| < 1.2 (zero yield at 1 radian
or ZYA1).
Figure 1b shows the 3-particle azimuthal distribution (J3) in ∆φaT = φa −
φTrigger and ∆φbT = φb −φT where φT , φa, and φb are the azimuthal angles of the
trigger particle and the two associated particles respectively. Combinatorial back-
grounds must be removed to extract the genuine jet-like 3-particle signal. Events are
treated 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 is jet-like correlated
with the trigger particle and the other uncorrelated, other than the correlation
due to flow. It is constructed from the 2-particle jet-like correlations, Ĵ2 folded
with the normalized 2-particle background, αBinc
. We shall refer to the hard-soft
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
Three-Particle Correlations from STAR 3
background as Ĵ2 ⊗ αBinc2 .
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 mixing the trigger particle with a dif-
ferent event of the same centrality. We shall refer to this background as Binc
. Since
the two associated particle are from the same event all correlations between them
that are independent of the trigger are preserved. This may include contribution
from minijets, other jets in the event and flow. The soft-soft background is shown
in figure 1c.
Although the flow correlations between the two associated particles is accounted
for by the soft-soft term, those between the associated particles and the trigger par-
ticle are not. Those correlations are added in triplet-wise from mixed events where
the trigger and the associated particles are all from different events in the same
centrality window. The v2 and v4 values are obtained from the same measurements
as used in the 2-particle background. The total number of triplets is determined
from the soft-soft. We shall refer to this background as B
inc,TF
The total background is then, Ĵ2 ⊗ αBinc2 + βα2(Binc3 + B
inc,TF
). Binc
inc,tf
are scaled by βα2. The normalization factor α is determined from 2-particle
correlations and deviates from unity due to the combined effects of trigger bias and
centrality definition. If the events are poisson then α2 is the correct multiplicity
scaling in 3-particle correlations. The normalization factor β corrects for the effect
of non-poisson multiplicity distributions and is obtained such that the number
of triplets in the background subtracted jet-like three-particles correlation equals
the square of the number of pairs in the background subtracted jet-like 2-particle
correlation. Figure 1d shows Ĵ2 ⊗ αBinc2 + βα2B
inc,TF
3. Results
Figure 2 shows background subtracted 3-particle jet-like correlation signals for dif-
ferent collisions and centralities. The pp and d+Au results are similar with peaks
clearly visible for the near-side, (0,0), 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 on-diagonal elongation which is consistent with kT broadening.
Additional on-diagonal elongation is present in the Au+Au results, possibly due
to deflected jets or large angle gluon radiation. The more central Au+Au colli-
sions display an off-diagonal structure, at about π± 1.45 radians, that is consistent
with conical emission. This structure increases in magnitude with centrality and is
prominent in the high statistics top 12% data provided by the online zero degree
calorimeter (ZDC) trigger.
Figure 3 shows away-side projections of on-diagonal strips to (∆φaT+∆φbT )/2−
π and off-diagonal strips to (∆φaT − ∆φbT )/2. In d+Au collisions only a strong
central peak is present for both on-diagonal and off-diagonal projections. The on-
diagonal projection is broader than the off-diagonal projection, likely due to kT
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
4 Jason Glyndwr Ulery For the STAR Collaboration
-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 jet-like 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.
-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. 3. (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 (∆φaT − ∆φbT )/2 and
on-diagonal projection (open) is (∆φaT +∆φbT )/2 − π. Shaded bands are systematic errors.
broadening. In central Au+Au collisions strong peaks are seen in the off-diagonal
projection, as expected for conical emission. The on-diagonal projection is similar
to the off-diagonal but with additional contribution between the peaks likely due to
deflected jets and/or large angle gluon radiation. The fitted angle of the side peaks
in the off-diagonal projection is about 1.45 radians.
Figure 4 shows the centrality dependence of the average signal strengths in
different regions. The right panel shows the away-side signal, average singal centered
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Three-Particle Correlations from STAR 5
0 1 2 3 4 5 6
-0.05
0 1 2 3 4 5 6
-0.05
0 1 2 3 4 5 6
-0.05
Deflected + Cone
partN(
Fig. 4. (color online) Average signals in 0.7 × 0.7 boxes at (0,0), left, (π ± 1.45,π ∓ 1.45), center,
and (π ± 1.45,π ± 1.45). 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.
at (π,π). It increases with centrality in pp, d+Au and perpherial Au+Au and then
seems to level off for mid-central and central Au+Au collisions. The middle panel
shows the average signal where we only expect conical emission, at (π ± 1.45,π ∓
1.45). It increases with centrality and significantly deviates from zero in central
Au+Au collisions. The right panel shows the average signal were conical emissions
deflected jets, and large angle gluon radiation could all contribute, at π ± 1.45,π±
1.45). This signal is similar to what we see where we only expect conical emission.
Figure 5 shows the difference between on-diagonal signals, where conical emis-
sion, deflected jets, and large angle gluon radiation could contribute, and off-
diagonal signals, where only conical emission contributes. Since conical emission
signals are expected to be of equal magnitude on-diagonal and off-diagonal, the
difference may indicate the contribution from deflected jets and large angle gluon
radiation. The centrality dependence is shown for three different angles. The differ-
ence decreases with distance from (π,π).
If we have Mach-cone emission, the emission angle is expected to be indepen-
dent of the associated particle momentum; however, the Čerenkov radiation model
in Ref. 10 predicts an emission angle that is sharply decreasing with associated
particle momentum. For this reason we shall look at the associated particle pT
dependence of our signal. Figure 6 shows the background subtracted 3-particle cor-
relations for different associated pT bins. The angle is determined from fitting the
off-diagonal projection, (∆φaT − ∆φbT )/2, to a central Gaussian and two symet-
ric side Gaussians. The strength of the off-diagonal signal decrease with increasing
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
6 Jason Glyndwr Ulery For the STAR Collaboration
partN
0 1 2 3 4 5 6
1.00)±πDeflected (
1.30)±πDeflected (
1.45)±πDeflected (
STAR Preliminary
Fig. 5. (color online) 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.
-1 0 1 2 3 4 5-1
-1 0 1 2 3 4 5-1
-0.15
-0.05
-1 0 1 2 3 4 5-1
-0.05
-1 0 1 2 3 4 5-1
-0.02
(a) (b) (c) (d)
Fig. 6. (color online) Background subtracted jet-like 3-particle correlations for 0.75 < p
< 1.0
GeV/c (left), 1.0 < p
< 1.5 GeV/c (left center), 1.5 < p
< 2.0 GeV/c (right center), and
2.0 < p
< 3.0 GeV/c (right). Trigger particle pT is 3 < p
< 4 GeV/c. Results are from ZDC
triggered top 12% central Au+Au collisons at
sNN=200 GeV.
pT and is almost gone in the highest pT bin. This is not surprising since we need
two away-side particles each with a pT that is a significant fraction of the trigger
particle pT . Figure 7 (left) shows the dependence of the angle of the off-diagonal
peaks on associated particle pT . The angle is consistent with remaining constant as
a function of associated particle pT .
Figure 7 (right) shows the centrality dependence of the angle of the off-diagonal
peaks obtained from fits to the projections as done for the pT dependence. The
angle is consistent with remaining constant from mid-central to central Au+Au
collisions. If we have Mach-cone emission this likely implies the speed of sound in
the medium does not greatly vary from mid-central to central Au+Au collisions.
The solid line at 1.46 on the plot is from a fit to a constant.
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Three-Particle Correlations from STAR 7
 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. 7. (color online) Emission angles from double Gaussian fits. (left) Angle as a function of
associated particle pT for Au+Au 0-12% ZDC triggered (filled) and Au+Au 0-50% from minimum
bias (open). Numbers on the plot are results from a fit to a constant for the data points with the
fit errors displayed. (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. The number is from a fit to a constant for the points, shown with
the solid line. The dashed line is at π/2. Solid error bars are statistical and shaded are systematic.
4. Systematics
The major sources of systematic error are from the elliptic flow measurements
and the background normalization. Our default v2 is the average of measurements
from the reaction plane and 4-particle cumulant methods. The systematic uncer-
tainty due to the v2 has been determined by varying it between the reaction plane
and 4-particle cumulant results. Figure 8a and b show the background subtracted
3-particle correlation for the reaction plane and 4-particle v2, respectively. Even
though the hard-soft background and trigger flow backgrounds individually vary a
great deal with the change in elliptic flow, the variations cancel out to first order.
Therefore the signal, as seen in Fig. 8 is robust with respect to the variation in
elliptic flow.
-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. 8. (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
November 4, 2018 14:16 WSPC/INSTRUCTION FILE IWCF˙v3
8 Jason Glyndwr Ulery For the STAR Collaboration
To study the effect of the background normalization the size of the normalization
window used to determine α was doubled to 0.6 < |∆φ| < 1.4. The signal is robust
with this change in normalization. Figure 8 shows the background subtracted 3-
particle correlation using this larger normalization window.
Other sources of systematic error include the effect on the trigger particle flow
from requiring a correlated particle (a 20% change on trigger particle v2 is applied),
uncertainity in the v4 parameterization, and multiplicity bias effects on the soft-
soft background. The systematic errors shown in Figures 3, 4, 5, and 7 reflect the
quadratic sum of all the systematic uncertainties mentioned.
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
collisions that is consistent with kT broadening. Additional on-diagonal broadening
has been observed in heavy ion collisions that may be due to contributions from
deflected jets and/or large angle gluon radiation. Off-diagonal peaks have been
detected in central Au+Au collisions that are consistent with conical emission.
A study of the angle as a function of associated particle pT was performed to
discriminate between hydrodynamic conical flow and Čerenkov gluon radiation. No
strong dependence on associated particle pT was beheld. This result is consistent
with Mach-cone emission.
References
1. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 95, 152301 (2005).
2. S.S. Adler et al. (PHENIX Collaboration), Phys. Rev. Lett. 97, 052301 (2006).
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Phys. G.
5. I. Vitev, Phys. Lett. B 630, 78 (2005).
6. A.D. Polosa and C.A. Salgado, hep-ph/0607295.
7. H. Stoecker, Nucl. Phys. A750, 121 (2005).
8. J. Casalderrey-Solana, E. Shuryak and D. Teaney, J. Phys. Conf. Ser. 27, 23 (2005).
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http://arxiv.org/abs/hep-ph/0607295
http://arxiv.org/abs/nucl-ex/0609016
	Introduction
	Analysis Procedure
	Results
	Systematics
	Conclusion
