Energy dependence of acceptance-corrected dielectron excess mass spectrum at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}} = 19.6$ and 200 GeV

The acceptance-corrected dielectron excess mass spectra, where the known hadronic sources have been subtracted from the inclusive dielectron mass spectra, are reported for the first time at mid-rapidity $|y_{ee}|<1$ in minimum-bias Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 and 200 GeV. The excess mass spectra are consistently described by a model calculation with a broadened $\rho$ spectral function for $M_{ee}<1.1$ GeV/$c^{2}$. The integrated dielectron excess yield at $\sqrt{s_{NN}}$ = 19.6 GeV for $0.4<M_{ee}<0.75$ GeV/$c^2$, normalized to the charged particle multiplicity at mid-rapidity, has a value similar to that in In+In collisions at $\sqrt{s_{NN}}$ = 17.3 GeV. For $\sqrt{s_{NN}}$ = 200 GeV, the normalized excess yield in central collisions is higher than that at $\sqrt{s_{NN}}$ = 17.3 GeV and increases from peripheral to central collisions. These measurements indicate that the lifetime of the hot, dense medium created in central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV is longer than those in peripheral collisions and at lower energies.

The acceptance-corrected dielectron excess mass spectra, where the known hadronic sources have been subtracted from the inclusive dielectron mass spectra, are reported for the first time at midrapidity |yee| < 1 in minimum-bias Au+Au collisions at √ sNN = 19.6 and 200 GeV. The excess mass spectra are consistently described by a model calculation with a broadened ρ spectral function for Mee < 1.1 GeV/c 2 . The integrated dielectron excess yield at √ sNN = 19.6 GeV for 0.4 < Mee < 0.75 GeV/c 2 , normalized to the charged particle multiplicity at mid-rapidity, has a value similar to that in In+In collisions at

I. INTRODUCTION
Dileptons are crucial probes for studying the properties of the strongly interacting, hot and dense matter which is created in ultrarelativistic heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) [1,2]. They are produced during the whole evolution of the created matter, and are not subject to strong interactions with the medium. Dielectron pairs are sensitive probes of the medium properties throughout the spacetime evolution of the medium [3,4] because they are produced through a variety of mechanisms and in several different kinematic regimes.
In the low invariant mass region, M ll < 1.1 GeV/c 2 (LMR), the dilepton production is dominated by inmedium decay of vector mesons (ρ, ω and φ) in the hadronic gas phase. In-medium modifications to the mass and width of the vector mesons are considered a link to chiral symmetry restoration [3,4]. In the vacuum, chiral symmetry is spontaneously breaking, which results in mass differences between chiral partners [e.g. ρ and a 1 (1260)]. In the hot, dense medium, chiral symmetry is expected to restore and the mass distributions of ρ and a 1 (1260) are expected to change and degenerate. Since it is extremely challenging to measure a spectral function for the a 1 (1260) meson, one cannot directly observe the disappearance of the mass splitting between the ρ and a 1 (1260) experimentally. Instead, efforts are devoted to studying the modification of vector meson spectral function. Two schematic scenarios are used to describe the in-medium ρ spectrum function: a broadened and a dropping-mass ρ. The broadened ρ scenario incorporates finite temperature effects into selfenergy corrections through medium interactions and ππ annihilations [5]. The dropping mass scenario uses the quark mean field from a high temperature/density regime wherein constituent quarks are the relevant degrees of freedom, and then extrapolates down to a low temperature/density regime wherein hadrons are appropriate degrees of freedom [6].
The CERES experiment at the CERN-SPS reported an excess dielectron yield with respect to the known hadronic sources in the LMR in Pb+Au collisions at √ s N N = 17.2 GeV, which indicates that the vector mesons are modified in medium [7]. More recently, NA60 published a precise measurement of the dimuon invariant mass spectra in In+In collisions at √ s N N = 17.3 GeV [8]. The results show a significant excess in the LMR above the hadronic sources. The excess is consistent with a broadened ρ spectral function [5], but not with a ρ dropping-mass scenario [6], where both models have been evaluated for the same fireball evolution. It is further found that the coupling to the baryons in the medium plays a dominant role in the broadening of the ρ spectral function [7,8].
At RHIC, a significant enhancement in the dielectron continuum, compared with the known hadronic sources, has been observed in the LMR by both the PHENIX and STAR collaborations in Au+Au collisions at √ s N N = 200 GeV [9,10]. Results from the STAR collaboration show that the excess dielectron yield in the mass region 0.3-0.76 GeV/c 2 follows an N 1.54±0.18 part dependence, where N part is the number of participant nucleons in a collision [10]. However, the PHENIX Collaboration reported significant higher excess dielectron yields in central collisions [9]. Theoretical calculations [11][12][13][14], which describe the SPS dilepton data, fail to consistently describe the low-mass enhancement at low transverse momentum (p T ) observed by PHENIX in both 0-10% and 10-20% central Au+Au collisions [9]. The same calculations, however, correctly describe the STAR measurement of the lowp T and low-mass enhancement from peripheral to central Au+Au collisions [10]. While the discrepancy between STAR and PHENIX in central Au+Au collisions at √ s N N = 200 GeV is still under investigation, it is important to have dilepton measurements at RHIC at lower beam energies with the same large acceptance as for the 200 GeV data. Since the total baryon density does not change significantly from √ s N N = 17.3 GeV to √ s N N = 200 GeV [15], it is essential to confirm that the broadened ρ spectral function, which describes the results at 17.3 GeV and the 200 GeV STAR data, is consistent with the 19.6 GeV results.
In the intermediate mass region, 1.1 < M ll < 3.0 GeV/c 2 (IMR), dilepton production is expected to be directly related to thermal radiation of the partonic phase, which is considered to be the prime signature of deconfinement [11,12]. An enhanced yield in this region was first observed by HELIOS/3 [16] and NA38/NA50 [17]. More recently, the NA60 collaboration reported an enhancement in the IMR which cannot be connected to decays of D mesons, but may be the result of thermal radiation [8]. However, it is experimentally challenging to extract the signal in the presence of significant background sources from open heavy-flavor semi-leptonic decays, such as cc → l + l − X or bb → l + l − X.
In this letter, we report the first dielectron measurements at mid-rapidity in minimum-bias Au+Au collisions at √ s N N = 19.6 GeV with the STAR detector [18]. Furthermore, we present the first acceptance-corrected dielectron excess mass spectra in Au+Au collisions at √ s N N = 19.6 and 200 GeV which are compared with measurements from NA60 and theoretical model calculations. The invariant excess dielectron spectra at different centralities and energies allow for a first systematic study of the lifetime of the hot, dense medium using electromagnetic probes at RHIC. It was pointed out that the excess dielectron yield at low mass is proportional to the total lifetime of the hot, dense medium at √ s N N = 6-200 GeV [19].

II. EXPERIMENT AND DATA ANALYSIS
In this analysis, 33 million minimum-bias (MB) Au+Au (0-80%) events at √ s N N = 19.6 GeV, recorded by the STAR experiment in the year 2011, were used. The MB trigger was defined as a coincidence of the two Beam Beam Counters [20]. Charged tracks were reconstructed by the Time Projection Chamber (TPC) [21], which has full azimuthal coverage over the pseudorapidity range |η| < 1. The absolute distance between collision vertices and the TPC center along the beam direction was required to be less than 70 cm. The transverse momentum resolution is measured to be ∆p T /p T = 0.01 × The Time-Of-Flight (TOF) [22] detector, which covers the pseudorapidity range |η| < 0.9, provides the arrival time of charged tracks from the collision vertex. Slow hadrons can be rejected by a velocity cut |1/β − 1/β exp | < 0.025 in the range of 0.2 < p T < 3 GeV/c, where β is the measured velocity and β exp is the expected velocity calculated using the track length and momentum with the assumption of the electron mass. After the velocity cut, electron identification is achieved by cutting on the normalized ionization energy loss (nσ e = log( dE dx /I e )/R e ) measured by the TPC, where dE/dx is the energy loss, I e is the expected dE/dx for an electron and R e is the dE/dx resolution of an electron, which is better than 8% [23]. The nσ e cut is momentum dependent and results in a high electron purity of > 93% and an efficiency of > 65% on average [10,24].
The electron and positron candidates are paired by opposite and same sign charges, called unlike-sign and likesign pairs, respectively. The like-sign pairs are used to statistically reproduce the combinatorial and correlated pair backgrounds. The combinatorial background comes from two random tracks without correlation. The correlated background is the result of two electrons, each of which comes from a different but correlated process of a particle decay or a jet fragmentation. For example, consider a π 0 → γe + e − Dalitz decay where the gamma may convert on some material to form an additional e + e − pair. The e ± from the π 0 paired with a e ∓ from the γ can produce a correlated background pair. This correlated background can be reproduced by like-sign pairs.
The unlike-sign and like-sign pairs have different acceptances due to dead areas of the detector and the different bending curvatures of positively and negatively charged particles in the magnetic field. A mixed-event technique [9] is applied to estimate the acceptance differences between the unlike-sign and like-sign distributions. Figure 1 (a) shows the ratio between mixed-event unlikesign pairs and mixed-event like-sign pairs as a function of dielectron mass.
We subtract the like-sign background (corrected for the acceptance difference using the mixed event technique mentioned above) from the unlike-sign distributions to obtain the raw dielectron signals. The mixedevent background is not used for background subtraction, since the correlated background contribution is difficult to address with limited statistics at M ee > 1.5 GeV/c 2 for √ s N N =19.6 GeV. Figure 1 (b) shows the invariant mass distributions of unlike-sign pairs, like-sign pairs and background-subtracted signals. The signal to back- ground ratio is shown in Fig. 1 (c). Dielectron pairs from photon conversions in the detector materials are suppressed by selecting tracks with a distance of closest approach to the collision vertex that is less than 1 cm, and a minimum opening angle cut between the two electron candidates [9,10]. The raw dielectron signal is corrected for the electron reconstruction efficiency. The single electron reconstruction efficiency includes TPC tracking, electron identification and TOF matching efficiencies. The TPC tracking efficiency is determined by embedding Monte Carlo (MC) tracks into real raw data events, processing the track reconstruction with a GEANT model of the STAR detector   GeV. The data to cocktail ratio is shown in the bottom panel.
Theoretical calculations [11,32] of a broadened ρ spectral function are shown up to 1.5 GeV/c 2 for comparison. Systematic uncertainties for the data points are shown as green boxes, and the grey band represents the uncertainties for the cocktail simulation. reproduced from real data. Detailed procedures to obtain the TPC and TOF efficiencies are explained in Ref. [24]. The energy loss and bremsstrahlung radiation effects for electrons are reproduced by the GEANT simulation. The single electron efficiency is convoluted into the pair efficiency with the decay kinematics in the simulation. The hadronic sources of dielectron pairs include: Dalitz decays π 0 → γe + e − , η → γe + e − and η ′ → γe + e − ; vector meson decays: ω → π 0 e + e − , ω → e + e − , ρ 0 → e + e − , φ → ηe + e − , φ → e + e − and J/ψ → e + e − ; heavy-flavor hadron semi-leptonic decays: cc → e + e − X; Drell-Yan. The ρ meson contribution is not evaluated in the simulation, but included in the model calculation (as described in Sec. III). The bb → e + e − X process is not included as it has negligible contribution to the cocktail in Au+Au collisions at √ s N N = 19.6 GeV. The input hadron spectra to the cocktail are derived from a Tsallis Blast Wave (TBW) function fit [26,27] to the NA49 p T spectra of pions, kaons and protons in Pb+Pb at √ s N N = 17.3 GeV [28]. Other meson p T spectra are predicted by the TBW function using the same freeze-out parameters from p T fit of pions, kaons and protons. The extra uncertainty caused by the input p T spectra is found to be less than 10% and has been propagated to the final cocktail uncertainty. For J/ψ, the p T shape is determined by an independent TBW function fit to the J/ψ p T spectra measured by NA50 [29].
The π 0 contribution is obtained by matching the dielectron mass distribution from simulated π 0 → γe + e − decays to the efficiency-corrected dielectron mass spectrum for M ee < 0.1 GeV/c 2 . We also match the J/ψ → e + e − distribution from simulation to the measured dielectron production in the corresponding mass region. The meson yields of other mesons are derived by the meson-to-pion ratios [7] and the pion yields. Table I lists the integrated yields used in the simulation at midrapidity for Au+Au collisions at √ s N N = 19.6 GeV. The branching ratios of mesons to dielectrons and their uncertainties are from Ref. [30].
The e + e − mass distribution from open heavy-flavor sources is generated using PYTHIA 6.416 [31]. Previous charm cross section measurements from the SPS, FNAL, STAR and PHENIX experiments [33] are well described by the upper limit of a Fixed-Order Next-to-Leading Logarithm (FONLL) calculation [34]. Therefore we obtain the charm cross section in p + p at √ s = 19.6 GeV by scaling the FONLL upper limit to the previous measurements using the minimum χ 2 method. This cross section is used to normalize the dielectron yield from the PYTHIA simulation, which is additionally scaled by the number of binary collisions for Au+Au at √ s N N = 19.6 GeV to be compared with the data. For the efficiency-corrected dielectron invariant mass distribution, the systematic errors are dominated by uncertainties on the TPC tracking efficiency (14% in the dielectron yields), the TOF matching efficiency (10% in the dielectron yields), hadron contamination (0-20%), and electron identification (2%). The total systematic uncertainty on the pair reconstruction efficiency is estimated to be 18%. For the cocktail simulation, the systematic uncertainties come from the uncertainties of particle yields, decay branching ratios and form factors. Table II lists all the contributions to the systematic uncertainties on the dielectron mass spectrum and cocktail simulation within the STAR acceptance at √ s N N = 19.6 GeV.
After efficiency correction, the dielectron excess mass spectrum is corrected for the detector acceptance. The acceptance correction is estimated by a Monte Carlo simulation with inputs of virtual photon yield spectra, phase space distributions and decay kinematics. The method is similar to the approach used by NA60 [35], in which one assumes that the excess yields are from medium emission. The acceptance is calculated by the yield ratio of reconstructed dielectrons in the STAR detector to the input dielectrons. Figure 2 shows the two-dimensional acceptance of the virtual photons with a Gaussian-like rapidity distribution in Au+Au at √ s N N = 19.6 GeV at STAR. The acceptance correction factor at √ s N N = 200 GeV differs from that at √ s N N = 19.6 GeV by 5% due to the input p T spectra of virtual photons.
For the dielectron excess mass spectrum, additional systematic uncertainties come from the subtraction of the cocktail contribution and the acceptance correction. The latter contains uncertainties from the rapidity distribution and input dielectron sources. A uniform rapidity distribution is compared with the Gaussian-like case, and the resulting uncertainty is 2% in the LMR. The uncertainty from the input p T spectrum is at the same level as the rapidity distribution uncertainty.
We also obtain the acceptance of the excess dielectrons from model calculations [32]. The difference between the simulation and theoretical calculation is about 20% for M ee < 0.4 GeV/c 2 and less than 10% for M ee > 0.4 GeV/c 2 . It is included in the excess yield uncertainties.

III. RESULTS AND DISCUSSION
The dielectron invariant mass distribution after efficiency correction is shown in the upper panel of Fig. 3 for Au+Au collisions at √ s N N = 19.6 GeV. It is compared with a hadronic cocktail simulation, which consists of all the dielectron hadronic sources except the ρ 0 . An enhancement of the dielectron yield is observed in the mass region M ee < 1 GeV/c 2 . A model calculation with a broadened ρ spectral function [12] is added to the hadronic cocktail and compared with the data, as shown in the bottom panel of Fig. 3. The dielectron yields in the model calculation were filtered by the STAR acceptance (p e T > 0.2 GeV/c and |η e | < 1). The model calculation involves a realistic space-time evolution, and includes contributions from quark-gluon-plasma (QGP), 4-pion annihilation and in-medium vector meson contributions. The initial temperature from the model is 224 MeV and the starting time τ 0 is 0.33 fm/c [32]. The comparison of the model with data shows that a broadened ρ-spectra scenario is consistent with the STAR data within uncertainties. The same conclusion has been drawn in Au+Au collisions at √ s N N = 200 GeV [10]. Using the broadened ρ spectral function, QCD and Weinberg sum rules, and inputs from Lattice QCD, theorists have demonstrated that when the temperature reaches 170 MeV, the derived a 1 (1260) spectral function is the same as the in-medium ρ spectral function, a signature of chiral symmetry restoration [36].
To quantify the yield, the known hadronic cocktail, cc → e + e − X and Drell-Yan contributions were subtracted from the dielectron mass spectrum at √ s N N = 19.6 GeV. At √ s N N = 200 GeV, the known hadronic sources, cc → e + e − X, bb → e + e − X, and Drell-Yan contributions were subtracted. The excess dielectron mass spectra, corrected for detector acceptance, are shown in Fig. 4 for Au+Au MB collisions at √ s N N = 19.6 and 200 GeV. The spectra are normalized to mid-rapidity dN ch /dy in absolute terms to cancel out the volume effect, and compared with the excess dimuon yields from the NA60 measurements in In+In collisions at √ s N N = 17.3 GeV. The model calculation [11,32]   17.3 GeV in the LMR and IMR, but within 2σ uncertainty. Further measurements with better precision are needed to obtain the average temperature of the hot, dense medium created. Figure 4 shows that the excess dielectron yield in the LMR at √ s N N = 19.6 GeV has a magnitude similar to the excess dimuon yield at  [19]. In addition, the lifetime has a strong centrality dependence in √ s N N = 200 GeV Au+Au collisions in the calculations, as indicated by the dashed curve in Fig. 5. With the total baryon density nearly a constant and the emission rate dominant in the critical temperature region at √ s N N = 17.3-200 GeV, the normalized excess dilepton yields in the low mass region from the measurements are proportional to the calculated lifetimes of the medium.

IV. SUMMARY
In summary, the dielectron mass spectrum is measured in Au+Au collisions at √ s N N = 19.6 GeV by the STAR experiment at RHIC. Compared with known hadronic sources, a significant excess is observed, which can be consistently described in all beam energies by a model calculation in which a broadened ρ spectral function scenario at low temperature and chiral symmetry restoration are included. Furthermore, the excess dielectron mass spectra, corrected for the STAR detector acceptance, are reported for the first time in Au+Au collisions at √ s N N = 19.6 and 200 GeV. In the LMR, the excess yield at √ s N N = 19.6 GeV, normalized to the charged particle multiplicity dN ch /dy, is comparable to that in In+In collisions at √ s N N = 17.3 GeV. For √ s N N = 200 GeV, the normalized excess yield is higher in central collisions than that at √ s N N = 17.3 GeV and increases from peripheral to central collisions. These measurements indicate that the hot, dense medium created in central Au+Au collisions at top RHIC energy has a longer lifetime than those in peripheral collisions and at √ s N N = 17.3 GeV.
V. ACKNOWLEDGEMENT