Dear Jens Jorgen, Michael, Trine, and all...
I am attaching version 3.8 at the end of this messages. Also, the
kansas account has been updated.
For people wanting a stable version to edit for final comments, please wait
for version 3.9 (3.10?) that should be ready by midday tomorrow
(US east coast time). There are still some final questions about
consistencies
of some of the numbers that need to be resolved. In particular,
I couldn't locate the final (Hijing?) Ncoll numbers that we want to quote in
the flurry of email messages sent earlier today. I also need to double
check with
Hiro some of the quoted cross sections in the table.
JJ- I removed the statement " ...the largest number of particles
observed so far
in energetic nuclear collisions" since this would certainly be disputed by
any of the Phobos collaborators. Although Phobos does not quote a
comparable
total charged particle number in their paper, they do show a 200 GeV
pseudorapidity distribution for central events. I also trimmed in a few
other spots
to get the length back down to four pages.
Michael and JJ-- Some the newer suggestions for the figures will be
very difficult
to achieve unless we give up on only using ROOT macros for their production.
Hiro can probably do some of them (such as changing from closed to open
symbols),
but others, such as closing the gaps between the four pane figures, are
not going to
be as readily accomplished.
Regards, Steve
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%% This file is part of the APS files in the REVTeX 3.0 distribution.
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%% Copyright (c) 1992 The American Physical Society.
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%% THIS FILE: dndeta200-draft37.tex
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%% October 13-2001. 23.00 GMT+1
%% Based on first text by SS and JJG
%% REVISED:
%% Oct 14-2001 JJG. Update text
%% Oct 16-2001 JJG. Update text
%% Oct 17-2001 JJG. Include hard/soft fit results + update text
%% Oct 17-2001 JJG. Fill out Table + update text, author
%% list,figure 4.
%% Oct 18-2001 JJG. update references and include eta = 1.5
%% for fits.
%% Oct 19-2001 JJG. smaller updates and corrections after
%% input from CEJ and TST
%% Nov 12-2001 JJG. text adjusted to HIRO's new figures
%% Nov 15-2001 JJG. text shortened. Prepare for 5 figures.
%% Nov 16-2001 JJG. various text revisions
%% Nov 19-2001 JJG. text revision with various input from
%% others. New fig 5 not described yet.
%% Nov 20-2001 MM + SS changed to Revtex 4. SS update
%% numbers + some text.
%% JJG. update text. Go back to Npart figure 5.
%% Keep figure 2.
%% Nov 21-2001 JJG. incorporated many comments from CC, MM,
%% PS, CEJ, etc...
%% Nov 25-2001 SJS incorporated comments of FV and JN
%% Nov 27-2001 JJG small text revisions, add discussion on
width decrease and p+p
%% Nov 27-2001 SJS small text revisions
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\documentclass[twocolumn,showpacs,preprintnumbers,amsmath,amssymb,superscriptaddress,unsortedaddress]{revtex4}
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%%\documentclass[prb]{revtex4}% Physical Review B
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\newcommand{\bnl}{Brookhaven National Laboratory, Upton,New York
11973}
\newcommand{\ires}{Institut de Recherches Subatomiques and
Universit{\'e} Louis Pasteur,Strasbourg, France}
\newcommand{\kraknuc}{Institute of Nuclear Physics, Krakow, Poland}
\newcommand{\krakow}{Jagiellonian University, Krakow, Poland}
\newcommand{\baltimore}{Johns Hopkins University, Baltimore, Maryland
21218}
\newcommand{\newyork}{New York University, New York, New York 10003}
\newcommand{\nbi}{Niels Bohr Institute, University of Copenhagen,
Denmark}
\newcommand{\texas}{Texas A$\&$M University, College Station,Texas
77843}
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Bergen,Norway}
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\newcommand{\kansas}{University of Kansas, Lawrence, Kansas 66049}
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\begin{document}
\title{Pseudorapidity distributions of charged particles from Au+Au
collisions at the maximum RHIC energy.}
\ifRevTexAuthor
\author{I.~G.~Bearden}\affiliation{\nbi}
\author{D.~Beavis}\affiliation{\bnl}
\author{C.~Besliu}\affiliation{\bucharest}
\author{Y.~Blyakhman}\affiliation{\newyork}
\author{J.~Brzychczyk}\affiliation{\krakow}
\author{B.~Budick}\affiliation{\newyork}
\author{H.~B{\o}ggild}\affiliation{\nbi}
\author{C.~Chasman}\affiliation{\bnl}
\author{C.~H.~Christensen}\affiliation{\nbi}
\author{P.~Christiansen}\affiliation{\nbi}
\author{J.~Cibor}\affiliation{\kraknuc}
\author{R.~Debbe}\affiliation{\bnl}
\author{E. Enger}\affiliation{\oslo} %\and
\author{J.~J.~Gaardh{\o}je}\affiliation{\nbi}
\author{K.~Grotowski}\affiliation{\krakow}
\author{K.~Hagel}\affiliation{\texas}
\author{O.~Hansen}\affiliation{\nbi}
\author{A.~Holm}\affiliation{\nbi}
\author{A.~K.~Holme}\affiliation{\oslo}
\author{H.~Ito}\affiliation{\kansas}
\author{E.~Jakobsen}\affiliation{\nbi}
\author{A.~Jipa}\affiliation{\bucharest}
\author{J.~I.~J{\o}rdre}\affiliation{\bergen}
\author{F.~Jundt}\affiliation{\ires}
\author{C.~E.~J{\o}rgensen}\affiliation{\nbi}
\author{T.~Keutgen}\affiliation{\texas}
\author{E.~J.~Kim}\affiliation{\bnl}
\author{T.~Kozik}\affiliation{\krakow}
\author{T.~M.~Larsen}\affiliation{\oslo}
\author{J.~H.~Lee}\affiliation{\bnl}
\author{Y.~K.~Lee}\affiliation{\baltimore}
\author{G.~L{\o}vh{\o}iden}\affiliation{\oslo}
\author{Z.~Majka}\affiliation{\krakow}
\author{A.~Makeev}\affiliation{\texas}
\author{B.~McBreen}\affiliation{\bnl}
\author{M.~Mikelsen}\affiliation{\oslo}
\author{M.~Murray}\affiliation{\texas}
\author{J.~Natowitz}\affiliation{\texas}
\author{B.~S.~Nielsen}\affiliation{\nbi}
\author{J.~Norris}\affiliation{\kansas}
\author{K.~Olchanski}\affiliation{\bnl}
\author{J.~Olness}\affiliation{\bnl}
\author{D.~Ouerdane}\affiliation{\nbi}
\author{R.~P\l aneta}\affiliation{\krakow}
\author{F.~Rami}\affiliation{\ires}
\author{D.~R{\"o}hrich}\affiliation{\bergen}
\author{B.~H.~Samset}\affiliation{\oslo}
\author{D.~Sandberg}\affiliation{\nbi}
\author{S.~J.~Sanders}\affiliation{\kansas}
\author{R.~A.~Sheetz}\affiliation{\bnl}
\author{Z.~Sosin}\affiliation{\krakow}
\author{P.~Staszel}\affiliation{\nbi}
\author{T.~F.~Thorsteinsen\textsuperscript{\dag}}\affiliation{\bergen,\textrm{\textsuperscript{\dag}\textit{Deceased}}}
\author{T.~S.~Tveter}\affiliation{\oslo}
\author{F.~Videb{\ae}k}\affiliation{\bnl}
\author{R.~Wada}\affiliation{\texas}
\author{A.~Wieloch}\affiliation{\krakow}
\author{I.~S.~Zgura}\affiliation{\bucharest}
\collaboration{BRAHMS Collaboration}
\noaffiliation
\else
\author{
I.~G.~Bearden\nbi, % \and
D.~Beavis\bnl, % \and
C.~Besliu\bucharest, % \and
Y.~Blyakhman\newyork, % \and
B.~Budick\newyork, % \and
H.~B{\o}ggild\nbi, % \and
C.~Chasman\bnl, % \and
C.~H.~Christensen\nbi, % \and
P.~Christiansen\nbi, % \and
J.~Cibor\kraknuc, % \and
R.~Debbe\bnl, % \and
E. Enger\oslo, %\and
J.~J.~Gaardh{\o}je\nbi, % \and
K.~Hagel\texas, % \and
O.~Hansen\nbi, % \and
A.~Holm\nbi, % \and
A.~K.~Holme\oslo, % \and
H.~Ito\kansas, % \and
E.~Jakobsen\nbi, % \and
A.~Jipa\bucharest, % \and
J.~I.~J{\o}rdre\bergen, % \and
F.~Jundt\ires, % \and
C.~E.~J{\o}rgensen\nbi, % \and
R.~Karabowicz\krakow, % \and
T.~Keutgen\texas, % \and
E.~J.~Kim\bnl, % \and
T.~Kozik\krakow, % \and
T.~M.~Larsen\oslo, % \and
J.~H.~Lee\bnl, % \and
Y.~K.~Lee\baltimore, % \and
G.~L{\o}vh{\o}iden\oslo, % \and
Z.~Majka\krakow, % \and
A.~Makeev\texas, % \and
B.~McBreen\bnl, % \and
M.~Mikelsen\oslo, % \and
M.~Murray\texas, % \and
J.~Natowitz\texas, % \and
B.~S.~Nielsen\nbi, % \and
J.~Norris\kansas, % \and
K.~Olchanski\bnl, % \and
J.~Olness\bnl, % \and
D.~Ouerdane\nbi, % \and
R.~P\l aneta\krakow, % \and
F.~Rami\ires, % \and
D.~R{\"o}hrich\bergen, % \and
B.~H.~Samset\oslo, % \and
D.~Sandberg\nbi, % \and
S.~J.~Sanders\kansas, % \and
R.~A.~Sheetz\bnl, % \and
P.~Staszel\nbi, % \and
T.~F.~Thorsteinsen\bergen$^+$,% \and
T.~S.~Tveter\oslo, % \and
F.~Videb{\ae}k\bnl, % \and
R.~Wada\texas, % \and
A.~Wieloch\krakow, and
I.~S.~Zgura\bucharest\\% \and
(BRAHMS Collaboration )\\[1ex]
\bnl~Brookhaven National Laboratory, Upton,New York 11973,
\ires~Institut de Recherches Subatomiques and Universit{\'e} Louis
Pasteur, Strasbourg, France,
\kraknuc~Institute of Nuclear Physics, Krakow, Poland,
\krakow~Jagiellonian University, Krakow, Poland,
\baltimore~Johns Hopkins University, Baltimore, Maryland 21218,
\newyork~New York University, New York, New York 10003,
\nbi~Niels Bohr Institute, University of Copenhagen, Denmark,
\texas~Texas A$\&$M University, College Station,Texas 77843,
\bergen~University of Bergen, Department of Physics, Bergen,Norway,
\bucharest~University of Bucharest,Romania,
\kansas~University of Kansas, Lawrence, Kansas 66049,
\oslo~University of Oslo, Department of Physics, Oslo,Norway,
$^+ Deceased$}
\noaffiliation
\fi
\date{\Version}
\begin{abstract}
We present charged particle densities as a function of
pseudorapidity and collision centrality for the
$^{197}$Au+$^{197}$Au reaction at $\sqrt{s_{NN}}$=200~GeV, the
maximum energy for RHIC. The charged particle multiplicity for the
5\% most central events is 632 $\pm$1 (stat) $\pm$55 (syst), i.e. a
14\% increase relative to $\sqrt{s_{NN}}$=130~GeV collisions. The
total multiplicity of charged particles for $-4.7\le \eta \le 4.7$
is 4630 $\pm$370, an increase by 20\% over the lower energy. The
data show an increase from 2.9 to 3.7 in the production of charged
particles per pair of participant nucleons from peripheral (40-50\%)
to central (0-5\%) collisions around midrapidity. These results
constrain current models based on high density QCD gluon saturation
and on the superposition of particle production from soft hadronic
and hard partonic collisions.
\end{abstract}
\pacs{25.75.Dw} % Revtex 4
\maketitle
A central question in the study of collisions between heavy nuclei at
the maximum energy of the RHIC facility,
$\sqrt{s_{NN}}$=200~GeV, is the role of hard scatterings between
partons and the interactions of these partons in a high density
environment. Indeed, it has been conjectured that new phenomena
related to non-perturbative QCD may come into play at this energy.
Among these, a saturation of the number of parton (mainly gluon)
collisions in central nucleus-nucleus collisions has been predicted to
limit the production of charged
particles~\cite{partonsat83,Eskola00,Kharzeev_and_Levin}. Recently,
indications for a reduction in the number of hadrons at high
transverse momentum for $\sqrt{s_{NN}}$=130~GeV collisions have been
presented that may hint at suppression of hadronic jets at high matter
densities~\cite{Phenix-jets,Star-jets}.
The present Letter addresses these issues with the first comprehensive
investigation of multiplicity distributions of emitted charged
particles in relativistic heavy ion collisions between $^{197}$Au
nuclei at the maximum RHIC energy. In particular, we have measured
pseudorapidity distributions of charged particles in the range $-4.7
\le \eta \le 4.7$ for such collisions at
$\sqrt{s_{\small{NN}}}$=200~GeV as a function of collision
centrality. The production of charged particles in these highly
energetic nuclear collisions can be due to hadronic as well as
partonic collision processes and thus depends on the presence of gluon
shadowing effects and, in general, on the relative importance of soft
and hard scattering processes. We find in this work that the
production of charged particles at midrapidity increases by 14$\pm$1\%
for the most central collisions relative to $\sqrt{s_{NN}}$=130~GeV
collisions~\cite{back00,Star-mult130,adcox01,bearden01a}, in agreement
with the results of the PHOBOS experiment~\cite{Phobos-mult200-1}. For
more peripheral collisions we find a slightly smaller increase, while
we observe a saturation of the baryon excitations at larger rapidities.
The BRAHMS experiment consists of two magnetic spectrometers for
measuring spectra of identified charged particles over a wide range of
rapidity and transverse momentum and a number of global
detectors for determining the location of the collision vertex, the
time of the collision, the collision centrality and the charged
particle densities~\cite{bearden01b}.
The present data were obtained using three of the
global detector systems at BRAHMS: the Multiplicity Array (MA), the
Beam-Beam Counter arrays (BBC), and the Zero-degree Calorimeters
(ZDC). An analysis of
charged particle densities for Au+Au reactions at
$\sqrt{s_{NN}}$=130~GeV that is very similar in method to that
presented here is described fully in ref.~\cite{bearden01a}.
The MA determines charged particle densities around midrapidity and
consist of a hexagonal-sided double barrel arrangment with a modestly
segmented Si strip detector array (SiMA) surrounded by an outer
plastic scintillator tile array (TMA).
Each of the 25 Si detectors (4~cm x 6~cm x 300~$\mu$m), placed 5.3~cm from
the beam axis, is subdivided into seven active strips. The TMA
was comprised of 35 plastic scintillator tiles (12~cm x 12~cm x 0.5~cm)
located 13.9 cm from the beam axis. Both the SiMA and TMA
cover a pseudorapidity range of $-2.2\le\eta\le2.2$ for collisions
occurring at the nominal interaction vertex. Using an extended range
of collision vertices, the effective coverage of the array is
$-3.0\le\eta\le3.0$ . Particle densities are deduced from the observed
energy loss in the SiMA elements using GEANT simulations~\cite{Geant}
to relate energy loss to the number of particles hitting
a given detector element~\cite{bearden01a}.
The BBC Arrays consist of two sets of Cherenkov UV transmitting
plastic radiators coupled to photomultiplier tubes. They are
positioned around the beam pipe on either side of the nominal
interaction point at a distance of 2.20~m. The time resolution of the
BBC elements permits the determination of the interaction point with an
accuracy of $\approx$ 0.9~cm. Charged particle multiplicities in the
pseudorapidity range $2.1\le |\eta| \le 4.7$ are deduced from the
number of particles hitting each tube, as found by dividing the
measured ADC signal by that corresponding to a single
particle hitting the detector.
The ZDC detectors are located $\pm$18m from the nominal
interaction vertex and measure neutrons that are emitted at small
angles with respect to the beam direction~\cite{adler00}. Clean
selection of minimum-biased events required a coincidence between the two
ZDCs and a minimum of 4 ``hits'' in the TMA and is estimated to
include 95\% of the nuclear reaction cross section of 7.1~b.
The ZDCs also
locate the interaction point with an accuracy of $\approx$~3.6~cm.
Reaction centrality is determined by selecting different regions
in the total multiplicity distribution in either the MA or BBC arrays.
In analyzing particle densities in dN/d$\eta$, the centrality dependence
of the MA and BBC distributions are based on the total multiplicity
measurements of the corresponding array. In the pseudorapidity range of
3.0$\le\eta\le$4.2, where it was possible to analyze the BBC data
using both centrality selections, the two analyses give
identical results to within 2\%. In general, statistical error on
the measurements are less than 1\%, while we estimate that the
systematic errors are 8\% and 10\% for the SiMA and BBC arrays,
respectively.
\begin{figure}
\epsfig{file=fig1.eps,width=8.5cm}
\caption{
Distributions of $dN_{ch}/d\eta$ for centrality ranges of, top to
bottom, 0-5\%, 5-10\%, 10-20\%, 20-30\%, 30-40\%, and 40-50\%.
The SiMA and BBC results are indicated by the circles and
triangles, respectively. Statistical error are shown for all
points where larger than the symbol size. Systematic errors are
8\% and 10\% for the SiMA and BBC points respectively.}
\label{dndeta}
\end{figure}
In Fig.~\ref{dndeta} we show the measured pseudorapidity distributions
for charged particles for centrality cuts of 0-5\%, 5-10\%, 10-20\%,
20-30\%, 30-40\% and 40-50\%. The
$dN/d\eta$ values for these cuts at $\eta$=0, 1.5, 3.0, 4.5 are listed
in Table~\ref{tb:dndeta}, together with the number of participating
baryons estimated from the HIJING model. For the most central
collisions (0-5\%) the multiplicities reach $dN/d\eta$=632 $\pm 55$ at
midrapidity. This corresponds to $3.7 \pm 0.3$ charged particles per
participating baryon
pair and indicates an increase in the multiplicities of about
14\% relative to $^{197}$Au+$^{197}$Au reactions at
$\sqrt{s_{NN}}$=130~GeV
~\cite{bearden01a,back00,Phobos-mult200-1,adcox01,Star-mult130}. By
integrating the 0-5\% multiplicity distribution we deduce that $N=4630
\pm 370$ charged particles are emitted in the considered rapidity
range. This value is 20$\pm$1\% higher than for
$\sqrt{s_{NN}}$=130~GeV reactions~\cite{bearden01a}. More detailed
inspection shows that the distributions at the two energies are quite
similar in shape. Indeed, the FWHM of the most central distributions
is $\Delta \eta = 7.5 \pm 0.5$ for $\sqrt{s_{NN}}$=200~GeV, as
compared to $\Delta \eta = 7.2 \pm 0.8$ for $\sqrt{s_{NN}}$=130~GeV
collisions. For the most peripheral collisions analyzed here (40-50\%)
the multiplicities at $\eta=0$ reach $dN/d\eta=110\pm 10$ while the
corresponding value scaled to the number of participating pairs is
2.9$\pm 0.3$. For comparison, the similar number for proton-proton
collisions at this energy is 2.5, also a 14\% increase over the lower
energy.
\begin{table} [ht]
\caption{\label{tb:dndeta} Charged particle densities in
$dN_{ch}/d\eta$ as a function of
centrality and pseudorapidity. Total uncertainties, dominated by
the systematics, are indicated. The average
number of participants $\langle N_{part}\rangle$ and collisions
$\langle N_{coll}\rangle$ is given for each centrality
class. $N_{ch}$ is the
integral charged particle multiplicity within %the pseudorapidity range
$-4.7 \le \eta \le 4.7$.}
%% Centrality & $N_{coll}$& $N_{part}$& $\eta = 0$ & $\eta =1.5$
%% $\eta = 3.0$ &
%% $\eta = 4.5$ & $N_{ch}$ \\
%% \begin{tabular}{|c|c|c|c|c|c|c|c|}
\begin{tabular}{cccccccc}
\hline
Cent- &
$\eta = 0$ &
$\eta =1.5$ &
$\eta = 3.0$ &
$\eta = 4.5$ &
$N_{ch}$ &
$N_{coll}$&
$N_{part}$
\\
rality & & & & & & & \\
0-5 & 632$\pm$55 & 628$\pm$57 & 453$\pm$41
& 181 $\pm$21 & 4630$\pm$370& 1086& 345 \\
5-10 & 498$\pm$44 & 509$\pm$46 & 379$\pm$37
& 156$\pm$17 & 3810$\pm$300& 866 & 293 \\
10-20 & 373$\pm$33 & 385$\pm$35 & 296$\pm$29
& 124$\pm$13 & 2920$\pm$230 & 561 & 228 \\
20-30 & 257$\pm$23 & 265$\pm$24 & 207$\pm$21
& 89 $\pm$10 & 2020$\pm$160 & 389 & 164 \\
30-40 & 170$\pm$15 & 178$\pm$16 & 140$\pm$15
& 62 $\pm$7 & 1380$\pm$110 & 232 & 114 \\
40-50 & 110$\pm$10 & 115$\pm$10 & 90$\pm$9
& 42 $\pm$5 & 890$\pm$70 & 114 & 75 \\
\hline
\end{tabular}
\end{table}
Figure~\ref{dndeta_fragment} shows, on the other hand, that the charged
particle multiplicities in an interval of approximately 0.5-1.5 units
below the beam rapidity are independent of the collision centrality
and energy, from CERN-SPS energy ($\sqrt{s_{NN}}$=17~GeV)
\cite{deines00} to the present RHIC energy. This is consistent with a
limiting fragmentation picture in which the excitations of the
fragment baryons saturate already at moderate collision energies
independently of the system size~\cite{bearden01a}. In contrast, the
increased projectile kinetic energy is utilized for particle
production in the region around midrapidity, as evidenced by the
observed increase of the multiplicities per participant pair around
the center of mass rapidity.
\begin{figure}
\epsfig{file=fig2.eps,width=8.5cm}
\caption{
Charged particle densities normalized to the number of participant
pairs (see table) for the present 0-5\% central (open circles) and
40-50\% central (open squares) Au+Au results at
$\sqrt{s_{NN}}$=200~GeV, the BRAHMS Au+Au
results~\cite{bearden01a} at $\sqrt{s_{NN}}$=130~GeV (closed
circles) and the 9.4\% central Pb+Pb data at
$\sqrt{s_{NN}}$=17~GeV(closed triangles) of ref~\cite{deines00}.
Data at different beam energies are plotted as a function of the
pseudorapidity shifted by the relevant beam rapidity. Representative
total
uncertainties are shown for a few Au+Au points. }
\label{dndeta_fragment}
\end{figure}
Figure~\ref{dndeta_models} presents the $dN/d\eta$ distributions
obtained by mirroring and averaging the negative and positive halves
of the measured distributions to further decrease errors. We also
compare the distributions with model calculations. The solid
lines are calculations using the model of Kharzeev and
Levin~\cite{Kharzeev_and_Levin} which is based on a classical QCD
calculation using parameters fixed to the $\sqrt{s_{NN}}$=130~GeV
data. This approach is able to reproduce the magnitude and shape of
the observed multiplicity distributions quite well. Also shown in
Fig.~\ref{dndeta_models} (dashed lines) are the results of
calculations with the AMPT model~\cite{zhang01,lin01a,lin01b}, which
is a cascade model based on HIJING~\cite{wang91} but including final
state rescattering of produced particles. The AMPT model is also able
to account for the general trend of the measured distributions,
particularly for the most central collisions. We also plot the similar
distributions~\cite{Alner86}from $p\bar p$ collisions at
($\sqrt{s}$=200~GeV)
scaled by the number of participant pairs.
For central collisions the Au+Au data
show a strong enhancement over the entire range relative to $p\bar p$,
decreasing to about 10\% for the most peripheral collisions.
The observed multiplicity excess of
$48\pm 9\%$ above the corresponding value for $p\bar p$ collisions clearly
demonstrates significant medium effects.
We note that
the measured distributions show a small increase in width with
decreasing centrality (from $\sigma_{RMS}=2.33\pm 0.02$ for 0-5\%
to $2.4 \pm 0.02$ for 40-50\%), to be compared to $RMS= 2.38 \pm 0.05$
for the p+p data.
\begin{figure}
\epsfig{file=fig3.eps,width=8.5cm}
\caption{
(a-d) Measured $dN_{ch}/d\eta$ distributions for centrality
ranges of 0-5\%, 10-20\%, 20-30\% and 40-50\%. Theoretical
predictions by Kharzeev and Levin (solid line) and by the
AMPT model (dashed line) are also shown. Result from p+p collisions
at this energy~\cite{Alner86} are shown with stars (a,d).}
\label{dndeta_models}
\end{figure}
The ratio of the pseudorapidity densities measured at
$\sqrt{s_{NN}}$=130~GeV and $\sqrt{s_{NN}}$=200~GeV for different
centralities are shown in Fig.~\ref{dndeta_ratios}. The figure shows a
systematic increase in multiplicity as a function of
energy for a central plateau in the range $\eta= 0-2.5 $. The increase is
14\% for the most central collisions and 12\% for the most peripheral.
The upturn of the ratios at the forward rapidities is due to the
widening of the multiplicity distribution at the higher energy
consistent with the increase in beam rapidity ($\Delta y = 0.45$).
The overlaid curves show the corresponding ratios resulting from the
two model calculations.
\begin{figure}
\epsfig{file=fig4.eps,width=8.5cm}
\caption{
Ratio of particle densities at $\sqrt{s_{NN}}$=200~GeV and 130~GeV
compared to the models. Points are only shown with statistical
errors as systematic errors tend to cancel out }
\label{dndeta_ratios}
\end{figure}
Finally in Fig.~\ref{Npart} we plot the dependence of the multiplicity
of charged particles per pair of participant baryons as a function of
the number of participants, $N_{part}$, for three narrow pseudrapidity
regions ($\Delta \eta \approx 0.2$) around $\eta$ =0, 3.0 and
4.5. While the figure shows that particle production per participant
pair is remarkably constant at the forward rapidities characteristic
of the fragmentation region and close to unity, this is not the case
for the central rapidities. Indeed, we find a significant increase of
particle production per pair of participant nucleons for the more
central collisions at $\eta=0$. Plotted using the $N_{part}$ values
listed in table 1, the curves for these rapidities rise as a function
of collision centrality. This has previously been attributed to the
onset of hard scatterings which are dependent on the number of
binary nucleon collisions
$N_{coll}$ rather than $N_{part}$.
Using for $N_{coll}$ the values from HIJING
~\cite{wang91} we fit the observed dependencies to a
functional $dN/d\eta=\alpha\cdot N_{part}+\beta \cdot N_{coll}$. For
rapidities $\eta=$ 0 and 3.0 we obtain: $\alpha=0.98 \pm 0.10$ and
$1.05 \pm 0.08$ and $\beta=0.25 \pm 0.04, 0.09 \pm 0.03$,
respectively. For comparison we find $\alpha=0.99 \pm 0.09, 0.99 \pm
0.07, $ and $\beta=0.18 \pm 0.04, 0.02 \pm 0.04 $ at
$\sqrt{s_{NN}}$=130~GeV. At $\eta=0.0$ we find that the hard
scattering component to the charged particle production increases from
36$\pm$7\% at the lower energy to about 43$\pm$7\% at
$\sqrt{s_{NN}}$=200~GeV. It should be stressed, however, that this
interpretation is highly model dependent. Using the $N_{part}$ values
from ~\cite{Kharzeev_and_Nardi} which are smaller than the
corresponding HIJING numbers for the more peripheral collisions the
curves become practically flat ($\beta \approx 0$) and thus inconstent
with a mixing of soft and hard scatterings.
\begin{figure}
\epsfig{file=fig5.eps,width=8.5cm}
\caption{
Distributions of $dN_{ch}/d\eta$ per participant pair as a
function of the number of participants (see table)
%% for $\eta$= 0, 3.0 and 4.5. The curves show predictions by the
%% Kharzeev and Levin model (solid line) and the AMPT
%% model (dashed
for $\eta$= 0,1.5, 3.0 and 4.5. The curves show predictions by
Kharzeev and Levin (solid line) and the AMPT model (dashed
line). The star denotes the p+p result at $\eta=0$.}
\label{Npart}
\end{figure}
In conclusion, we find that the charged particle production scales
smoothly from $\sqrt{s_{NN}}$=130~GeV to $\sqrt{s_{NN}}$=200~GeV in a
wide region around midrapidity. The data are well reproduced by
calculations based on high density QCD and by the AMPT/HIJING
microscopic parton model. A phenomenological two component analysis in
terms of a superposition of particle production due to soft/hard
scatterings also accounts well for the data but does not show
significant differences between the two energies. We find good
consistency with the gluon saturation model of Kharzeev and Levin, but
stress that within errors of models and data alike, the data can be
equally well reproduced by other models not requiring saturation
effects in the description of parton collisions. While the current
work establishes the baseline for particle production at the maximum
energy available for nucleus-nucleus collisions for several years to
come, the full understanding of these energetic collisions must await
more detailed analyses of hadronic and leptonic observables over a
wide region of phase space and rapidity.
We thank the RHIC collider team for their efforts.
This work was supported by the Division of Nuclear Physics
of the U.S. Department of Energy,
%% under contracts DE-AC02-98-CH10886, DE-FG03-93-ER40773,
%% DE-FG03-96-ER40981, and DE-FG02-99-ER41121,
the Danish Natural Science Research Council, the Research Council of
Norway, the Polish State Committee for Scientific Research (KBN)
%%Grant
%%no. 5 P03B 015 21, the Korea Research Foundation,
and the Romanian
Ministry of Research.
%%(5003/1999,6077/2000).
We are grateful to Drs D. Kharzeev %%, BNL, and
E. Levin, %%Tel Aviv,
Zi-Wei Lin, and %%, Texas A\&M
H. Heiselberg for stimulating discussions and
%%for supplying us withthe
model calculations. %% shown and discussed in this article.
\ifUseBibTeX
\bibliography{dndeta}
\else
\begin{thebibliography}{99}
%%Parton saturation.
\bibitem{partonsat83} L. V. Gribov, E. M. Levin and M. G. Ryskin,
Phys.Rep. {\bf 100} (1983) 1.
%% ``Centrality dependence of multiplicities in ultrarelativistic
nuclear collisions''
\bibitem{Eskola00} K. J. Eskola, K. Kajantie and K. Tuominen, Phys. Lett. %%
{\bf B497}, 39 (2001). %; hep-ph/0009246.
\bibitem{Kharzeev_and_Levin} D. Kharzeev and E. Levin. nucl- th/0108006
and private communication. %
%%jet quenching
\bibitem{Phenix-jets} K. Adcox {\it et al.}, subm. to Phys. Rev. Lett.
(2001),
nucl-ex/0109003.
\bibitem{Star-jets}
J. C. Dunlop {\it et al.}, %STAR Collaboration,
Nucl. Phys. {\bf A698}
515c (2002), and
B. Lasiuk, Workshop on High $p_T$ phenomenen at RHIC, BNL (2002),
unpublished.
%, Nov. 2001
% http://skipper.physics.sunysb.edu/highpt/lasiuk.ppt
%%
%%
%%Phobos dN/deta paper 2000 (56 and 130)
\bibitem{back00} B. B. Back {\it et al.}, Phys. Rev. Lett. {\bf 85},
3100 (2000).
%%STAR paper on mult at 130GeV
\bibitem{Star-mult130} C. Adler {\it et al.}, Phys. Rev Lett. {\bf 87},
112303 (2001)
%%
%%PHENIX dN/deta paper 130GeV
\bibitem{adcox01} K. Adcox {\it et al.}, Phys. Rev. Lett. {\bf 86}, 3500
(2001).
%%BRAHMS mult 130 reference PLB
\bibitem{bearden01a} I. G. Bearden {\it et al.},
Phys. Lett. B in press; nucl-ex/0108016.
% \bibitem{bearden01a} I. G. Bearden
{\it et al.}, accepted for pub in
% Phys. Lett. B.; nucl-ex/0108016.
%%Phobos 200 Gev mult at midrapidity 2001. subm to PRL
\bibitem{Phobos-mult200-1} B. B. Back {\it et al.}, submitted. to Phys.
Rev. Lett.(2001), nucl.exp/0108009.
%%
%%BRAHMS NIM reference
\bibitem{bearden01b} I. G. Bearden {\it et al.}, submitted to Nucl.
Inst. Meth A.
%%http://cyclotron.tamu.edu/hagel/BrahmsNimPaper.doc
%%
%%GEANT reference
\bibitem{Geant} GEANT 3.2.1, CERN program library.
%%ZDC reference
\bibitem{adler00} C. Adler, {\it et al.}, %A. Denisov, E. Garcia, M.
Murray, H. Stroebele and S. White,
Nucl. Inst. Meth., {\bf A470} 488 (2001). % nucl-ex/0008005.
%%
%%
%%SPS multiplicity
\bibitem{deines00} P. Deines-Jones {\it et al.} Phys. Rev. C {\bf 62},
014903(2000). %hep-ex/9912008.
%%
\bibitem{zhang01} Bin Zhang, C. M. Ko, Bao-An Li and Zi-wei Lin,
Phys. Rev. C {\bf 61} 067901 (2001).
\bibitem{lin01a} Zi-wei Lin, Subrata Pal, C. M. Ko, Bao-An Li and Bin
Zhang, %
Phys. Rev. C {\bf 64} 011902R (2001).
\bibitem{lin01b} Zi-wei Lin, Subrata Pal, C.M. Ko, Bao-An Li and Bin Zhang,
Nucl. Phys. {\bf A698} 375c-378c (2002), nucl-th/0105044; and Zi-wei
Lin, private communication.
%% p+p at 200 GeV
\bibitem{Alner86} G. J. Alner {\it et al.}, Zeit. Phys. {\bf 33}, 1 (1986).
%%Hijing Paper
\bibitem{wang91} X. N. Wang and M. Gyulasy, Phys. Rev. D {\bf 44}, 3501
(1991).
%%
%%AMPT model
%%
\bibitem{Kharzeev_and_Nardi} D. Kharzeev and M. Nardi.
Phys. Lett. {\bf B507}, 121 (2001). %, nucl-th/0012025.
\end{thebibliography}
\fi
\end{document}
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