NewCramer_053005.tex
%% ****** Start of file template.aps ****** %
%%
%%
%%   This file is part of the APS files in the REVTeX 4 distribution.
%%   Version 4.0 of REVTeX, August 2001
%%
%%
%%   Copyright (c) 2001 The American Physical Society.
%%
%%   See the REVTeX 4 README file for restrictions and more information.
%%
%
% This is a template for producing manuscripts for use with REVTEX 4.0
% Copy this file to another name and then work on that file.
% That way, you always have this original template file to use.
%
% Group addresses by affiliation; use superscriptaddress for long
% author lists, or if there are many overlapping affiliations.
% For Phys. Rev. appearance, change preprint to twocolumn.
% Choose pra, prb, prc, prd, pre, prl, prstab, or rmp for journal
%  Add 'draft' option to mark overfull boxes with black boxes
%  Add 'showpacs' option to make PACS codes appear
%  Add 'showkeys' option to make keywords appear
%\documentclass[aps,prl,preprint,groupedaddress]{revtex4}
\documentclass[aps,prl,twocolumn,superscriptaddress,showpacs]{revtex4}
%\documentclass[aps,prl,preprint,superscriptaddress,showpacs]{revtex4}
%\documentclass[aps,prl,twocolumn,groupedaddress]{revtex4}
%\topmargin = 1.2cm
\usepackage{graphicx}
% You should use BibTeX and apsrev.bst for references
% Choosing a journal automatically selects the correct APS
% BibTeX style file (bst file), so only uncomment the line
% below if necessary.
\bibliographystyle{apsrev}

\begin{document}

% Use the \preprint command to place your local institutional report
% number in the upper righthand corner of the title page in preprint mode.
% Multiple \preprint commands are allowed.
% Use the 'preprintnumbers' class option to override journal defaults
% to display numbers if necessary
%\preprint{}

%Title of paper
{\bf Comment on ``Quantum Opacity, the RHIC HBT Puzzle, and the Chiral
Phase Transition''}
\vspace{1mm}
% repeat the \author .. \affiliation  etc. as needed
% \email, \thanks, \homepage, \altaffiliation all apply to the current
% author. Explanatory text should go in the []'s, actual e-mail
% address or url should go in the {}'s for \email and \homepage.
% Please use the appropriate macro foreach each type of information

% \affiliation command applies to all authors since the last
% \affiliation command. The \affiliation command should follow the
% other information
% \affiliation can be followed by \email, \homepage, \thanks as well.
%\author{\input{Phobos_authors_current}}
%\email[]{Your e-mail address}
%\homepage[]{Your web page}
%\thanks{}
%\altaffiliation{}
%\affiliation{}

%Collaboration name if desired (requires use of superscriptaddress
%option in \documentclass). \noaffiliation is required (may also be
%used with the \author command).
%\collaboration can be followed by \email, \homepage, \thanks as well.
%\collaboration{}
%\noaffiliation

%\date{\today}


%\begin{abstract}
In a recent Letter, Cramer, Miller, Wu and Yoon \cite{cramer} (CMWY) presented 
a model based on a relativistic quantum mechanical treatment of opacity
and refractive effects on momentum correlations between pairs of identical
particles and particle transverse momentum ($p_T$) spectra. The values
of the ten model parameters were obtained from a simultaneous fit to 
the HBT radii and pion $p_T$ spectra measured for central Au+Au collisions at
$\sqrt{s_{_{NN}}} =$ 200~GeV. CMWY conclude from the fitted values of their
model parameters that the data are consistent with the emission of pions 
from a 
dense medium in which chiral symmetry has been restored. In addition,
the authors provide predictions of the momentum dependence
of the HBT radii and pion $p_T$ spectra in the region below
200 MeV/c. However, the authors chose not to compare their model
predictions with the published
experimental data for pion yields at very low $p_T$ obtained using the 
PHOBOS detector at RHIC. The purpose of this
Comment is to make the comparison of the CMWY model predictions 
with the PHOBOS data.

The PHOBOS experiment has a unique capability of measuring charged particles
down to very low $p_T$. The results \cite{phostop} reach $p_T$ as
low as 30 MeV/c for charged pions, and cover the region where the CMWY
model predicted notable structure in the pion $p_T$ spectrum. The 
published model predictions are shown as a dashed curve in Fig.~\ref{fig:fig1}.
However, in the 
original paper \cite{cramer} there was an error in the representation
of the STAR pion momentum spectra \cite{star}, consequently leading to the
extraction of incorrect values of the 
model parameters. As a result, the dashed curve, shown in Fig.~\ref{fig:fig1},
disagrees with the STAR data at higher $p_T$.
This mistake was pointed out to CMWY by the authors of this comment and, 
as a result,
a new set of model predictions for the spectral behavior
at very low transverse momenta was generated \cite{cramer_private}. 
The corrected model predictions, shown by a dotted  curve in
Fig.~\ref{fig:fig1}, differ significantly from those published in 
\cite{cramer}. More
recently, an alternative fit was performed in which the pion momentum
distribution used in the fit was modified ``to remove from the spectrum
those pions that did not participate in the Bose-Einstein symmetrization''
\cite{cramer_private}. The results from this version of the fit are shown 
as the solid curve in Fig.~\ref{fig:fig1}.
It is clear that the predicted yield at low $p_T$ is very sensitive to the 
values of the parameters and the details of the model.

The low-transverse momentum charged pion yields, measured by PHOBOS 
\cite{phostop}, are overlayed on the model curves in Fig.~\ref{fig:fig1}.
Since our analysis of
particle production in this momentum region does not allow for 
separation of positive and negative pions, the invariant
$p_T$ yields measured for charged pions are divided
by 2. It should be noted that our results correspond to the
15\% most central Au+Au collisions. The centrality of the predictions
is not clearly specified, but we infer from the data shown that they are
for the 5\% most central collisions. The number of pions per event is expected
to be higher for more central data. Thus, imposing a more stringent
centrality selection leads to yields higher than
those measured by PHOBOS. One can roughly estimate the size of this increase 
from the $p_T$ spectra measured by PHENIX at higher $p_T$ for centrality bins
of 0-5\% and 0-15\% \cite{phenix} or from the centrality dependence of the 
$p_T$ integrated charged particle $dN/d\eta$ yields measured by PHOBOS 
\cite{phobosmult}. Both
estimates give scaling factors in a range from 15 to 20\%. 
Interpolation of the STAR
published data at higher $p_T$ \cite{star} for centrality bins of 0-10\% 
and 0-20\% suggests a similar
increase.
Multiplying our measured points
by factors of 1.15 to 1.20 gives the thick crossed curve shown in 
Fig.~\ref{fig:fig1}.

It is clear that it would be best to test models, such as those 
discussed here, in
a range of centralities. This requires more  central data, which will be
provided by PHOBOS, as well as model calculations for less central 
collisions.
%One can see that the most recent model
%predictions(solid curve) exceed the data by more than 30\% even after 
%accounting for differences in centrality. 
We conclude that the low $p_T$ pion yields uniquely measured
by PHOBOS provide valuable information for evaluating models of 
the dense medium created in heavy ion collisions
at RHIC energies.


\begin{figure}
\includegraphics[width=7.2cm]{Fig3_lin_15p_v1}
\caption{\label{fig:fig1} $p_T$ spectra of charged pions. Points 
show PHOBOS published data for ($\pi^{+}+\pi^{-}$)/2  yields measured in the 
15\%
most central Au+Au collisions at $\sqrt{s_{_{NN}}} =$ 200~GeV. 
Bars denote statistical 
errors and the boxes correspond to  90\% C.L. systematic uncertainties. 
The crossed curve shows the extent to which the yield is expected to increase
(15-20\%) for a more central event selection in the data. 
Other curves show results of the CMWY
model calculations with the dashed curve representing the published results
\cite {cramer}. The dotted and solid curves  represent
more recent model predictions \cite{cramer_private}. See text 
for more details.}
\end{figure}


PHOBOS Collaboration: \\  
B.B.Back$^1$,
M.D.Baker$^2$,
M.Ballintijn$^4$,
D.S.Barton$^2$,
R.R.Betts$^6$,
A.A.Bickley$^7$,
R.Bindel$^7$,
A.Budzanowski$^3$,
W.Busza$^4$,
A.Carroll$^2$,
M.P.Decowski$^4$,
E.Garc\'{\i}a$^6$,
N.George$^{1,2}$,
K.Gulbrandsen$^4$,
S.Gushue$^2$,
C.Halliwell$^6$,
J.Hamblen$^8$,
G.A.Heintzelman$^2$,
C.Henderson$^4$,
D.J.Hofman$^6$,
R.S.Hollis$^6$,
R.Ho\l y\'{n}ski$^3$,
B.Holzman$^2$,
A.Iordanova$^6$,
E.Johnson$^8$,
J.L.Kane$^4$,
J.Katzy$^{4,6}$,
N.Khan$^8$,
W.Kucewicz$^6$,
P.Kulinich$^4$,
C.M.Kuo$^5$,
W.T.Lin$^5$,
S.Manly$^8$,
D.McLeod$^6$,
A.C.Mignerey$^7$,
R.Nouicer$^6$,
A.Olszewski$^3$,
R.Pak$^2$,
I.C.Park$^8$,
H.Pernegger$^4$,
C.Reed$^4$,
L.P.Remsberg$^2$,
M.Reuter$^6$,
C.Roland$^4$,
G.Roland$^4$,
L.Rosenberg$^4$,
J.Sagerer$^6$,
P.Sarin$^4$,
P.Sawicki$^3$,
W.Skulski$^8$,
S.G.Steadman$^4$,
P.Steinberg$^2$,
G.S.F.Stephans$^4$,
A.Sukhanov$^2$,
J.-L.Tang$^5$,
A.Trzupek$^3$,
C.Vale$^4$,
G.J.van~Nieuwenhuizen$^4$,
R.Verdier$^4$,
F.L.H.Wolfs$^8$,
B.Wosiek$^3$,
K.Wo\'{z}niak$^3$,
A.H.Wuosmaa$^1$,
B.Wys\l ouch$^4$\\
\noindent
{\footnotesize
$^1$~Argonne National Laboratory, Argonne, IL 60439\\
$^2$~Brookhaven National Laboratory, Upton, NY 11973\\
$^3$~Institute of Nuclear Physics PAN, Krak\'{o}w, Poland\\
$^4$~Massachusetts Institute of Technology, Cambridge, MA 02139\\
$^5$~National Central University, Chung-Li, Taiwan\\
$^6$~University of Illinois at Chicago, Chicago, IL 60607\\
$^7$~University of Maryland, College Park, MD 20742\\
$^8$~University of Rochester, Rochester, NY 14627\\}

%
% If you have acknowledgments, this puts in the proper section head.
%\begin{acknowledgments}
% put your acknowledgments here.
%This work was partially supported by U.S. DOE grants DE-AC02-98CH10886,
%DE-FG02-93ER40802, DE-FC02-94ER40818, DE-FG02-94ER40865, DE-FG02-99ER41099, 
%and
%W-31-109-ENG-38 as well as NSF grants 9603486, 9722606 and 0072204.  
%The Polish
%group was partially supported by KBN grant 2-P03B-10323.  The NCU group was
%partially supported by NSC of Taiwan under contract NSC 89-2112-M-008-024.
%\end{acknowledgments}

% Create the reference section using BibTeX:
%\bibliography{stopping_v110503.bib}
\begin{thebibliography}{20}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Cramer and Miller}(2000)}]{cramer}
\bibinfo{author}{\bibfnamefont{J.~G.}~\bibnamefont{Cramer}},
\bibinfo{author}{\bibfnamefont{G.~A.}~\bibnamefont{Miller}},
\bibinfo{author}{\bibfnamefont{J.~M.~S.}~\bibnamefont{Wu}},
 \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Yoon}},
  \bibinfo{journal}{Phys.\ Rev.\ Lett.} \textbf{\bibinfo{volume}{94}},
  \bibinfo{pages}{102302} (\bibinfo{year}{2005}).


\bibitem[{\citenamefont{Back et~al.}(2004)}]{phostop}
\bibinfo{author}{\bibfnamefont{B.~B.} \bibnamefont{Back}} \bibnamefont{et~al.},
  \bibinfo{journal}{Phys.\ Rev.} \textbf{\bibinfo{volume}{C70}},
  \bibinfo{pages}{051901(R)} (\bibinfo{year}{2004}).

\bibitem[{\citenamefont{Adams et~al.}(2004)}]{star}
\bibinfo{author}{\bibfnamefont{J.} \bibnamefont{Adams}} \bibnamefont{et~al.},
  \bibinfo{journal}{Phys.\ Rev.\ Lett.} \textbf{\bibinfo{volume}{92}},
  \bibinfo{pages}{112301} (\bibinfo{year}{2004}).


\bibitem[{\citenamefont{Cramer et~al.}(2004)}]{cramer_private}
\bibinfo{author}{\bibfnamefont{J.~G.} \bibnamefont{Cramer}} \bibnamefont{and}
\bibinfo{author}{\bibfnamefont{G.~A.}~\bibnamefont{Miller}},
\bibinfo{comment}{\bibfnamefont{private communication}}.

\bibitem[{\citenamefont{Adler et~al.}(2003)}]{phenix}
\bibinfo{author}{\bibfnamefont{S.~S.} \bibnamefont{Adler}} 
 \bibnamefont{et~al.}, \bibinfo{journal}{Phys.\ Rev.}
  \textbf{\bibinfo{volume}{C69}}, \bibinfo{pages}{034909}
  (\bibinfo{year}{2004}).   

\bibitem[{\citenamefont{Back et~al.}(2003)}]{phobosmult}
\bibinfo{author}{\bibfnamefont{B.~B.} \bibnamefont{Back}} 
 \bibnamefont{et~al.}, \bibinfo{journal}{Phys.\ Rev.}
  \textbf{\bibinfo{volume}{C70}}, \bibinfo{pages}{021902(R)}
  (\bibinfo{year}{2004}).   

\end{thebibliography}

\end{document}
%
% ****** End of file template.aps ******


nucl-ex0506008.extracted_bib
\begin{thebibliography}{20}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Cramer and Miller}(2000)}]{cramer}
\bibinfo{author}{\bibfnamefont{J.~G.}~\bibnamefont{Cramer}},
\bibinfo{author}{\bibfnamefont{G.~A.}~\bibnamefont{Miller}},
\bibinfo{author}{\bibfnamefont{J.~M.~S.}~\bibnamefont{Wu}},
 \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Yoon}},
  \bibinfo{journal}{Phys.\ Rev.\ Lett.} \textbf{\bibinfo{volume}{94}},
  \bibinfo{pages}{102302} (\bibinfo{year}{2005}).


\bibitem[{\citenamefont{Back et~al.}(2004)}]{phostop}
\bibinfo{author}{\bibfnamefont{B.~B.} \bibnamefont{Back}} \bibnamefont{et~al.},
  \bibinfo{journal}{Phys.\ Rev.} \textbf{\bibinfo{volume}{C70}},
  \bibinfo{pages}{051901(R)} (\bibinfo{year}{2004}).

\bibitem[{\citenamefont{Adams et~al.}(2004)}]{star}
\bibinfo{author}{\bibfnamefont{J.} \bibnamefont{Adams}} \bibnamefont{et~al.},
  \bibinfo{journal}{Phys.\ Rev.\ Lett.} \textbf{\bibinfo{volume}{92}},
  \bibinfo{pages}{112301} (\bibinfo{year}{2004}).


\bibitem[{\citenamefont{Cramer et~al.}(2004)}]{cramer_private}
\bibinfo{author}{\bibfnamefont{J.~G.} \bibnamefont{Cramer}} \bibnamefont{and}
\bibinfo{author}{\bibfnamefont{G.~A.}~\bibnamefont{Miller}},
\bibinfo{comment}{\bibfnamefont{private communication}}.

\bibitem[{\citenamefont{Adler et~al.}(2003)}]{phenix}
\bibinfo{author}{\bibfnamefont{S.~S.} \bibnamefont{Adler}} 
 \bibnamefont{et~al.}, \bibinfo{journal}{Phys.\ Rev.}
  \textbf{\bibinfo{volume}{C69}}, \bibinfo{pages}{034909}
  (\bibinfo{year}{2004}).   

\bibitem[{\citenamefont{Back et~al.}(2003)}]{phobosmult}
\bibinfo{author}{\bibfnamefont{B.~B.} \bibnamefont{Back}} 
 \bibnamefont{et~al.}, \bibinfo{journal}{Phys.\ Rev.}
  \textbf{\bibinfo{volume}{C70}}, \bibinfo{pages}{021902(R)}
  (\bibinfo{year}{2004}).   

\end{thebibliography}