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<caption ALIGN="TOP">
<h3>
STAR Software for Analysis of Anisotropic Flow</h3>
<i>R.J. Snellings and A.M. Poskanzer</i>
<br><i>Nuclear Science Division, Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA</i></caption>

<tr VALIGN=TOP>
<td VALIGN=TOP WIDTH="50%"><!C- First column starts here>In the <a href="http://root.cern.ch/">ROOT</a>
for <a href="http://www.star.bnl.gov/STAR/html/star_computing.html">STAR</a>
environment, c++ programs have been written to analyze STAR data for anisotropic
(directed and elliptic) flow. This document is a road map to the available
documentation. The software consists of 7.3k lines of code in 33 files
in three directories. The three "maker" modules are called from the STAR
software chain and described in the overview <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/ebe_l/pub/flow/HTML_Presentation/">presentation</a>.
The presentation is also available as a <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/ebe_l/pub/flow/Presentation.ps">postscript</a>
file together with an overview <a href="http://duvall.star.bnl.gov/STARAFS/comp/pkg/dev/StRoot/StFlowMaker/doc/Diagram.ps">diagram</a>
using the Unified Modeling Language. The chain of three makers is run off-line
by the macro <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/macros/analysis/doFlowEvents.C">doFlowEvents.C</a>
. In this macro, parameters can be set for the event cuts, track cuts,
flags, event plane selections, and PID windows. Also in this macro <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowSelection.cxx">StFlowSelection</a>
can be instantiated and passed to the Tag, Analysis, and Cumulant makers.
This object can be set to select track PID.
<p><b><a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/">StFlowMaker</a></b>
is the interface with the STAR DST. It creates <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowEvent.cxx">StFlowEvent</a>
from <a href="http://www.star.bnl.gov/STARAFS/comp/root/special_docs.html">StEvent</a>
or <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowPicoEvent.cxx">StFlowPicoEvent</a>
after <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowCutEvent.cxx">event</a>
and <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowCutTrack.cxx">track</a>
cuts. StFlowEvent consists of a <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowTrackCollection.h">track
collection</a> of <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowTrack.h">tracks</a>.
It also contains methods for calculating event-by-event quantities, like
the event plane vector, from the data members of the tracks. The event
plane is made isotropic in the laboratory with weights which are the inverse
of the acceptance as determined from the azimuthal distribution of particles.
This is all described in the <a href="http://duvall.star.bnl.gov/STARAFS/comp/pkg/dev/StRoot/StFlowMaker/README">README</a>
document. One can also view the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowMaker.h">header</a>,
the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowMaker.cxx">implementation,</a>
and the <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/comp_l/root/html/StFlowMaker.html">interface</a>.
A persistent sub-set of StFlowEvent can be written out to disk as <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowPicoEvent.cxx">StFlowPicoEvent</a>.
Constants which are needed in more than one file are kept in <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowMaker/StFlowConstants.h">StFlowConstants</a>.
<p><b><a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowTagMaker/">StFlowTagMaker</a></b>
fills the <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/comp_l/root/html/St_FlowTag.html">tag</a>
database from StFlowEvent. This is described in the <a href="http://duvall.star.bnl.gov/STARAFS/comp/pkg/dev/StRoot/StFlowTagMaker/README">README</a>
document. One can also view the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowTagMaker/StFlowTagMaker.h">header</a>,
the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowTagMaker/StFlowTagMaker.cxx">implementation,</a>
and the <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/comp_l/root/html/StFlowTagMaker.html">interface</a>.
<p><b><a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/">StFlowAnalysisMaker</a></b>
reads the event-by-event quantities from the tag database, if it exists,
or if it does not, from StFlowEvent. It reads the particle quantities from
StFlowEvent and does the flow analysis<sup>1</sup> by correlating the particles
with the event plane after removing autocorrelations. The main results
are double-differential flow values contained in 2D histograms of the flow
variables, v_n, as a function of pseudorapidity and transverse momenta.
For identified particles rapidity is used instead of pseudorapidity. A
second analysis is done in terms of the normalized vector q which is equal
to the length of the flow vector Q divided by the square-root of the sum
of the squares of the weights. This integral measure of flow is good for
studying the fluctuations in flow. This is all described in the <a href="http://duvall.star.bnl.gov/STARAFS/comp/pkg/dev/StRoot/StFlowAnalysisMaker/README">README</a>
document. One can also view the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/StFlowAnalysisMaker.h">header</a>,
the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/StFlowAnalysisMaker.cxx">implementation,</a>
and the <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/comp_l/root/html/StFlowAnalysisMaker.html">interface</a>.
The macros <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/plot.C">plot.C</a>
and <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/plotCen.C">plotCen.C</a>
are used to plot the resulting histograms. The macro <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/minBias.C">minBias.C</a>
combines the histograms from different centralities to make a minimum bias
histogram file.
<p><b><a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/StFlowCumulantMaker.cxx">StFlowCumulantMaker</a></b>
which is in the StFlowAnalysisMaker directory, can perform a multiparticle
analysis using the cumulant method.<sup>7</sup> One can also view the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/StFlowCumulantMaker.h">header</a>,
the <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/StFlowCumulantMaker.cxx">implementation,</a>
and the <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/comp_l/root/html/StFlowCumulantMaker.html">interface</a>.
The macro <a href="http://duvall.star.bnl.gov/lxr/source/StRoot/StFlowAnalysisMaker/plotCumulant.C">plotCumulant.C</a>
is used to plot the resulting histograms.
<p>Simulated events which have been run through GEANT have been analyzed
and <a href="http://www.star.bnl.gov/star/starlib/doc/www/html/ebe_l/pub/flow/index.html">results</a>
produced. There is also a STAR Note<sup>2</sup> which contains predictions
for STAR, a paper<sup>3</sup> on the expected behavior of the directed
flow,&nbsp; and a paper<sup>4</sup> on how to interpret the physics results.
Now there are also first results for charged particles<sup>5 </sup>and
identified particles.<sup>6</sup>
<p><!C- End of first column></td>

<td VALIGN=TOP WIDTH="50%"><!C- Begin second column>
<br><i>Acknowledgments</i>
<br>We thank Glenn Cooper for considerable help with c++ and ROOT. Markus
Oldenburg contributed the FTPC code and Aihong Tang the cumulant analysis.&nbsp;
<p><!C- References and footnotes here><i>Footnotes and References</i>
<br><font size=-1>1. A.M. Poskanzer and S.A. Voloshin, "Methods for Analyzing
Anisotropic Flow in Relativistic Nuclear Collisions", <a href="http://pubster.aip.org/AIPcgipath/doc/getabs-PRVCAN/disk3/journals/journal_cgi/getabs?KEY=PRVCAN&cvips=PRVCAN000058000003001671000001&gifs=yes">Phys.
Rev. C <b>58</b>, 1671 (1998)</a>.</font>
<p><font size=-1>2. R.J.M. Snellings, A.M. Poskanzer, and S.A. Voloshin,
"Anisotropic Flow at STAR", STAR Note <a href="http://www.star.bnl.gov/STAR/sno/sno.html">SN0388(</a>1999).</font>
<p><font size=-1>3. R.J.M. Snellings, H. Sorge, S.A. Voloshin, F.Q. Wang,
and N. Xu, "Novel Rapidity Dependence of Directed Flow in High Energy Heavy
Ion Collisions", Phys. Rev. Letters <b>84</b>, 2803 (2000). <a href="http://arXiv.org/abs/nucl-ex/9908001">nucl-ex/9908001</a>.</font>
<p><font size=-1>4. S.A. Voloshin and A.M. Poskanzer, "The Physics of the
Centrality Dependence of Elliptic Flow", Phys. Letters <b>B474</b>, 27
(2000). <a href="http://xxx.lanl.gov/abs/nucl-th/9906075">nucl-th/9906075</a>.</font>
<p><font size=-1>5. K.H. Ackermann <i>et al.</i>, "Elliptic Flow in Au+Au
Collisions at sq_root(s)=130 GeV", Phys. Rev. Letters <b>86</b>, 402 (2001).
<a href="http://xxx.lanl.gov/abs/nucl-ex/0009011">nucl-ex/0009011</a>.</font>
<p><font size=-1>6. C. Adler <i>et al.</i>, "Identified Particle Elliptic
Flow in Au+Au Collisions at sq_root(s)=130 GeV", Phys. Rev. Letters <b>87</b>,
182301 (2001). <a href="http://xxx.lanl.gov/abs/nucl-ex/0107003">nucl-ex/0107003</a>.</font>
<p><font size=-1>7. N. Borghini, P.M. Dinh, and J.Y. Ollitrault, "Flow
Analysis from Cumulants: a Practical Guide". <a href="http://xxx.lanl.gov/abs/nucl-ex/0110016">nucl-ex/0110016.</a></font></td>
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