System-Size Independence of Directed Flow Measured at the BNL Relativistic Heavy-Ion Collider

TLDR: It is found that the directed flow depends on the incident energy but, contrary to all available model implementations, not on the size of the colliding system at a given centrality.

Abstract: We measure directed flow (v(1)) for charged particles in Au + Au and Cu + Cu collisions at root s(NN) = 200 and 62.4 GeV, as a function of pseudorapidity (eta), transverse momentum (p(t)), and collision centrality, based on data from the STAR experiment. We find that the directed flow depends on the incident energy but, contrary to all available model implementations, not on the size of the colliding system at a given centrality. We extend the validity of the limiting fragmentation concept to v(1) in different collision systems, and investigate possible explanations for the observed sign change in v(1)(p(t)).

Figures

FIG. 1 (color online). Charged particle v1ð Þ for three centralities in Auþ Au collisions at 200 GeV. The arrows indicate the algebraic sign of v1 for spectator neutrons, and their positions on the axis correspond to beam rapidity. The inset shows the mid- region in more detail. The error bars are statistical, and the shaded bands show systematic errors. PHOBOS results [18] are also shown for midcentral collisions.

FIG. 4 (color online). Charged particle v1 versus centrality, for Auþ Au and Cuþ Cu at 200 and 62.4 GeV. The upper (lower) panels show results from the main TPC (FTPC). The plotted error bars are statistical, and systematic errors (see Figs. 1 and 5) are within 10%.

FIG. 3 (color online). Charged particle v1ð Þ for midcentral (30%–60%) Auþ Au and Cuþ Cu at 200 and 62.4 GeV. The solid curves and dashed curves are odd-order polynomial fits to guide the eye and demonstrate the forward-backward symmetry of the data. The wider shaded bands are from AMPT for the same conditions as the data. For clarity, 200 (62.4) GeV calculations are shown only at negative (positive) . The plotted error bars are statistical, and systematic errors (see Figs. 1 and 5) are within 10%.

FIG. 2 (color online). Charged particle v1ðptÞ in 200 GeV Auþ Au for three centralities. The dashed curve and dotted curve are hydrodynamic calculations for the labeled rapidities at impact parameter 6.8 fm (15%–25% most central collisions). See the text for an explanation of the solid curve. The plotted error bars are statistical, and systematic errors (see Fig. 1) are within 10%.

Full text

System-Size Independence of Directed Flow Measured at the BNL Relativistic Heavy-Ion Collider
B. I. Abelev,
10
M. M. Aggarwal,
32
Z. Ahammed,
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B. D. Anderson,
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D. Arkhipkin,
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(STAR Collaboration)
PRL 101, 252301 (2008)
PHYSICAL REVIEW LETTERS
week ending
19 DECEMBER 2008
0031-9007=08=101(25)=252301(6) 252301-1 Ó 2008 The American Physical Society

1
Argonne National Laboratory, Argonne, Illinois 60439, USA
2
University of Birmingham, Birmingham, United Kingdom
3
Brookhaven National Laboratory, Upton, New York 11973, USA
4
California Institute of Technology, Pasadena, California 91125, USA
5
University of California, Berkeley, California 94720, USA
6
University of California, Davis, California 95616, USA
7
University of California, Los Angeles, California 90095, USA
8
Universidade Estadual de Campinas, Sao Paulo, Brazil
9
Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
10
University of Illinois at Chicago, Chicago, Illinois 60607, USA
11
Creighton University, Omaha, Nebraska 68178, USA
12
Nuclear Physics Institute AS CR, 250 68 R
ˇ
ez
ˇ
/Prague, Czech Republic
13
Laboratory for High Energy (JINR), Dubna, Russia
14
Particle Physics Laboratory (JINR), Dubna, Russia
15
University of Frankfurt, Frankfurt, Germany
16
Institute of Physics, Bhubaneswar 751005, India
17
Indian Institute of Technology, Mumbai, India
18
Indiana University, Bloomington, Indiana 47408, USA
19
Institut de Recherches Subatomiques, Strasbourg, France
20
University of Jammu, Jammu 180001, India
21
Kent State University, Kent, Ohio 44242, USA
22
University of Kentucky, Lexington, Kentucky, 40506-0055, USA
23
Institute of Modern Physics, Lanzhou, China
24
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
25
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
26
Max-Planck-Institut fu
¨
r Physik, Munich, Germany
27
Michigan State University, East Lansing, Michigan 48824, USA
28
Moscow Engineering Physics Institute, Moscow Russia
29
City College of New York, New York City, New York 10031, USA
30
NIKHEF and Utrecht University, Amsterdam, The Netherlands
31
Ohio State University, Columbus, Ohio 43210, USA
32
Panjab University, Chandigarh 160014, India
33
Pennsylvania State University, University Park, Pennsylvania 16802, USA
34
Institute of High Energy Physics, Protvino, Russia
35
Purdue University, West Lafayette, Indiana 47907, USA
36
Pusan National University, Pusan, Republic of Korea
37
University of Rajasthan, Jaipur 302004, India
38
Rice University, Houston, Texas 77251, USA
39
Universidade de Sao Paulo, Sao Paulo, Brazil
40
University of Science and Technology of China, Hefei 230026, China
41
Shanghai Institute of Applied Physics, Shanghai 201800, China
42
SUBATECH, Nantes, France
43
Texas A&M University, College Station, Texas 77843, USA
44
University of Texas, Austin, Texas 78712, USA
45
Tsinghua University, Beijing 100084, China
46
Valparaiso University, Valparaiso, Indiana 46383, USA
47
Variable Energy Cyclotron Centre, Kolkata 700064, India
48
Warsaw University of Technology, Warsaw, Poland
49
University of Washington, Seattle, Washington 98195, USA
50
Wayne State University, Detroit, Michigan 48201, USA
51
Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China
52
Yale University, New Haven, Connecticut 06520, USA
53
University of Zagreb, Zagreb, HR-10002, Croatia
(Received 10 July 2008; published 16 December 2008)
We measure directed flow (v
1
) for charged particles in Au þ Au and Cu þ Cu collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼
200 and 62.4 GeV, as a function of pseudorapidity (), transverse momentum (p
t
), and collision centrality,
based on data from the STAR experiment. We find that the directed flow depends on the incident energy
but, contrary to all available model implementations, not on the size of the colliding system at a given
centrality. We extend the validity of the limiting fragmentation concept to v
1
in different collision
systems, and investigate possible explanations for the observed sign change in v
1
ðp
t
Þ.
PRL 101, 252301 (2008)
PHYSICAL REVIEW LETTERS
week ending
19 DECEMBER 2008
252301-2

DOI: 10.1103/PhysRevLett.101.252301 PACS numbers: 25.75.Ld
The heavy-ion program at the Relativistic Heavy-Ion
Collider (RHIC) seeks to understand the nature and dy-
namics of strongly interacting matter under extreme con-
ditions. It is widely expected that in collisions at RHIC, a
new partonic phase of matter is created, strongly interact-
ing quark gluon plasma [1]. In particular, its bulk nature is
revealed in strong elliptic flow, which in central collisions
approaches the predictions of ideal hydrodynamics, assum-
ing system thermalization on an extremely short time scale
(  0:5fm=c)[2]. However, the mechanism behind such
rapid thermalization remains far from clear and is under
active theoretical study [3–5]. This may be related to
another novel phenomenon that could be relevant at
RHIC—saturation of the gluon distribution—which char-
acterizes the nuclear parton distribution prior to collision
[6]. Various theoretical approaches to connect collision
geometry, saturated gluon distributions, and the onset of
bulk collective behavior are being explored [2]; more
experimental input would guide these efforts.
Directed flow refers to collective sidewards deflection of
particles and is characterized by a first-order harmonic (v
1
)
of the Fourier expansion of particle’s azimuthal distribu-
tion with respect to the reaction plane [7]. At large  (in the
fragmentation region) the directed flow is believed to be
generated during the nuclear passage time (2R= 
0:1fm=c)[8,9]. It therefore probes the onset of bulk
collective dynamics during thermalization, providing valu-
able experimental guidance to models of the preequili-
brium stage. In this Letter, we present multiple-
differential measurements of v
1
for Au þ Au and Cu þ
Cu collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 200 and 62.4 GeV as a function of
, p
t
, and collision centrality. Here, we report an intriguing
new universal scaling of the phenomenon with collision
centrality. Existing implementations of Boltzmann or cas-
cade and hydrodynamic models are unable to explain the
measured trends.
At RHIC energies, it is a challenge to measure v
1
accurately due to the relatively small signal and a poten-
tially large systematic error arising from nonflow (azimu-
thal correlations not related to the reaction plane
orientation). In this work, the reaction plane was deter-
mined from the sideward deflection of spectator neutrons
[9,10] measured in the Shower Maximum Detectors
(SMD) of the Zero Degree Calorimeters (ZDC) [11,12].
The v
1
based on this quantity, denoted v
1
fZDC-SMDg
[11], should have minimal contribution from nonflow ef-
fects due to the large  gap between the spectator neutrons
used to establish the reaction plane and the  region where
the measurements were performed.
Charged-particle tracks were reconstructed in STAR’s
main time projection chamber (TPC) [13] and forward
TPCs [14], with pseudorapidity coverage jj < 1:3 and
2:5 < jj < 4:0, respectively. The centrality definition (in
which zero represents the most central collisions) and track
quality cuts are the same as in Ref. [15]. This study is based
on Au þ Au samples of 8  10
6
events at 200 GeV, 5 
10
6
at 62.4 GeV, and Cu þ Cu samples of 12  10
6
events
at 200 GeV, and 8  10
6
at 62.4 GeV. All were obtained
with a minimum-bias trigger. Systematic uncertainties on
v
1
measurements are estimated to be within 10% for the 
range studied. This limit is based on comparisons of
v
1
fZDC-SMDg and independent analysis methods
[11,15], and we also make use of forward-backward sym-
metry to constrain estimates of systematic errors. Nonflow
is not the dominant source of systematic uncertainty. More
details about these errors can be found in Refs. [11,15].
The resolution [7] of the first-order event plane recon-
structed using the ZDC-SMDs is a crucial quantity for this
analysis. The magnitude of the event-plane resolution,
defined as hcosð
EP
 
RP
Þi [7], increases with the spec-
tator v
1
and the number of neutrons per event detected by
the ZDC-SMDs. The ZDC size is optimized for 200 GeV,
and its acceptance for spectator neutrons decreases at lower
energies due to spectator neutrons being emitted within a
cone whose apex angle increases with the inverse of the
beam momentum. For the 30%–60% most central colli-
sions, resolutions for 200 GeV Au þ Au and Cu þ Cu, and
for 62.4 GeV Au þ Au and Cu þ Cu are about 0.4, 0.15,
0.15, and 0.04, respectively (more details are provided in
Table 1 of Ref. [16]). The 30%–60% centrality interval is
the only region where the ZDC-SMD event-plane resolu-
tion can be reliably determined for all four systems.
The charged particle v
1
ðÞ is shown in Fig. 1 for Au þ
Au at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 200 GeV in three centralities. The inset
η
-6 -4 -2 0 2
46
(%)
1
v
-3
-2
-1
0
1
2
3
PHOBOS: 6% - 40%
0% - 5%
: 0% - 5%〉
t
p〈 / 〉
x
p〈
5% - 40%
40% - 80%
-1 -0.5 0 0.5 1
-0.4
-0.2
0
0.2
0.4
FIG. 1 (color online). Charged particle v
1
ðÞ for three central-
ities in Au þ Au collisions at 200 GeV. The arrows indicate the
algebraic sign of v
1
for spectator neutrons, and their positions on
the  axis correspond to beam rapidity. The inset shows the
mid- region in more detail. The error bars are statistical, and
the shaded bands show systematic errors. PHOBOS results [18]
are also shown for midcentral collisions.
PRL 101, 252301 (2008)
PHYSICAL REVIEW LETTERS
week ending
19 DECEMBER 2008
252301-3

shows, on expanded scales, the mid- region measured by
the main TPC, where v
1
is resolvable below the 0.1% level.
Within the studied  range, the sign of charged particle v
1
is opposite to that of the spectators, and the v
1
magnitude
increases from central to peripheral collisions. For 0%–5%
centrality, the slope dv
1
=d changes sign above the
middle of the forward time projection chamber (FTPC)
pseudorapidity acceptance, and our results agree with the
pattern reported by PHOBOS over a broader  range
[17,18].
The ratio hp
x
i=hp
t
i is shown in Fig. 1 for the most
central data (0%–5%), in comparison to v
1
. Here, p
x
refers
to the in-plane component of a track’s transverse momen-
tum, a quantity commonly used prior to the 1990s [10]. As
elaborated below, there is interest in the behavior of both
v
1
and hp
x
i when v
1
ðp
t
Þ changes sign.
To further examine v
1
, the 200 GeV Au þ Au data are
divided into bins of p
t
(Fig. 2). The upper and lower panels
show results from the main TPC and the FTPCs, respec-
tively. In the main TPC, v
1
ðp
t
Þ crosses zero at 1 <p
t
<
2 GeV=c for central and midcentral collisions. A zero-
crossing behavior in v
1
ðp
t
Þ is necessarily exhibited by a
hydrodynamic calculation in which hp
x
i, presumably im-
parted during the passing time of the initial-state nuclei,
has been neglected and set equal to zero [19]. Because of
the poor momentum resolution of the FTPCs at higher p
t
,
we cannot test the zero crossing at forward . It is note-
worthy that the observed hp
x
i, presented in Fig. 1, is far
from negligible, which contradicts the assumptions used in
the hydrodynamic calculations.
The observed v
1
ðp
t
Þ dependence can be explained by
assuming that pions and baryons flow with opposite sign,
coupled with the measured baryon enhancement at higher
p
t
[20]. For example, taking linear functions [21] for pion
and baryon v
1
ðp
t
Þ, we obtain a satisfactory description of
our data (see the solid curve in Fig. 2) with pion v
1
slopes,
dv
1
=dp
t
¼0:18  0:02, 0:34  0:02, and 0:52 
0:04, and baryon v
1
slopes 0:56  0:12, 0:86 0:10, and
1:02  0:12 for centralities 0%–5%, 5%–40%, and 40%–
80%, respectively. Note that the opposite v
1
slope for pions
and protons, with the magnitude of proton slopes being
larger, in this case is consistent with calculations [22]
where the ‘‘wiggle’’ rapidity dependence of identified par-
ticles has been predicted to result from the interplay of
stopping and radial flow. Currently, we are unable to test
the wiggle effect in v
1
ðyÞ with identified particles due to
limited statistics and limited particle identification.
To study the energy and system-size dependence of v
1
,
Fig. 3 shows Cu þ Cu data compared to Au þ Au in the
centrality range 30%–60% for both 200 and 62.4 GeV.
There is a clear trend for v
1
ðÞ to decrease with increasing
beam energy for both Au þ Au and Cu þ Cu. In the
studied pseudorapidity and centrality range, v
1
ðÞ is,
within errors, independent of the system size at each
beam energy, despite the three-to-one mass ratio between
gold and copper. This remarkable feature holds for almost
all centrality bins studied, as shown in Fig. 4, and persists
even near mid- (as shown in the upper panel), where
elliptic flow (v
2
) of charged particles in Cu þ Cu is con-
(GeV/c)
t
p
01234
(%)
1
v
-0.2
0
0.2
0.4
| < 1.3η|
200 GeV Au+Au
y = 1
(GeV/c)
t
p
0 0.5 1 1.5 2
(%)
1
v
-4
-2
0
0% - 5%
5% - 40%
40% - 80%
| < 4η2.5 < |
y = 3
FIG. 2 (color online). Charged particle v
1
ðp
t
Þ in 200 GeV
Au þ Au for three centralities. The dashed curve and dotted
curve are hydrodynamic calculations for the labeled rapidities at
impact parameter 6.8 fm (15%–25% most central collisions). See
the text for an explanation of the solid curve. The plotted error
bars are statistical, and systematic errors (see Fig. 1) are within
10%.
η
-4 -3 -2 -1 0 1 2 3 4
(%)
1
v
-8
-6
-4
-2
0
2
4
6
8
30% - 60%
Data AMPT
200 GeV Au+Au
200 GeV Cu+Cu
62.4 GeV Au+Au
62.4 GeV Cu+Cu
FIG. 3 (color online). Charged particle v
1
ðÞ for midcentral
(30%–60%) Au þ Au and Cu þ Cu at 200 and 62.4 GeV. The
solid curves and dashed curves are odd-order polynomial fits to
guide the eye and demonstrate the forward-backward symmetry
of the data. The wider shaded bands are from AMPT for the
same conditions as the data. For clarity, 200 (62.4) GeV calcu-
lations are shown only at negative (positive) . The plotted error
bars are statistical, and systematic errors (see Figs. 1 and 5) are
within 10%.
PRL 101, 252301 (2008)
PHYSICAL REVIEW LETTERS
week ending
19 DECEMBER 2008
252301-4

siderably lower than in Au þ Au [23]. Unlike v
2
=, the
ratio of the elliptic flow to the system initial eccentricity,
which scales with the particle density in the transverse
plane ð1=SÞdN
ch
=dy [24] (also interpreted to be the mid-
rapidity area density [25] or the system length [26]), v
1
ðÞ
at a given centrality is found to be independent of the
system size, and varies only with the incident energy.
The different scalings for v
2
= and v
1
might arise from
the way in which they are developed: to produce v
2
, many
momentum exchanges among particles must occur (and the
number of momentum exchanges is related to the partici-
pant density and the dimensions of the system), while to
produce v
1
, an important feature of the collision process is
that different rapidity losses need to occur (related to the
incident energy) for particles at different distances from the
center of the participant zone [22].
The hybrid transport model AMPT (a multiphase trans-
port model) [27] lies consistently below the measured data,
as evident from Fig. 3. STAR’s prior v
1
study [11]inAu þ
Au at 62 GeV also showed this trend for AMPT and other
transport models. It is noteworthy that AMPT does not
exhibit the observed pattern of system-size independence.
UrQMD (ultrarelativistic quantum molecular dynamics)
[28] (not shown here) is similar to AMPT in exhibiting a
significant change in v
1
between Au þ Au and Cu þ Cu.
Further scaling behavior is seen by transforming the data
presented in Fig. 3 into the projectile frame (see Fig. 5),
where zero on the horizontal axis corresponds to the beam
rapidity, y
beam
, for each of the collision energies. Within
three units from y
beam
, most data points lie on a universal
curve for v
1
versus  y
beam
. This incident-energy scal-
ing of directed flow has previously been reported for Au þ
Au [11,18], and it is now evident that the limiting frag-
mentation hypothesis [29] holds even for much lighter
collision systems like Cu þ Cu. AMPT adheres less
closely to limiting fragmentation for Cu þCu. Note that
the quantity  y
beam
introduces some uncertainty due to
the use of  instead of rapidity; the latter requires particle
identification. The system-size independence at a given
fractional cross section and longitudinal scaling of scaled
multiplicity distributions, dN
ch
=d=ðN
part
=2Þ, have been
previously reported by the PHOBOS Collaboration [30].
In summary, we have presented measurements of
charged-particle directed flow as a function of p
t
, , and
centrality in Au þ Au and Cu þ Cu collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼
200 and 62.4 GeV. The observed trend of decreasing v
1
with increasing beam energy agrees with models. The lack
of system-size dependence in v
1
for Au þ Au and Cu þ
Cu is quite remarkable and is a feature not observed or
predicted by any existing model implementation. The pre-
sented  dependence of v
1
provides further support for
limiting fragmentation scaling by extending its applicabil-
ity to Cu þ Cu. The observed p
t
dependence of directed
flow motivates further theoretical investigations and ex-
perimental measurements with identified particles.
We thank the RHIC Operations Group and RCF at BNL,
and the NERSC Center at LBNL and the resources pro-
vided by the Open Science Grid consortium for their sup-
port. This work was supported in part by the Offices of NP
and HEP within the U.S. DOE Office of Science, the U.S.
NSF, the Sloan Foundation, the DFG Excellence Cluster
EXC153 of Germany, CNRS/IN2P3, RA, RPL, and EMN
of France, STFC and EPSRC of the United Kingdom,
FAPESP of Brazil, the Russian Ministry of Science and
beam
- yη
-4 -2 0
(%)
1
v
-8
-6
-4
-2
0
30% - 60%
Data AMPT
= 0
CM
y
200 GeV Au+Au
200 GeV Cu+Cu
62.4 GeV Au+Au
62.4 GeV Cu+Cu
FIG. 5 (color online). Charged particle v
1
versus   y
beam
,
for 30%–60% Au þ Au and Cu þ Cu at 200 and 62.4 GeV. The
plotted error bars are statistical, and the shaded bars show
systematic errors.
(%)
1
v
-0.6
-0.4
-0.2
0
| < 1.3η|
% Most Central
0 1020304050607080
(%)
1
v
-8
-6
-4
-2
0
200 GeV Au+Au
200 GeV Cu+Cu
62.4 GeV Au+Au
62.4 GeV Cu+Cu
| < 4η2.5 < |
FIG. 4 (color online). Charged particle v
1
versus centrality, for
Au þ Au and Cu þ Cu at 200 and 62.4 GeV. The upper (lower)
panels show results from the main TPC (FTPC). The plotted
error bars are statistical, and systematic errors (see Figs. 1 and 5)
are within 10%.
PRL 101, 252301 (2008)
PHYSICAL REVIEW LETTERS
week ending
19 DECEMBER 2008
252301-5

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "System-size independence ofdirected flowmeasured at the bnlrelativistic heavy-ioncollider" ?

In this paper, the authors present a survey of the state-of-the-art work in this area.