Di-electron spectrum at mid-rapidity in $p+p$ collisions at $\sqrt{s}=200$ GeV

We report on the mid-rapidity mass spectrum of di-electrons and cross sections of pseudoscalar and vector mesons via $e^{+}{e}^{-}$ decays, from $\sqrt{s}=200$ GeV $p+p$ collisions, measured by the large-acceptance experiment STAR at the Relativistic Heavy Ion Collider. The ratio of the di-electron continuum to the combinatorial background is larger than 10$\%$ over the entire mass range. Simulations of di-electrons from light-meson decays and heavy-flavor decays (charmonium and open charm correlation) are found to describe the data. The extracted $\omega \to e^{+}{e}^{-}$ invariant yields are consistent with previous measurements. The mid-rapidity yields ($dN/dy$) of $\phi$ and $J/\psi$ are extracted through their di-electron decay channels and are consistent with the previous measurements of $\phi \to K^{+}{K}^{-}$ and $J/\psi \to e^{+}{e}^{-}$. Our results suggest a new upper limit of the branching ratio of the $\eta \to e^{+}{e}^{-}$ of $1.7\times {10}^{-5}$ at the 90$\%$ confidence level.

Figure 1

(a) $1/\beta$ vs momentum of tracks from the TOF with $\left|\eta \right|<1$ from 200-GeV $p+p$ collisions. The line indicates the cut of $|1/\beta -1|<0.03$. (b) The normalized $dE/dx$ distribution from the TPC as a function of $p_T$. (c) The normalized $dE/dx$ distribution from the TPC as a function of $p_T$ with the cut of $|1/\beta -1|<0.03$. An electron band, indicated by the lines, is prominent, with the requirement of velocity close to the speed of light from the TOF measurement.

Figure 2

The $n{\sigma }_e$ distribution in $0.4<p_T<0.5$ GeV/$c$ after the cut of $|1/\beta -1|<0.03$ is applied. The solid curve represents a Gaussian plus exponential fit to the $n{\sigma }_e$ distribution. The dot-dashed line is for the hadron component and the dashed line is for the electron contribution. The two dashed lines perpendicular to the $x$ axis represent the range of the $n{\sigma }_e$ cut to ensure a high purity for electron candidates in this $p_T$ range.

Figure 3

The purity and the $n{\sigma }_e$ cut efficiency for electron candidates as a function of $p_T$ in $\left|\eta \right|<1$ for $p+p$ collisions at $\sqrt{s}=200$ GeV. The squares represent the purity and closed circles represent the $n{\sigma }_e$ efficiency. The $p_T$ positions of the last three data points for the efficiency are slightly shifted for clarity. The error bars are the quadrature sum of statistical and systematic uncertainties. A function form of $A+B/[C+\exp (D\times p_T)]$ is used to fit the efficiency data points and for the efficiency correction, in which $A$, $B$, $C,$ and $D$ are the fit parameters. A constant component in the fit for $p_T>0.8$ GeV/$c$ is driven by the study in Ref. [23].

Figure 4

The electron-pair invariant-mass distributions for unlike-sign pairs, like-sign pairs, and mixed-event (combinatorial) background in minimum-bias $p+p$ collisions. The electron candidates are required to be in the range of $\left|\eta \right|<1$ and have a $p_T$ value greater than 0.2 GeV/$c$. The $ee$ pairs were required to be in the rapidity range of $|y_{ee}|<1$. The uneven bin widths are used based on the yields and the signal-to-background ratios.

Figure 5

(a) The ratio of like-sign to mixed-event distributions in minimum-bias $p+p$ collisions. (b) The distribution of the difference of the azimuthal angles ($\Delta \phi$) of the two electrons in the unlike-sign, like-sign, and mixed-event pairs in minimum-bias $p+p$ collisions. (c) The $\Delta \phi$ distributions of unlike-sign, like-sign, and mixed-event pairs for $M_{ee}>0.4$ GeV/$c^2$ in minimum-bias $p+p$ collisions. Errors are statistical.

Figure 6

(a) The di-electron ($e^{+}{e}^{-}$) continuum after background subtraction without efficiency correction in $\sqrt{s}=200$ GeV minimum-bias $p+p$ collisions. Two methods of obtaining the background are indicated. Errors are statistical only. (b) The signal over background ratio, plotted as a function of $M_{ee}$ for NSD $p+p$ collisions at $\sqrt{s}=200$ GeV. Errors are statistical.

Figure 7

(a) The invariant yields of measured mesons fit with the Tsallis functions [31] in $p+p$ collisions at $\sqrt{s}=200$ GeV. See text for details. (b) The simulated raw di-electron continuum within STAR acceptance for $\sqrt{s}=200$ GeV minimum-bias $p+p$ collisions. Different cocktail contributions are shown.

Figure 8

The efficiency for single electrons as a function of $p_T$ in the pseudo-rapidity range of $\left|\eta \right|<1$ from $p+p$ collisions at $\sqrt{s}=200$ GeV. Open circles represent the TPC tracking efficiency. With additional TOF matching and response, the efficiency is shown as triangles. With additional $dE/dx$ cuts, the final efficiency is shown as squares.

Figure 9

The TOF efficiency as a function of azimuthal angle in the positive and negative $\eta$ regions. The hole in the negative $\eta$ region corresponds to the trays (28$\%$) missing from the 2009 run installation. The three trays around 270${}^{\circ }$ in the positive $\eta$ region have smaller matching efficiencies but have similar performances in other aspects.

Figure 10

(a) The $M_{ee}$ distribution within STAR’s acceptance ($|y_{e^{+}{e}^{-}}|<1$, $|{\eta }_e|<1$, and $p_T\left(e\right)>0.2$ GeV/$c$) from simulation. The solid line represents the input cocktail. The dashed line represents the cocktail from geant simulations taking into account the proper efficiency factors described in the text. (b) The efficiency of the di-electron continuum as a function of $M_{ee}$ within the STAR acceptance in $p+p$ collisions at $\sqrt{s}=200$ GeV.

Figure 11

Systematic uncertainties as a function of mass from different source contributions. Also shown are the systematic uncertainties of the cocktail simulation.

Figure 12

The comparison of the di-electron continuum between data and simulation after efficiency correction within the STAR acceptance in $\sqrt{s}=200$ GeV NSD $p+p$ collisions. The di-electron continuum from simulations with different source contributions is also shown. The statistical errors on the data are shown as bars, while the systematic uncertainties are shown as boxes. The 11$\%$ normalization uncertainty on the data is not shown. The band on top of the solid curve illustrates the systematic uncertainties on the cocktail simulation.

Figure 13

The $M_{ee}$ distribution in the range $0.65<M_{ee}<0.95$ GeV/$c^2$ for three different $p_T$ bins after the mixed-event background subtraction in $p+p$ collisions at $\sqrt{s}=200$ GeV. The curves represent fits in the range $0.7<M_{ee}<0.85$ GeV/$c^2$ as described in the text. Errors on data points are statistical.

Figure 14

The efficiency including STAR acceptance for $\omega \to e^{+}{e}^{-}$ for $\left|y\right|<1$ in $p+p$ collisions at $\sqrt{s}=200$ GeV.

Figure 15

The $\omega \to e^{+}{e}^{-}$ invariant yield, divided by its B.R., in NSD $p+p$ collisions at $\sqrt{s}=200$ GeV. The open circles represent PHENIX published results [49]. The bars are statistical errors and boxes are systematic uncertainties. A normalization uncertainty of 11$\%$ is not shown. The yields at the center of the $p_T$ bin are corrected for finite bin width. The line represents the yields of $\omega$ from the Tsallis function fit to high-$p_T$$\omega$ yields measured from its hadronic decay and described in Sec. 4a.

Figure 16

(a) The $M_{ee}$ distribution after the mixed-event background subtraction for $0.96<M_{ee}<1.08$ GeV/$c^2$ in $p+p$ collisions at $\sqrt{s}=200$ GeV. The curve represents the fit in the range of $0.98<M_{ee}<1.04$ GeV/$c^2$. Errors on data points are statistical. (b) The $M_{ee}$ distribution after the mixed-event background subtraction for $2.98<M_{ee}<3.22$ GeV/$c^2$ in $p+p$ collisions at $\sqrt{s}=200$ GeV. The curve represents the fit in the range of $3<M_{ee}<3.16$ GeV/$c^2$. There is no count in the unlike-sign and like-sign electron-pair distributions for $3.02<M_{ee}<3.04$ GeV/$c^2$ due to statistical fluctuations. Errors on data points are statistical.

Figure 17

$M_{ee}$ distribution for di-electron production in $p+p$ collisions at $\sqrt{s}=200$ GeV. The dashed curve is the cocktail with the $\eta \to e^{+}{e}^{-}$ decay channel included in the fit. The $\eta \to e^{+}{e}^{-}$ contribution is shown as the solid curve. The dot-dashed peak is the $\eta \to e^{+}{e}^{-}$ contribution with the upper limit of its branching ratio from the Particle Data Group [52], which is $2.7\times {10}^{-5}$.