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\journal{Nuclear Physics A}

\begin{document}

\begin{frontmatter}

% Your Title - please insert
\title{Dielectron differential cross section in Au+Au collisions at different beam energies at STAR}


%% Single author (and collaboration) - please insert
\author{Bingchu Huang (for the STAR Collaboration)}
%\fntext[col1] {A list of members of the EMPIRE Collaboration and
%acknowledgements can be found at the end of this issue.}
\address{Brookhaven National Laboratory, Upton, NY, 11973, USA}

%% Multiple authors
%\author[auth2]{Marcus Junius Brutus}
%\address[auth1]{Somewhere, Rome}
%\address[auth2]{Somewhere else, Rome}


\begin{abstract}
    Dielectron invariant mass spectra have been measured at mid-rapidity by the STAR
    experiment at RHIC in Au+Au collisions at \sNN=19.6, 39,
    62.4, and 200 GeV. The spectra exhibit excess yields for $M_{ee}<1.0$ \gevcc,
    when compared to the expected contributions from known hadronic
    sources. The enhanced production rates can be consistently described by a
    broadened $\rho$ spectral function. In addition, the elliptic flow, $v_{2}$,
    has been measured for dielectron invariant mass $M_{ee}<1.1$ \gevcc~ in Au+Au
    collisions at \sNN=200 GeV.
\end{abstract}

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\section{Introduction}
A hot and dense medium can be created in heavy-ion collisions at
the Relativistic Heavy Ion Collider (RHIC). One of the important
physics goals at RHIC is to study the properties of this medium
using dileptons. Leptons originate from all stages of the
collision and, once produced, do not undergo strong interaction
with the medium. Hence, lepton pairs are excellent candidates to
probe the entire space-time evolution of the medium. The
dominant dilepton sources in the low mass range (LMR) at
$M_{ll}<1.1$ \gevcc~are vector mesons, including $\rho$,
$\omega$, $\phi$. The in-medium modifications of vector mesons
can be directly accessed by means of their dilepton decay
channels. The modifications of their spectral functions may
provide a possible link to chiral symmetry
restoration~\cite{Ralf}. As an additional observable, the
differential measurements of dilepton elliptic flow provide very
rich information on the fireball evolution and the dilepton
radiation sources. Elliptic flow is generated in the early stage
of heavy-ion collisions and develops in the expanding fireball
due to the initial spatial eccentricity of the nuclear overlap
region~\cite{ellipticflow}. Thus, the measured elliptic flow
could disentangle the components of dilepton sources.

In this paper, we present the measurements of dielectron
production in Au+Au collisions at beam energies from 19.6 to 200
GeV at STAR, taking advantage of the newly installed full barrel
Time-of-Flight detector (TOF)~\cite{TOF}. The centrality
dependence of dielectron production, as well as the mass
dependence of dielectron elliptic flow, $v_{2}$, in Au+Au
collisions at 200 GeV are also presented.

\section{Analysis}
The data were taken from the RHIC runs of 2010-2011. The
analysis is based on two sub-detectors of the STAR detector
system~\cite{STARdetector}, namely the Time Projection Chamber
(TPC)~\cite{TPC} and the Time-Of-Flight detector (TOF) each with
2$\pi$ azimuthal coverage at mid-rapidity. The TPC measures
track momentum and ionization energy loss ($dE/dx$) in the TPC
gas for the purpose of particle identification. The $dE/dx$ of
electrons overlaps with slow $\pi$, $K$, and protons at momenta
$p<1$ \gevc. The TOF provides track velocity information, and
enables us to separate the slow hadrons from electrons.
Combining TPC $dE/dx$ and TOF velocity information, we can
select clean electron candidates~\cite{eID}. An electron purity
of $>95\%$ is reached in Au+Au analyses.

The dielectron foreground is reconstructed through the
combination of $e^{+}$ and $e^{-}$ candidates within the same
events. The background is reconstructed using like-sign and
mixed-event techniques. In the like-sign technique, the same-charged electrons are combined into pairs within the same
events. The mixed-event technique picks up two electron
candidates from different events with similar vertex positions,
event plane angles, and charged-particle multiplicities. The
like-sign technique can reproduce correlated cross pair
background well in LMR, but suffers from limited statistics in
the higher mass region. The mixed-event technique, on the other
hand, allows for the generation of basically unlimited
statistics but can only reproduce the combinatorial background.
We subtract the like-sign background in the low mass region, and
the mixed-event background at higher invariant masses. The
mixed-event background subtraction range is chosen as
$M_{ee}>0.9$ \gevcc~for 39 and 62.4 GeV, and $M_{ee}>0.75$
\gevcc~for 200 GeV. At 19.6 GeV, we subtract like-sign
background in the full mass range. The acceptances of the
like-sign and unlike-sign pairs are slightly different due to
acceptance gaps in the detector system. The like-sign background
spectra are corrected for this acceptance difference and then
subtracted from the foreground spectra. The final dielectron
production is measured within the STAR acceptance ($p^{e}_{T}>0.2$
GeV/$c$, $|\eta_{e}|<1$ for 19.6 and 200 GeV, $|\eta_{e}|<0.9$
for 39 and 62.4 GeV, $|y_{ee}|<1$) and corrected for efficiency
losses.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=1.\textwidth]{Centrality_mass1_new.eps}
\end{center}
\caption{(Color online) Centrality dependence of dielectron
production in Au+Au collisions at \sNN = 200 GeV. The left panel
shows the mass spectra compared to hadronic cocktails, and the
right panel depicts the ratios of data to
cocktail~\cite{qmposterYi}. Systematic uncertainties are
represented by boxes.} \label{fig:auau200allcen}
\end{figure}

\section{Results}
The invariant mass spectra for various centralities in
collisions at \sNN=200 GeV are shown in
Fig.~\ref{fig:auau200allcen}. The spectra for centrality bins
10-40\% and 40-80\% complement the results already presented
in~\cite{qm11proceeding}. The hadronic cocktail consists of
Dalitz decays: $\pi^{0}, \eta, \eta^{'} \rightarrow \gamma
e^{+}e^{-}$, $\omega\rightarrow \pi^{0} e^{+}e^{-}$,
$\phi\rightarrow \eta e^{+}e^{-}$, direct dielectron decays:
$\omega, \rho^{0}, \phi, J/\psi \rightarrow e^{+}e^{-}$,
semi-leptonic decays of heavy flavor hadrons: $c\bar{c},
b\bar{b} \rightarrow e^{+}e^{-}X$, and Drell-Yan processes.
$b\bar{b} \rightarrow e^{+}e^{-}X$ and Drell-Yan processes are
not included in the analyses at 19.6, 39, and 62.4 GeV due to
their cross sections being negligible at these beam energies.
The $c\bar{c} \rightarrow e^{+}e^{-}X$ component is not included
in the 19.6 GeV cocktail spectra. The analyses at 39 and 62.4
GeV do not evaluate the contribution of $\eta^{'}$. The
$c\bar{c}$ components are simulation results in p+p collision
scaled by number of binary collisions in Au+Au.


\bfig \bmn[t]{0.45\textwidth}
\includegraphics[width=1.\textwidth]{di_electron_v2_auau200.eps}
\caption{Invariant mass dependence of elliptic flow $v_{2}$ of
dielectrons in Au+Au collisions at \sNN=200
GeV~\cite{qmposterXiangli}. Vertical error bars denote
statistical errors, and boxes are systematic uncertainties.}
\label{fig:auau200v2} \emn \hspace{0.05in}
\bmn[t]{0.55\textwidth} \centering
\includegraphics[width=1.\textwidth]{AllEnergiesData.eps}
\caption{(Color online) Dielectron production in Au+Au minimum
bias collisions (0-80\%) at \sNN=19.6, 39, 62.4, and 200 GeV
within STAR acceptance~\cite{qmposterBingchu,qmposterPatrick}.
The colored bands denote systematic uncertainties due to
uncertainties in the hadronic yields.}
\label{fig:auauallenergies} \emn \efig

Figure~\ref{fig:auau200v2} shows the invariant mass dependence
of dielectron $v_{2}$. Experimental data is based on the
integrated yields in the respective invariant mass bins. The
simulated $v_{2}$ is derived from azimuthal distributions of the
dielectron decayed mother particles ($\pi^{0}$, $\eta$,
$\omega$, and $\phi$). The mother particles' $v_{2}$ are taken
from previous measurements~\cite{v2input}. As a result, the
measured dielectron $v_{2}$ is consistent with our simulated
$v_{2}$ within the given uncertainties.

The inclusive dielectron mass spectra in Au+Au collisions from
19.6 to 200 GeV are shown in Fig.~\ref{fig:auauallenergies}. All
the cocktails do not include contributions due to $\rho$ meson
decays. The vacuum $\rho$ contribution clearly fails to describe
the excess in LMR~\cite{CERES}. The comparison of data and
cocktail suggests that the $\rho$ spectral function undergoes
in-medium modifications in Au+Au collisions at 19.6, 39, 62.4,
and 200 GeV.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=.85\textwidth]{InMedRhoPanel.eps}
\end{center}
\caption{Comparisons of dielectron mass spectra to in-medium
$\rho$ spectral functions at \sNN=19.6, 62.4, and 200
GeV~\cite{qmposterBingchu,qmposterPatrick,Ralf1}. The dashed
curve shows the sum of theoretical calculation and hadronic
cocktail. The bands are systematic uncertainties.}
\label{fig:theorycomp}
\end{figure}

Such an extensive measurement of dielectron production over a
wide range of beam energies allows for the systematic comparison
to theoretical model calculations. The scenario of a broadened
$\rho$ spectral function~\cite{Ralf} is currently favored in
order to describe the CERES~\cite{CERES} and especially the
dimuon results from NA60~\cite{NA60}. The underlying model
incorporates finite temperature effects into $\rho$ self-energy
corrections through resonant baryonic and mesonic interactions
as well as pion-cloud polarization. The resulting broadened
$\rho$ spectral function is integrated over a cylindrical
fireball expansion to obtain the pair production rates. Our
results in Au+Au collisions at 19.6, 62.4 and 200 GeV are
compared to this model, shown in Fig.~\ref{fig:theorycomp}. The
enhanced dielectron rates in the LMR can be consistently
described by the broadened $\rho$ spectral function scenario in
Au+Au collisions from 19.6 to 200 GeV. This is suggestive of a
partial chiral symmetry restoration possibly happening in heavy
ion collisions at these energies.

\section{Summary}
STAR has measured dielectron production in Au+Au collisions at
\sNN=19.6, 39, 62.4, and 200 GeV. The centrality dependence of
the LMR enhancement are measured at 200 GeV. Within systematic
and statistical uncertainties dielectron elliptic flow $v_{2}$
is consistent with the simulated flow caused by known hadronic
sources. The LMR enhancement in Au+Au collisions from SPS up to
top RHIC energies can be consistently described via the scenario
of a broadened $\rho$ spectral function.

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\end{thebibliography}
\end{document}
\bye
