15 pages, 17 figures, 4 tables. Submitted to Phys. Rev. C ; We report on 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 RHIC. 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 $\omega\rightarrow e^{+}e^{-}$ 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 $\phi\rightarrow K^{+}K^{-}$ and $J/\psi\rightarrow e^{+}e^{-}$. Our results suggest a new upper limit of the branching ratio of the $\eta \rightarrow e^{+}e^{-}$ of $1.7\times10^{-5}$ at 90% confidence level.
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