Measurement of electrons from open heavy-flavor hadron decays in Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV with the STAR detector

A track reconstructed in the TPC is selected only if its Distance of Closest Approach (DCA) to the collision vertex is less than 1.5 cm, in order to suppress particles produced at secondary vertices. The number of TPC space points, also called “TPC hits”, used for track reconstruction should be 20 or more to ensure good track quality, and also be larger than 52% of the maximum possible number of TPC hits ($\leq$ 45) along the track trajectory to avoid split tracks. For achieving good $dE/dx$ resolution, the number of TPC hits used for $dE/dx$ calculation is required to be at least 15. Finally, only tracks within $|\eta|<0.7$ and with at least one hit in the first three TPC padrows are retained in order to minimize photonic electron background from photon conversions in the beam pipe support structure and TPC gas, respectively.

Electron candidates are identified using $dE/dx$ measured in the TPC, the ratio of track momentum measured by the TPC over energy deposition of the most energetic tower in the matched BEMC cluster ($p/E$), and the shower shape measured by the BSMD. To eliminate the momentum dependence of the $dE/dx$ value and its resolution, a normalized quantity, $n\sigma_{\rm e}=\frac{ln(dE/dx_{mea})-ln(dE/dx_{th})}{\sigma(ln(dE/dx))}$, is used, where $dE/dx_{mea}$ is the measured value, $dE/dx_{th}$ is the theoretical value for electrons based on the Bichsel formalism Bichsel:2006cs , and $\sigma(ln(dE/dx))$ is the resolution. Tracks with $0.3<p/E<1.5$ and $-1.5<n\sigma_{\rm e}<3.0$ are selected. To further discriminate electrons against hadrons, electron candidates are required to fire at least two strips in both the $\phi$ and $\eta$ planes of the BSMD, and the distances from the projected TPC track position to the reconstructed BEMC cluster position in the $\phi$ and $\eta$ planes to be less than 0.015 rad and 3 cm, respectively.

TPC tracks that pass all the aforementioned cuts are classified as INE candidates. Figures 1 (a) and (b) show examples of $n\sigma_{\rm e}$ distributions for 4.5 $<p_{\rm T}<$ 5.0 GeV/$c$ in 0-10% central and 40-80% peripheral Au+Au collisions, respectively, for tracks satisfying all selection cuts except the $n\sigma_{\rm e}$ cut. The integrals of $n\sigma_{\rm e}$ distributions within $-1.5<n\sigma_{\rm e}<3.0$ are the raw yields of INE candidates. To estimate the purity of the electron sample ($P_{\rm e}$) in the INE sample, a constrained fit to the $n\sigma_{\rm e}$ distribution with three Gaussian functions representing $\pi^{\pm}$, $K^{\pm}$+$p$($\bar{p}$) and $e^{\pm}$, is performed and shown in Figs. 1 (a) and (b). For $\pi^{\pm}$ and $K^{\pm}$+$p$($\bar{p}$), initial mean $n\sigma_{\rm e}$ values in the fit function are obtained from the Bichsel formalism Bichsel:2006cs , while initial widths are set to be 1. The mean and width of the Gaussian function for electrons are fixed according to the $n\sigma_{\rm e}$ distribution of a pure electron sample consisting of photonic electrons (as described in Sec. 3.2) selected with an invariant mass cut of $M_{e^{+}e^{-}}<0.1$ GeV/$c^{2}$. A good agreement between data and the fit function is seen, as evidenced by the $\chi^{2}/\rm ndf$ values shown in Figs. 1 (a) and (b). The electron purity is extracted by taking the ratio of the integral of the electron fit function to that of the overall fit function in the $n\sigma_{\rm e}$ cut range ($-1.5<n\sigma_{\rm e}<3.0$). The resulting purities as a function of electron $p_{\rm T}$ in 0-10% central and 40-80% peripheral Au+Au collisions are shown in Fig. 1 (c). The purity decreases with increasing $p_{\rm T}$ because the pion peak gets closer to the electron peak and the relative yield of pion to electron increases. At $p_{\rm T}>$ 5.5 GeV/$c$, the purity seems smaller in 40-80% peripheral collisions than that in 0-10% central collisions, which is caused by the larger relative pion to electron yield in peripheral collisions.

There are primarily two sources of PHEs: photon conversion and Dalitz decays of $\pi^{0}$ and $\eta$ mesons. Among the INE candidates, PHEs are found by paring them (tagged electrons) with oppositely-charged tracks (partner electrons) reconstructed in the TPC, denoted as unlike-sign pairs STAR:ppNPE . Tagged electrons are also paired with tracks of the same charge to construct like-sign distributions from a sum of $e^{+}e^{+}$ and $e^{-}e^{-}$ pairs, as estimates of misidentified PHEs arising from combinatorial background. Raw yields of PHEs are extracted by subtracting the invariant mass spectra of like-sign electron pairs from the unlike-sign ones, and applying an invariant mass cut of $M_{e^{+}e^{-}}<0.24$ GeV/$c^{2}$, which takes into account the broadening of the invariant mass distribution with increasing tagged-electron $p_{\rm T}$. Partner electrons are required to have $|\eta|<1$, at least 15 TPC hits used for reconstruction, the ratio of the number of used to the maximum possible number of TPC hits larger than 0.52 and $p_{\rm T}>0.3$ GeV/$c$. These requirements are less strict than those for tagged electrons in order to enhance the probability of finding PHEs. In addition, a maximum DCA of 1.0 cm between the two electron tracks is applied to ensure that the partner electron originates from the same production vertex as the tagged electron. Figures 2 (a) and (b) show examples of invariant mass distributions for unlike-sign pairs, like-sign pairs, as well as differences between unlike- and like-sign pairs, for tagged electrons of $4.5<p_{\rm T}<5.0$ GeV/$c$ in 0-10% central and 40-80% peripheral Au+Au collisions, respectively. The like-sign distributions are seen to match well unlike-sign distributions at $M_{e^{+}e^{-}}>0.24$ GeV/$c^{2}$, where combinatorial background dominates.

The PHE identification efficiency, $\varepsilon_{\rm PHE}$, which accounts for finding a partner electron and passing the pair DCA and invariant mass cuts, is evaluated by embedding full GEANT ref:geant simulations of $\gamma$, $\pi^{0}$ and $\eta$ decays in the STAR detector into real events, which then go through the same reconstruction and analysis software chain as real data. The decay processes are simulated with pythia 6.419 ref:pythia . Input $\pi^{0}$ $p_{\rm T}$ spectra in different centrality classes are taken as the average of charged and neutral pion spectra in 200 GeV Au+Au collisions measured by STAR and PHENIX experiments STAR:pi0 ; PHENIX:pi01 ; PHENIX:pi02 , while the input $p_{\rm T}$ spectra for $\eta$ are obtained from $\pi^{0}$ spectra assuming traverse mass ($m_{\rm T}$) scaling, i.e. replacing $p_{\rm T}$ in the $\pi^{0}$ spectra by $\sqrt{p_{\rm T}^{2}-m_{\rm\pi}^{2}+m_{\rm\eta}^{2}}$. The input rapidity distributions of $\pi^{0}$ and $\eta$ are parametrized with a Gaussian-like function $\cosh^{-2}\left(\frac{3y}{4\sigma(1-y^{2}/(2\sqrt{s}/m))}\right)$, where $\sigma=\sqrt{\ln(\sqrt{s}/(2m_{\rm N}))}$, $\sqrt{s}$ is a nucleon-nucleon center of mass energy, $m$ is the particle mass, $y$ is the particle rapidity, and $m_{\rm N}$ is the nucleon mass ref:INP ; STAR:dielectron ; CERES:dielectron . On the other hand, input spectra for photons are a combination of direct photon spectra measured by the STAR experiment STAR:photon and decayed photon spectra from $\pi^{0}\rightarrow\gamma\gamma$/$e^{+}e^{-}\gamma$ and $\eta\rightarrow\gamma\gamma$/$e^{+}e^{-}\gamma$ processes obtained using the aforementioned $\pi^{0}$ and $\eta$ spectra for the Dalitz decay as inputs to pythia. Figure 2 (c) shows the combined PHE identification efficiency from photon conversion and Dalitz decays as a function of $p_{\rm T}$ in 0-10% central Au+Au collisions, along with a fit using the functional form $A/(e^{-(p_{\rm T}-p_{\rm 0})/p_{\rm 1}}+1)+C$, where $A$, $p_{\rm 0}$, $p_{\rm 1}$, and $C$ are free parameters. The individual $\varepsilon_{\rm PHE}$ distributions for $\gamma$ conversion and two types of Dalitz decays are also shown in Fig. 2 (c). Figure 2 (d) shows fits to combined $\varepsilon_{\rm PHE}$ as a function of $p_{\rm T}$ in 0-10% central and 40-80% peripheral Au+Au collisions. As expected, $\varepsilon_{\rm PHE}$ is lower in central collisions than in peripheral collisions due to the decreasing tracking efficiency for partner electrons with increasing TPC occupancy in central collisions.

The raw NPE yields can be obtained by statistically subtracting hadron contamination and efficiency-corrected PHE yields from INE candidates. Figure 3 (a) shows the yield ratios of NPE [$N_{\rm INE}\times P_{\rm e}-N_{\rm PHE}/\varepsilon_{\rm PHE}$ in Eq. (LABEL:eq:NPEyield)] to PHE background [$N_{\rm PHE}/\varepsilon_{\rm PHE}$ in Eq. (LABEL:eq:NPEyield)] as a function of $p_{\rm T}$ in 0-10% central and 40-80% peripheral Au+Au collisions, which are seen to be similar. These ratios are smaller than those in the previous STAR analysis based on 200 GeV $p$+$p$ collisions recorded in 2012 STAR:ppNPE , due to the added material of the heavy flavor tracker hft and its support structure installed in 2014.

The NPE yields are obtained by correcting raw NPE yields for the overall efficiency [$\epsilon_{\rm total}$ in Eq. (LABEL:eq:NPEyield)]. The $\epsilon_{\rm total}$ is evaluated using the same approach as in Ref. STAR:ppNPE , which is briefly summarized here. The detector acceptance and efficiencies of TPC tracking, BEMC electron identification, and HT triggering are estimated by embedding single electrons into real data. The electron identification efficiencies of the TPC $n\sigma_{\rm e}$ and BSMD requirements are evaluated using a data-driven method, i.e., taking the ratio of electrons with and without the $n\sigma_{\rm e}$ or BSMD selection in the pure electron sample. Figure 3 (b) shows the overall efficiencies as a function of $p_{\rm T}$ for HT1- and HT2-triggered electrons in 0-10% central and 40-80% peripheral Au+Au collisions. The higher efficiency in peripheral collisions than central collisions is again due to the reduced TPC occupancy. The increasing efficiency with $p_{\rm T}$ for HT1 and HT2 trigger, and the efficiency dropping from HT1 to HT2 trigger are mainly driven by the HT trigger threshold.

There are four sources for HDEs, including quarkonia, light vector mesons, Drell-Yan and Kaon semileptonic decays, as mentioned at the beginning of this section.

The EvtGen event generator ref:evtgen is used to decay prompt $J/\psi$ to electrons. The input $p_{\rm T}$ spectra for prompt $J/\psi$ production are obtained from the published inclusive $J/\psi$ measurements STAR_jpsi parametrized with the Tsallis statistics ref:TS ; ref:TS1 ; ref:TS2 and with the non-prompt $J/\psi$ contribution subtracted based on Fixed Order plus Next-to-Leading Logarithms (FONLL) calculation ref:QCDCB plus Color Evaporation Model (CEM)  ref:fcem1 ; ref:fcem2 . The rapidity distribution of prompt $J/\psi$ is taken from pythia. The resulting invariant yields of decayed electrons in 0-10% central and 40-80% peripheral Au+Au collisions are represented by dot-dashed lines in Fig. 4. For the $\Upsilon$ contribution, a model calculation ref:upsilonmodel indicates no significant $p_{\rm T}$ dependence of $\Upsilon$ suppression in Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV, which is consistent with STAR measurements within uncertainties ref:upsilon . Therefore, the $\Upsilon$ decayed electrons in Au+Au collisions are estimated by scaling up their yield in 200 GeV $p$+$p$ collisions STAR:ppNPE by the average number of binary collisions ($N_{\rm coll}$) D0_STAR , incorporating model predictions of $\Upsilon$ suppression in the QGP ref:upsilonmodel . Invariant yields of electrons from $\Upsilon$ decays are shown as dotted lines in Fig. 4.

The $p_{\rm T}$ spectra of light vector mesons, $\rho$, $\omega$, and $\phi$, in different centrality classes of Au+Au collisions are obtained by assuming $m_{\rm T}$ scaling based on the $\pi^{0}$ spectra in corresponding centrality classes, which are further scaled by the integrated yield ratio of light vector mesons over $\pi^{0}$ in 0-80% centrality class STAR:dielectronau . Their rapidity distributions are obtained following the Gaussian-like function introduced in Sec. 3.2. pythia is used to model the di-electron decay of the $\rho$ meson, while EvtGen is used for $\omega$ and $\phi$. Invariant yields of resulting decayed electrons are illustrated as long dashed lines in Fig. 4 for 0-10% central and 40-80% peripheral Au+Au collisions.

For the Drell-Yan contribution, it is estimated as the Drell-Yan $\rightarrow e$ yield from pythia simulation of 200 GeV $p$+$p$ collisions STAR:ppNPE scaled by $N_{\rm coll}$ assuming no cold or hot nuclear matter effects, and shown as long dash-dotted lines in Fig. 4. Furthermore, simulation studies based on STAR acceptance have shown that the $K_{\rm e3}$ contribute less than 2% to HDE for $p_{\rm T}>$ 3 GeV/$c$ in Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV ref:ke3 , and are thus neglected.

The overall $\rm HDE$ contributions in 0-10% central and 40-80% peripheral collisions, represented by solid lines in Fig. 4, are subtracted from the NPE sample, and the remaining HFE yields are reported in Sec. 4. These contributions amount to a $\sim$15%, $\sim$16%, $\sim$18% and $\sim$19% reduction to the NPE yield in the measured $p_{\rm T}$ region for 0-10%, 10-20%, 20-40% and 40-80% collisions, respectively.

For the NPE reconstruction efficiency, the uncertainties are estimated partially by changing the track quality and PID cuts in data and simulation simultaneously and checking variations in the corrected NPE yield. These include: (i) the number of TPC hits used for track reconstruction ($dE/dx$ calculation) from 20 (15) to 25 (18), and the larger variation of the two is taken; (ii) DCA from 1.5 cm to 1.0 cm; and (iii) $0.3<p/E<1.5$ to 0.6 $<p/E<$ 1.5 and $0.3<p/E<1.8$. Uncertainty in the HT trigger efficiency is evaluated by adjusting the trigger threshold in simulation by $\pm$ 5%, originating from the uncertainties of the BEMC energy scale calibration. For the PID efficiency arising from BSMD requirements, its uncertainties are taken as the statistical errors of the pure electron sample in data used for estimating such an efficiency. The uncertainty of the $n\sigma_{\rm e}$ cut efficiency is estimated from the parameter errors in fitting the $n\sigma_{\rm e}$ distribution of the pure electron sample with a Gaussian function, taking into account the correlation between the mean and width parameters, and from varying the selection cut from $-1.5<n\sigma_{\rm e}<3.0$ to $-1.0<n\sigma_{\rm e}<3.0$. The uncertainties in electron purity are similarly estimated based on the uncertainties in the mean and width of Gaussian fits to the pure electron $n\sigma_{\rm e}$ distributions.

The PHE identification efficiency uncertainty stems from the uncertainties in simulation statistics, parametrizations of $\pi^{0}$ and $\eta$ spectra, branching ratios of electrons from $\pi^{0}$ and $\eta$ decays, tracking efficiency of partner electrons and variations in the PHE selection criteria, i.e., changing maximum $M_{e^{+}e^{-}}$ from 0.24 GeV/$c^{2}$ to 0.15 GeV/$c^{2}$ and minimum partner electron $p_{\rm T}$ from 0.3 GeV/$c$ to 0.2 GeV/$c$. The parametrization uncertainty is taken as the 68% confidence interval of the fit function. Such an approach is also used in estimating the uncertainties in spectrum parametrization as described in the following.

The uncertainty in estimating the HDE contribution includes those from $J/\psi$, $\Upsilon$, light vector meson, and Drell-Yan contributions. Uncertainties from parametrizating the inclusive $J/\psi$ spectrum and from FONLL+CEM calculations of the non-prompt $J/\psi$ contribution are taken into account. For the $\Upsilon$ contribution, uncertainties arise from measurements of $\Upsilon$ yields in $p$+$p$ collisions STAR:ppNPE and model calculations ref:upsilonmodel . Parametrization uncertainties of the $\pi^{0}$ spectra STAR:pi0 ; PHENIX:pi01 ; PHENIX:pi02 as well as uncertainties in the measured yield ratios of light vector mesons to $\pi^{0}$ STAR:dielectronau are also propagated to the decayed electron invariant yields. Finally, the uncertainty in the Drell-Yan contribution is from that of the results in $p$+$p$ collisions STAR:ppNPE .

The total systematic uncertainty is obtained as the square root of the quadratic sum of individual sources. Table 1 summarizes the uncertainties from different sources and total uncertainties for HFE invariant yield measurements in different centrality intervals (0-10%, 10-20%, 20-40%, 40-80%). Global uncertainties, referred to in the following section, include those from the non-single diffractive cross section of $p$+$p$ collisions STAR:D0 and $N_{\rm coll}$ D0_STAR .